High-density
QCD
General references
Dense QCD reviews
Collaboration
papers
Conference
papers
Papers
Other
papers
LOFF
papers
Astrophysical applications
General References
- L.N. Cooper,
Phys. Rev. 104, 1189 (1956).
- J. Bardeen, L.N. Cooper
and J.R.Schrieffer, Phys. Rev. 106, 162 (1957); 108, 1175 (1957).
- Y. Nambu and G.
Iona-Lasinio, Phys. Rev. 122, 345 (1960);
124, 246 (1961).
- D. J. Gross and F.
Wilczek, Ultraviolet
Behavior of Non-Abelian Gauge Theories. (Phys.
Rev. Lett. 30, 1343 (1973))
- H. D. Politzer, Reliable
Perturbative
Results for Strong Interactions? (Phys. Rev.
Lett. 30, 1346 (1973))
- J. C. Collins and M. J.
Perry, Superdense Matter: Neutrons or Asymptotically Free Quarks?
We note the following: The quark
model implies that superdense matter (found in neutron-star cores,
exploding black holes,
and the early big-bang universe) consists of quarks rather
than of hadrons. Bjorken scaling implies that the quarks interact
weakly. An asymptotically free gauge theory allows realistic
calculations taking full account of strong interactions. (Phys. Rev. Lett. 34, 1353 (1975))
- T. Eguchi,New
approach to collective
phenomena in superconductivity models, (Phys.
Rev. D, 2755 (1976))
- B. Barrois, Nucl. Phys. B129, 390 (1977)
- S. Frautschi, Proceedings of workshop on hadronic matter at extreme
density, Erice 1978
- B. Barrois,
Nonperturbative effects in dense quark matter, Cal Tech PhD thesis, UMI 79-04847-mc (1979).
- D. Bailin and A. Love,
Phys. Rept. 107, 325 (1984)
Dense QCD reviews
- J. Polchinski, hep-th/9210046.Effective field theory and
the Fermi surface, The method of
effective field theory applied to superconductivity. (Lectures
presented at TASI 1992)
- R. Shankar. A review of interacting fermions (Rev. Mod. Phys. 66, 129 (1993))
- V.B. Eltsov, M.
Krusius, G.E. Volovik, cond-mat/9809125.
Superfluid 3He: a Laboratory Model System of Quantum Field Theory. Recently a new phenomenon was discovered in rotating
superfluid 3He-B: the formation of
quantized vortices within bulk superflow in the presence of ionizing
radiation. This ``mini bang'' allows one to explore the superfluid
transition within the clean bulk medium on
the microsecond time scale. The experiment appears to provide
the first quantitative test of the theories on defect formation in a
time-dependent second order phase transition.
- F. Wilczek, hep-ph/9907340. What QCD Tells Us About
Nature -- and Why We Should Listen. I
discuss why QCD is our most perfect physical theory. Then I visit a few
of its current frontiers. Finally I draw some appropriate conclusions.
(Nucl. Phys. A663 (2000) 3-20)
- J. Zinn-Justin, hep-ph/0005272.
Quantum field theory at finite temperature: an introduction. Review of statistical quantum field theory at
equilibrium
- M.-P. Lombardo, hep-ph/0103141. Finite temperature field
theory. These lectures review phases and
phase transitions of the Standard Model, with emphasis on those aspects
which are amenable
to a first principle study. Model calculations and theoretical ideas of
practical applicability are discussed as well. (lectures given at the
Summer School on Astroparticle Physics and Cosmology, ICTP, Trieste,
12-30 June 2000)
- K. Rajagopal and F.
Wilczek, hep-ph/0011333.The condensed matter physics of QCD. A complete review of high-density QCD, including CFL,
2SC, LOFF and applications. ('At the Frontier of Particle Physics /
Handbook of QCD', M. Shifman, ed.,
(World Scientific).
In *Shifman, M. (ed.))
- S.H.D. Hsu, hep-ph/0003140.Color superconductivity in
high density quark matter. A review of
color superconductivity from the point of view of the R-Group.
(TMU-Yale Symposium on Dynamics of Gauge Fields)
- H. Satz, hep-ph/0009099. The
Search for the QGP: A Critical Appraisal. The
start of RHIC this year
will increase the highest available collision energy by a factor 10.
This seems a good time for a critical assessment: what have we learned
so far and what can we hope to learn in the coming years?
(Nucl.Phys.Proc.Suppl. 94 (2001) 204-218)
- D.K. Hong, hep-ph/0101025.Aspects of color superconductivity. A review about the evaluation of the gap and of the
NG boson masses. (Acta Phys.Polon. B32 (2001) 1253-1276)
- M. Alford, hep-ph/0102047.Color superconducting quark matter. A review of color superconducting phases and
applications to compact stars. (Ann.Rev.Nucl.Part.Sci. 51 (2001)
131-160)
- G.E. Brown, Mannque
Rho, hep-ph/0103102. On the Manifestation
of Chiral Symmetry in Nuclei and Dense Nuclear Matter. his article reviews our view on how chiral symmetry,
its pattern of breaking and restoration under extreme conditions
manifest themselves in the nucleon, nuclei, nuclear matter and dense
hadronic matter. (Physics Reports 363 (2002) 85)
- S. Hands, physics/0105022.
The Phase Diagram of QCD. I use simple
thermodynamic reasoning to argue that at temperatures of order a
trillion kelvin, QCD, the theory which describes strongly interacting
particles
such as protons and neutrons under normal conditions, undergoes
a phase transition to a plasma of more elementary constituents called
quarks and gluons. (Popular lecture). (Contemporary Physics 42 (2001)
209-225)
- D. F. Litim, C.
Manuel, hep-ph/0110104. Semi-classical
transport theory for non-Abelian plasmas.
We review a semi-classical transport theory for non-Abelian plasmas
based on a classical picture of
coloured point particles. Within this formalism, kinetic
equations for the mean particle distribution, the mean
fields and their fluctuations are obtained using an ensemble-average in
phase space. The framework permits the
integrating-out of fluctuations in a systematic manner. This leads to
the derivation of collision integrals, noise
sources and fluctuation-induced currents for the effective
transport equations of QCD. (Phys. Rept. 364 (2002) 451-539)
- H. Satz, hep-ph/0201051. States of Strongly
Interacting Matter. I discuss
the phase structure of strongly interacting matter
at high temperatures and densities, as predicted by statistical QCD,
and consider in particular the nature of the transition of hot hadronic
matter to a plasma of deconfined quarks and gluons. (Fortsch.Phys. 50
(2002) 541-551)
- G. Nardulli, hep-ph/0202037.Effective description of QCD at very high densities. A review of effective field theory applied to color
superconductivity. Evaluation of the parameters appearing in the
effective lagrangians for the CFL, 2SC and LOFF phases. (Rivitsta del
Nuovo Cimento)
- Mannque Rho, nucl-th/0202078.Lectures on effective field theories for nuclei,
nuclear matter and dense matter. A review
of effective field theory in various domains including high-density QCD.
- Mannque Rho, hep-ph/0206003.
The Cheshire Cat Hadrons Revisited. The
notion of Cheshire Cat Principle in hadron structure developed in a
1993 lecture note is revisited by correcting nontrivial errors
committed in the lecture and bringing up to date with the recent
developments on the "vector manifestation" of chiral symmetry a la
Harada-Yamawaki. (Corrected and updated version of Phys. Rep. 240
(1994) 1)
- T. Schafer,
nucl-th/0208070.
EFFECTIVE THEORY OF
THE COLOR FLAVOR LOCKED PHASE. 16th International Conference on
Ultrarelativistic Nucleus-Nucelus Collisions, Quark Matter 2002 (QM
2002), Nantes, France, 18-24
Jul 2002
- K. Rajagopal, SLAC Beam Line 31N2:9-15,2001. Free the quarks. Popular lecture.
- T. Schafer,
Nucl.Phys.A702:167-176,2002.
THE GROUND STATE OF STRANGE
QUARK MATTER. International Symposium On Statistical QCD, 26-30
Aug 2001, Bielefeld, Germany
- S. Reddy, nucl-th/0211045.
NOVEL PHASES AT HIGH DENSITY AND THEIR ROLES IN THE
STRUCTURE AND EVOLUTION OF NEUTRON STARS. We present a
pedagogic discussion on the role of novel phases of dense baryonic
matter in
``neutron'' stars. Qualitative aspects of the physics that drives phase
transitions and some of its astrophysical consequences are discussed.
Observable aspects of neutron star structure and early evolution of the
newly born neutron star are discussed in some detail. (lectures presented at the Zakopane Summer School on
Flavor Dynamics, 2002)
- D. K. Hong, hep-ph/0301125.
Positivity of QCD at asymptotic
density. In this talk, I try to show
that the sign problem of dense QCD is due to modes whose frequency
is higher than the chemical potential. An effective theory of
quasi-quarks near the Fermi surface has a positive measure in the
leading order. The higher-order corrections make the measure complex,
but they
are suppressed as long as the chemical potential is sufficiently larger
than $\Lambda_{\rm QCD}$. As a consequence of the positivity of the
effective theory, we can show that the global vector symmetries except
the U(1) baryon number are unbroken at asymptotic density (contribution
to Strong and Electroweak Matter '02 (Heidelberg))
- R. Casalbuoni, hep-ph/0301162.
Anisotropic Color Superconductivity. We discuss the possibility that in finite density QCD
an anisotropic phase is realized. This case might arise for quarks with
different chemical potential and/or different masses. In
this phase crystalline structures may be formed. We consider this
possibility and we describe, in the context of an effective lagrangian,
the corresponding phonons as the Nambu-Goldstone bosons associated
to the breaking of the space symmetries. (Contributed paper
to the International Workshop SCGT 02 "Strong Coupling Gauge
Theories and Effective Field Theories", 10-13 December 2002, Nagoya,
Japan)
- K. Rajagopal,
COLOUR SUPERCONDUCTIVITY. Published in *Beatenberg
2001, High-energy physics* 345-384
- T. Schafer, hep-ph/0304281. Quark
Matter.
- R. Casalbuoni
and G. Nardulli, hep-ph/0305069.
Inhomogeneous Superconductivity in Condensed matter and QCD.
- D. H. Rischke, nucl-th/0305030.
The Quark-Gluon Plasma in Equilibrium. Our
current knowledge of the quark-gluon plasma in thermodynamical
equilibrium is reviewed. The phase diagram of strongly interacting
matter is discussed, with emphasis on the quark-hadron phase transition
and the color-superconducting phases of quark matter. Lattice QCD
results on the order of the phase transition, the thermodynamical
functions, the heavy quark free energy, mesonic spectral functions, and
recent results for nonzero quark chemical potential are presented.
Analytic attempts to compute the thermodynamical properties of strongly
interacting matter, such as perturbation theory, quasiparticle models,
``hard-thermal-loop''(HTL)-resummed perturbation theory, the
Polyakov-loop model, as well as linear sigma models are discussed.
Finally, color-superconducting quark matter is considered in the limit
of weak coupling. The gap equation and the excitation spectrum are
derived. The solution of the gap equation, gap parameters in various
color-superconducting phases, and critical temperatures for the
transition to normal-conducting quark matter are presented. A summary
of gluon and photon properties in color superconductors is given.
- J. A. Bowers, hep-ph/0305301. Color
Superconducting Phases of Cold Dense Quark Matter. We investigate color superconducting phases of cold
quark matter at densities relevant for the interiors of compact stars.
At these densities, electrically neutral and weak-equilibrated quark
matter can
have unequal numbers of up, down, and strange quarks. The QCD
interaction
favors Cooper pairs that are antisymmetric in color and in flavor, and
a crystalline color superconducting phase can occur which accommodates
pairing between flavors with unequal number densities. In the
crystalline
color superconductor, quarks of different flavor form Cooper pairs with
nonzero total momentum, yielding a condensate that varies in space like
a sum of plane waves. Rotational and translational symmetry are
spontaneously
broken. We use a Ginzburg-Landau method to evaluate candidate crystal
structures
and predict that the favored structure is face-centered-cubic. We
predict
a robust crystalline phase with gaps comparable in magnitude to those
of
the color-flavor-locked phase that occurs when the flavor number
densities
are equal. Crystalline color superconductivity will be a generic
feature
of the QCD phase diagram, occurring wherever quark matter that is not
color-flavor
locked is to be found. If a very large flavor asymmetry forbids even
the
crystalline state, single-flavor pairing will occur; we investigate
this
and other spin-one color superconductors in a survey of generic color,
flavor,
and spin pairing channels. Our predictions for the crystalline phase
may
be tested in an ultracold gas of fermionic atoms, where a similar
crystalline
superfluid state can occur. If a layer of crystalline quark matter
occurs
inside of a compact star, it could pin rotational vortices, leading to
observable
pulsar glitches. Ph.D. thesis, submitted to the MIT Department of
Physics,
May 2003
Collaboration papers
- R. Casalbuoni and R.
Gatto, hep-ph/9908227, Effective theory for
color-flavor locking in high density QCD.
The paper introduces the low-energy effective lagrangian for the CFL
phase of QCD. (Phys.Lett. B464 (1999) 111-116)
- R. Casalbuoni and R.
Gatto, hep-ph/9909419, The Color-Flavor
Locking Phase
at T \not =0$. Evaluation of the
condensate at
small temperatures. (Phys.Lett. B469 (1999) 213-219)
- R. Casalbuoni and R.
Gatto, hep-ph/9911223, Pseudoscalar
Masses in the Effective Theory for Color-Flavor Locking in high density
QCD. A possible non-perturbative
contribution to the masses of the NG bosons is exhibited (not
published).
- R. Casalbuoni, Z. Duan
and F. Sannino, hep-ph/0004207, Low
Energy Theory for 2 flavors at High Density QCD. Construction of the effective lagrangian
for the 2SC phase. (Phys.Rev. D62 (2000) 094004)
- R. Casalbuoni, R.
Gatto and G. Nardulli, hep-ph/0010321,
Dispersion Laws for In-medium Fermions and Gluons in the CFL Phase of
QCD. Evaluation of the two-point function
for gluons and NG bosons in the
CFL phase, using the effective theory of frmions close to the Fermi
surface. (Phys.Lett. B498 (2001) 179-188; Erratum-ibid. B517 (2001) 483)
- R. Casalbuoni, Z. Duan
and F. Sannino, hep-ph/0011394, Electroweak Physics for Color Superconductivity. Effective theory for the 2SC and CFL phases including
electro-weak interactions. (Phys.Rev. D63 (2001) 114026)
- R. Casalbuoni, R.
Gatto, M. Mannarelli and G. Nardulli, hep-ph/0101326,
Effective Field Theory for the Crystalline Colour Superconductive Phase
of QCD. Effective lagrangian for the LOFF
phase. Anisotropic dispersion relation
for the phonon. (Phys.Lett. B511 (2001) 218-228)
- R. Casalbuoni, R.
Gatto, M. Mannarelli and G. Nardulli, hep-ph/0107024,
Effective gluon interactions in
the Colour Superconductive Phase of two flavor
QCD. Evaluation of the two- three- and
four- point functions of the gluons in the 2SC phase. (Phys.Lett. B524
(2002) 144-152)
- R. Casalbuoni, R.
Gatto, M. Mannarelli and G. Nardulli, hep-ph/0201059,
Anisotropy Parameters for the
Effective Description of Crystalline Color Superconductors. The parameters of the effective lagrangian describing
the LOFF phase are evaluated. (Phys.Rev. D66 (2002) 014006)
- R. Casalbuoni, R.
Gatto and G. Nardulli, hep-ph/0205219, Crystalline Color Superconductivity: Effective
Lagrangian and Phonon Dispersion Law. Effective
lagrangian for the cubic crystalline phase of QCD. (Phys. Lett. B543
(2002) 139)
- R. Casalbuoni, E.
Fabiano, R. Gatto, M. Mannarelli and G. Nardulli, hep-ph/0208121.
Phonons and gluons in the
crystalline color superconducting phase of QCD.The High Density Effective Theory formalism is used
to calculate the low energy properties of the phonons and gluons in the
Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of two-flavor QCD.
Calculations are done for the phonons of the cubic crystal and of the
gluons for the cube and for the single plane wave.
- R. Casalbuoni, F. De Fazio, R.
Gatto, G. Nardulli and M.Ruggieri, hep-ph/0209105.
Massive quark effects in two flavor color superconductors.
The high density effective theory formalism
(HDET) is employed to describe high density QCD with two massive
flavors (2SC). The gap equation is derived and explicitly solved
for the gap parameter. The parameters associated to the pseudo
Nambu-Goldstone boson of $U(1)_A$ are evaluated in the limit
$\mu\to\infty$ and$m/\mu$ fixed.
- R. Casalbuoni,
R. Gatto, G. Nardulli, M. Ruggieri, hep-ph/0302077. Aspects of the Color Flavor Locking phase of QCD in
the Nambu-Jona Lasinio approximation. We study two aspects of the CFL
phase of QCD in the
NJL approximation. The first one is the issue of the dependence on \mu
of
the ultraviolet cutoff in the gap equation, which is solved allowing a
running
coupling constant. The second one is the dependence of the gap on the
strange
quark mass; using the high density effective theory we perform an
expansion
in the parameter (m_s/\mu)^2 after checking that its numerical validity
is
very good already at first order.
Conference papers
- M. G. Alford, K.
Rajagopal and F. Wilczek, hep-ph/9802284. Color superconductivity and sign of its formation. Suggestions that the formation of a color
superconducting condensate in a heavy ion collision may be
accompanied by radiation of negative pions, and its decay may yield
more protons than
were present in the incident nuclei. (Nucl.Phys. A638 (1998)
515c-518c)
- K. Rajagopal, hep-ph/9803341.
QCD at finite baryon density: chiral
symmetry restoration and color superconductivity. Review of
hep-ph/9711395. (Prog.Theor.Phys.Suppl.
131 (1998) 619-631)
- K. Rajagopal, hep-ph/9807318. Three
flavor QCD at high density: color
flavor locking and chiral symmetry breaking. A symmetry breaking scheme is proposed for QCD with
three massless quarks at high baryon density wherein the color and
flavor SU(3)_{color}xSU(3)_{L}xSU(3)_{R}
symmetries are broken down to the diagonal subgroup SU(3)_{color+L+R}
by the formation of a condensate of quark Cooper pairs. (Nucl.Phys.
A642 (1998) 26-38)
- K. Rajagopal, hep-ph/9808348, The
QCD tricritical point: beyond monotony in heavy ion physics. Tricritical point in QCD and superconducting phases.
(Talk given at 3rd Workshop on Continuous Advances in QCD (QCD 98),
Minneapolis, MN, 16-19 Apr 1998.)
- K. Rajagopal, hep-ph/9908360. Mapping
the QCD phase diagram. Tricritical point
and high density QCD. (Nucl.Phys.A661:150-161,1999)
- Deog Ki Hong, hep-ph/0003215. Color Superconductivity in
High Density Effective Theory. In this
talk, I discuss the recent development in
color superconductivity in terms of effective field theory. By
investigating
the Cooper pair gap equations at high density, we see that the
effective
theory simplifies the gap analysis very much, especially in finding
the ground state, the precise form of the gap, and the
critical temperature. (contribution to TMU-Yale
Symposium on Dynamics of Gauge Fields)
- K. Rajagopal, hep-ph/0009058. The
phases of QCD in heavy ion collisions and compact stars. Review of
the arguments for the existence of a critical point in the
QCD phase diagram as a function of temperature and baryon
chemical potential and of the phenomena expected in
cold dense quark matter: color superconductivity andcolor-flavor
locking. (7th Conference on Intersections Between Particle and Nuclear
Physics (CIPANP 2000), Quebec City, Quebec, Canada, 22-28 May 2000, and
of 40th Jubilee Cracow School of Theoretical Physics: Quantum Phase
Transitions in High Energy and Condensed Matter Physics, Zakopane,
Poland, 3-11 Jun 2000. Published in Acta Phys.Polon.B31:3021,2000)
- M. G. Alford, J. A.
Bowers and K. Rajagopal, hep-ph/0009357. Color superconductivity in compact stars. Some implications of recent developments in our
understanding of cold dense quark matter for the physics of compact
stars. (Strong and Electroweak Matter 2000, Marseille, France, June
2000. Strangeness 2000, Berkeley, CA, July 2000. ECT International
Workshop on Physics of Neutron Star Interiors (NSI00), Trento, Italy,
19 Jun - 7 Jul 2000. Published in J.Phys.G27:541-556,2001, Lect.Notes
Phys.578:235-252,2001 Also in *Trento 2000, Physics of
neutron star interiors 235-252)
- R. Casalbuoni, hep-th/0108195, Effective lagrangians for
QCD at high density. A review
of CFL and LOFF phases (Martina Franca 2001, QCD@WORK).
- K. Rajagopal, hep-ph/0109135, Crystalline
color superconductivity. Review of the
LOFF phase (AIP Conf.Proc.602:339-351,2001, Nucl.Phys.A702:25-38,2002,
Martina Franca 2001,
QCD@WORK)
- S.D.H.
Hsu, hep-ph/0111049. The QCD Phase
Diagram and Explosive Astrophysics. I give a brief overview of
our current understanding of the QCD phase diagram at finite
temperature and baryon density. I emphasize phase transitions which
occur at high density and low temperature (relative to the QCD scale),
such as transition(s) to the color superconducting and chirally
symmetric phases. These transitions might occur during violent
astrophysical activity such as type II supernovae core bounce or
neutron star mergers, and
I discuss the possible consequences. (eConf C010815 (2002) 64-75)
- R. Casalbuoni, hep-ph/0110107, Effective
description of QCD at high density. Review
of CFL and of the evaluation of the parameters for the NG bosons and
gluons (Copenhagen 2001, eConf C010815: 88-103, 2002)
- G. Nardulli,hep-ph/0111178, Effective theory for QCD in the LOFF phase. Review of the LOFF phase (Copenhagen 2001, eConf
C010815:104-109, 2002)
- D.K. Hong, hep-ph/0112028.
Crystalline Color Superconductivity in Dense Matter. In this talk I discuss a recently proposed color
superconducting phase of asymmetric quark matter where the up and down
quark have different chemical potential, being in chemical equilibrium
with electrons. Using Schwinger-Dyson equations derived from an
effective theory of low-energy quasiparticles, a
critical coupling for LOFF phase is estimated
for both the case
of an effective four Fermi interaction and Landau-damped
one gluon exchange. (eConf C010815 (2002) 116-124)
- T. Schaefer, nucl-th/0201031. Superdense Matter. We review recent work on the phase structure of QCD
at very high baryon density. We introduce the phenomenon of color
superconductivity and discuss the use of weak coupling methods. We
study the phase structure as a function of the number of flavors and
their masses. We also introduce effective theories that describe low
energy excitations at
high baryon density. Finally, we study the possibility of kaon
condensation at very large baryon density. (talk at ICPAQGP, Jaipur,
India, Nov. 26-30, 2001)
- F. Sannino, hep-ph/0205007. Aspects of the Quantum
Chromo Dynamics Phase Diagram. I briefly
review some aspects of the Quantum Chromo Dynamics phase diagram at non
zero temperature and quark chemical potential. I then suggest new
possible phases which can appear in strongly interacting theories at
non zero chemical potential. Finally I describe the phase diagram as
function of the number of flavors and colors at zero quark chemical
potential and zero temperature. (Invited review talk for the GISELDA
Meeting held in Frascati, 14-18 January 2002)
- M.Mannarelli, hep-ph/0205098.Effective
description of the LOFF phase of QCD. We present
an effective field theory for the crystalline color superconductivity
phase of QCD. It
is kown that at high density and at low temperature QCD
exhibits a transition to a color superconducting phase
characterized by energy gaps in the fermion spectra. Under specific
circumstances the gap parameter has a crystalline pattern, breaking
translational and rotational invariance.(Talk at the Giselda Meeting,
Frascti (Roma), 14-18 Jan 2001
- G. Nardulli,hep-ph/0206065, Effective fields in
dense quantum cromodynamics. Review of
LOFF phase and discussion about vortices and
glitches (Frascati 2002)
- Compact stars in the QCD phase diagram. Conference at NORDITA, August 2001.
- T. Schaefer, nucl-th/0208070. Effective Theory of the
Color-Flavor-Locked Phase. We explain how
an effective theory of the CFL phase can be used to study the effect of
the strange quark mass on the ground state and the excitation spectrum.
We also apply the effective theory to the problem of neutrino emission
from a CFL quark core inside a neutron star.
- J.A. Bowers, K. Rajagopal, hep-ph/0209168. The crystallography of
color superconductivity. We describe the
crystalline phase of color superconducting quark matter. This phase may
occur in quark matter at densities relevant for compact star physics,
with possible implications for glitch phenomena in pulsars. We use a
Ginzburg-Landau approach to determine that the crystal has a
face-centered-cubic (FCC) structure. Moreover, our results indicate
that the phase is robust, with gaps, critical temperature, and free
energy comparable to those of the color-flavor-locked (CFL) phase. Our
calculations also predict ``crystalline superfluidity'' in ultracold
gases of fermionic atoms. (Quark Matter 2002, Nantes, France)
- M.G. Alford, hep-ph/0209287.
QCD at high density/temperature. I give a
survey of recent progress in our understanding of QCD at high density
and temperature. I pay particular attention to color superconductivity,
applications of lattice gauge theory at nonzero density as well as high
temperature, perturbative results at high temperature, and
non-equilibrium calculations. (ICHEP 2002 plenary review talk)
Papers
- M. G. Alford, K.
Rajagopal and F. Wilczek, hep-ph/9711395. QCD at finite baryon density: nucleon droplets and
color superconductivity. A study of
finite density QCD in an approximation in which the interaction between
quarks is modelled by that induced by instantons. At all
densities high enough tit is found that color symmetry is
broken by the formation of a <qq> condensate of quark Cooper
pairs. (Phys.Lett. B422 (1998) 247-256)
- M. G. Alford, K.
Rajagopal and F. Wilczek, hep-ph/9804403. Color flavor locking and chiral symmetry breaking in
high density QCD. A symmetry
breaking
scheme for QCD is proposed with three massless quarks at high baryon
density wherein the color and flavor SU(3)_color times SU(3)_L
times SU(3)_R symmetries are broken down to the diagonal subgroup
SU(3)_{color+L+R}
by the formation of a condensate of quark Cooper pairs. Discussion
of NGB's and modified QED. (Nucl.Phys. B537 (1999) 443-458)
- M. G. Alford, J.
Berges and K. Rajagopal, hep-ph/9908235. Gapless color superconductivity. Derivation of the dispersion relations for
quasiparticle excitations about the color-flavor locked ground state of
QCD at high baryon density. In the presence of
condensates which pair light and strange quarks there need not be an
energy gap in the quasiparticle spectrum.
(Phys.Rev.Lett.84:598-601,2000)
- M. G. Alford, J.
Berges and K. Rajagopal, hep-ph/9910254. Magnetic fields within color superconducting neutron
star cores. Discussion of the
Meissner effect for a color superconductor formed
by cold dense quark matter. (Nucl.Phys.B571:269-284,2000)
- K. Rajagopal, E.
Shuster, hep-ph/0004074. On the applicability of weak coupling results in high
density QCD. It is shown that
present weak-coupling calculations of Delta can only be trusted
for mu >> mu_c ~ 10^8 MeV. (Phys.Rev.D62:085007,2000)
- M. G. Alford, J. A.
Bowers and K. Rajagopal, hep-ph/0008208.
Crystalline color superconductivity. In the case of pairing between species
of quarks with differing chemical potentials, for
suitable values of the differences between chemical potentials, Cooper
pairs with nonzero total momentum are favored, as was first realized by
Larkin, Ovchinnikov, Fulde and Ferrell (LOFF). Condensates of this sort
spontaneously break translational and rotational invariance, leading to
gaps which vary periodically in a crystalline pattern.
(Phys.Rev.D63:074016,2001)
- K. Rajagopal and F.
Wilczek, hep-ph/0012039. Enforced electrical
neutrality of the color flavor locked phase. It is shown that quark matter in the CFL phase of QCD
is rigorously electrically neutral, despite the unequal quark
masses, and even in the presence of an electron chemical
potential. (Phys.Rev.Lett.86:3492-3495,2001)
- J. A. Bowers, J.
Kundu, K. Rajagopal and E. Shuster, hep-ph/0101067.
A Diagrammatic approach to
crystalline color superconductivity. Derivation
of the gap equation through the Schwinger-Dyson equation and
Nambu-Gorkov propagator. (Phys.Rev. D64 (2001) 014024)
- A. K. Leibovich, K.
Rajagopal and E. Shuster, hep-ph/0104073. Opening the crystalline color superconductivity
window. The window for the LOFF phase is
re-evaluated using one-gluon exchange interaction. (Phys.Rev. D64
(2001) 094005)
- M. Alford, K.
Rajagopal, S. Reddy and F. Wilczek, hep-0105009.
The minimal CFL nuclear interface.
The interface betwwen CFL and nuclear
phase is studied. (Phys.Rev.D64:074017,2001)
- C. Manuel and K.
Rajagopal, hep-ph/0107211.Illuminating
dense quark matter. Evaluation of angles
of reflections and rifractions for light illuminating a lump of cold
dense quark matter. (Phys.Rev.Lett.88:042003,2002 )
- J. Kundu and, K.
Rajagopal, hep-ph/0112206.Mass induced
crystalline color superconductivity. The
LOFF phase is obtained by allowing a quark with non zero mass.
(Phys.Rev.D65:094022,2002)
- M. Alford and K.
Rajagopal, hep-ph/0204001.Absence of two
flavor color superconductivity in compact stars. Evidence for absence of the 2SC phase in favor of CFL
and/or LOFF phase
- J. A. Bowers and K.
Rajagopal, hep-ph/0204079.The
crystallography of color superconductivity.Calculation
of the crystalline structure minimizing the free energy in the LOFF
phase
- A. Gerhold, A. Rebhan, hep-ph/0305108. Gauge dependence identities
for color superconducting QCD. Using generalized
Nielsen identities a formal proof is given that the fermionic
quasiparticle
dispersion relations in a color superconductor are gauge independent.
This turns out to involve gluonic tadpoles which are calculated to
one-loop
order in a two-flavor color superconductor. Regarding the appearance of
gluon tadpoles, we argue that in QCD the color superconducting phase is
automatically color neutral.
- I. Giannakis, Hai-cang Ren, hep-ph/0305235. The Ginzburg-Landau Theory
and the Surface Energy of a Colour Superconductor. We apply the Ginzburg-Landau theory to the colour
superconducting phase of a lump of dense quark matter. We calculate the
surface energy
of a domain wall separating the normal phase from the super phase with
the bulk equilibrium maintained by a critical external magnetic field.
Because of the symmetry of the problem, we are able to simplify the
Ginzburg-Landau equations and express them in terms of two components
of the di-quark
condensate and one component of the gauge potential. The equations also
contain two dimensionless parameters: the Ginzburg-Landau parameter
${\kappa}$
and ${\rho}$. The main result of this paper is a set of inequalities
obeyed by the critical value of the Ginzburg-Landau parameter--the
value of ${\kappa}$ for which the surface energy changes sign--and its
derivative with respect to ${\rho}$. In addition we prove a number of
inequalities of the functional dependence of the surface energy on the
parameters of the problem and
obtain a numerical solution of the Ginzburg-Landau equations. Finally
a criterion for the types of colour superconductivity (type I or type
II) is established in the weak coupling approximation.
- D. K. Hong and S.D.H. Hsu, hep-ph/0304156. Positivity and Dense Matter.
We elaborate on previous results concerning the positivity of the
Euclidean path integral measure for low-energy modes in dense fermionic
matter. We show that the sign problem usually
associated
with fermions is absent if one considers only low-energy degrees of
freedom.
We describe a method for simulating dense QCD on the lattice and give
a proof using rigorous inequalities that the color-flavor locked (CFL)
phase is the true vacuum of three flavor, massless QCD. We also discuss
applications to electronic systems in condensed matter, such as
generalized
Hubbard models.
Other papers
- C. Manuel, hep-ph/9512365. Hard
Dense Loops in a Cold Non-Abelian Plasma. Classical transport theory is used to study the
response of a non-Abelian plasma at zero temperature and high chemical
potential to weak color electromagnetic fields. In this article the
parallelism between the transport phenomena occurring in a non-Abelian
plasma at high temperature and high density is stressed. (Phys.Rev. D53
(1996) 5866-5873)
- Robert D. Pisarski,
Michel Tytgat, hep-ph/9604404.
Propagation of Cool Pions. For an exact
chiral symmetry which is spontaneously broken
at zero temperature, we show that at nonzero temperature, generally
pions travel at less than the speed of light.
- R. Rapp, T. Schafer,
E.V. Shuryak and M. Velkovsky, hep-ph/9711396. Diquark bose condensates in high density matter and
instantons. Study of the non perturbative
effects on the gap Phys.Rev.Lett.81:53-56,1998
- J. Berges and K.
Rajagopal, hep-ph/9804233.Color Superconductivity and Chiral Symmetry
Restoration at Nonzero Baryon Density and Temperature. Exploration of the phase diagram of strongly
interacting matter as a function of temperature and baryon number
density, using a class of models for two-flavor QCD in which the
interaction between quarks is modelled by that
induced by instantons. (Nucl. Phys. B538, 215 (1999))
- N. Evans, S. D. H. Hsu
and M. Schwetz, hep-ph/9808444.An Effective Field Theory Approach to Color
Superconductivity at High Quark Density. Investigation
of the Fermi Liquid theory of
high density QCD. Using the renormalization group (RG),
we determine the behavior of effective fermion interactions near the
Fermi surface. (Nucl. Phys. B551, 275 (1999))
- T. Schafer and F.
Wilczek, hep-ph/9810509.High Density Quark Matter and the Renormalization
Group in QCD with two and three flavors. We
consider the most general four fermion operators in QCD for two and
three massless flavors and study their renormalization in the vicinity
of the Fermi surface. (Phys. Lett. B450, 325
(1999))
- N. Evans, S. D. H. Hsu
and M. Schwetz, hep-ph/9810514.Non-Perturbative Couplings and Color Superconductivity. We study the renormalization
group flow to the Fermi surface of the full set of couplings generated
by gluonic and instanton interactions. (Phys. Lett. B449, 281 (1999))
- R. D. Pisarski and D.
H. Rischke, nucl-th/9811104.A first order transition and parity violation in a
color superconductor.
At densities sufficiently high to (effectively) restore the axial U(1)
symmetry, then relative to the ordinary vacuum, the condensation of up
with down quarks (effectively) breaks parity spontaneously. Phys. Rev.
Lett. 83, 37 (1999)
- Kurt Langfeld, Mannque
Rho, hep-ph/9811227. Quark Condensation,
Induced Symmetry Breaking and Color Superconductivity at
High Density. The phase structure of
hadronic matter at high density relevant to the physics of compact
stars and relativistic heavy-ion collisions is studied in a low-energy
effective quark theory. The relevant phases that
figure are (1) chiral condensation, (2) diquark color condensation
(color superconductivity) and (3) induced Lorentz-symmetry breaking
(ISB). (Nucl. Phys. A660 (1999) 475-505)
- J. Berges, D.-U.
Jungnickel, C. Wetterich, hep-ph/9811387.
Quark and Nuclear Matter in the Linear Chiral Meson Model. The equation of state for quark and nuclear matter is
encoded in the effective potential of a linear sigma model. We exploit
an exact
differential equation for its dependence upon the chemical potential
associated to conserved baryon number.
- T. Schafer and F.
Wilczek, hep- ph/9811473. Continuity of Quark and Hadron Matter. We present evidence that for three degenerate flavors
the qualitative features of the color-flavor locked state, reliably
predicted for high density, match the expected features of hadronic
matter at low density. (Phys. Rev. Lett.
82, 3956 (1999))
- D. T. Son, hep-ph/9812287. Superconductivity
by long-range color magnetic interaction in high-density quark matter.We argue that in quark matter at high densities,
the color magnetic field remains unscreened and leads
to the phenomenon of color superconductivity. (Phys. Rev. D59, 094019
(1999))
- G. W. Carter and D.
Diakonov, hep-ph/9812445.Light Quarks in the Instanton Vacuum at Finite Baryon
Density. Since the instanton-induced
interactions are attractive in both $\bar{q}q$ and $qq$ channels, a
competition ensues between phases of matter with condensation in either
or both. It results in chiral symmetry restoration due to the onset of
diquark
condensation, a `colour supercondutor', at finite density. (Phys. Rev.
D60, 016004 (1999))
- D.K. Hong, hep-ph/9812510.
An effective field theory of QCD at high density. We derive a (Wilsonian) effective field theory of QCD
at finite density by integrating out the states in the Dirac sea when
the chemical potential$\mu\gg\Lambda_{\rm QCD}$. The
quark-gluoncoupling is effectively (1+1)-dimensional and the theory
contains four-quark operators which become relevant as we
approach to the Fermi sea. (Phys.
Lett. B473, 118 (2000))
- J. Hosek, hep-ph/9812516. Macroscopic quantum phases
of a deconfined QCD matter at finite density. Formalism for a unified description of distinct
superfluid phases of a deconfined QCD matter at finite density together
with the phase of spontaneously broken chiral symmetry is presented.
Dispersion laws of the quasiquark excitations in both diamagnetic and
ferromagnetic phases with spontaneously broken chiral symmetry are
exhibited explicitly.
- UKQCD Collaboration, Phys. Rev. D59
(1999) 116002.
- S. Hands, J. B. Kogut,
M. Lombardo and S. E. Morrison, hep-lat/9902034.
Symmetries and spectrum of SU(2) Lattice Gauge Theory at finite
chemical potential. We study SU(2) Lattice
Gauge Theory with
dynamical fermions at non-zero chemical potential $\mu$. The symmetries
special to SU(2) for staggered fermions on
the lattice are discussed explicitly and their relevance to
spectroscopy and condensates at non-zero chemical potential
are considered.(Nucl. Phys. B558, 327 (1999))
- S. Chandrasekharan and
U. Wiese, cond-mat/9902128. Meron-Cluster
Solution of Fermion Sign Problems. We
present a general strategy to solve the notorious fermion sign problem
using cluster algorithms. The method applies to various systems in the
Hubbard model family as well as to relativistic fermions. (Phys. Rev.
Lett. 83, 3116 (1999)
- N. O. Agasian, B. O.
Kerbikov and V. I. Shevchenko, hep-ph/9902335.Nonperturbative QCD vacuum and Colour
superconductivity. We argue, that
nonperturbative gluonic fields might play a crucial role in colour
superconductivity scenario. (Phys. Rept. 320, 131 (1999))
- R. D. Pisarski and D.
H. Rischke, nucl-th/9903023. Superfluidity in a Model of Massless Fermions Coupled
to Scalar Bosons. We study superfluidity
in a model of massless fermions coupled to a massive scalar field
through a Yukawa interaction.(Phys. Rev. D60, 094013 (1999))
- T.M. Schwarz, S.P.
Klevansky and G. Papp, nucl-th/9903048. The phase diagram and bulk thermodynamical quantities
in the NJL model at finite temperature and density. Comparison of the instanton model and NJL at finite
temperature and density. (Phys.Rev. C60 (1999) 055205)
M. Alford, J. Berges and K.
Rajagopal, hep-ph/9903502. Unlocking Color and Flavor in Superconducting Strange
Quark Matter. We explore the phase
diagram of strongly interacting matter with massless u and d quarks as
a function of the strange quark mass m_s and the chemical potential mu
for baryon number. As the density is reduced, for sufficiently large
m_s we observe a first order transition from the color-flavor locked
phase to a color superconducting phase analogous to that in two flavor
QCD. (Nucl. Phys. B558, 219 (1999)) - T. Schafer and F. Wilczek, hep-ph/9903503.Quark Description of Hadronic Phases. We extend our proposal that major universality
classes of hadronic matter can be understood, and in favorable cases
calculated, directly in the microscopic quark variables, to allow for
splitting between strange and light quark masses. A surprisingly simple
but apparently viable picture emerges, featuring essentially three
phases, distinguished by whether strangeness is conserved (standard
nuclear matter), conserved modulo two (hypernuclear matter), or locked
to color (color flavor locking). These are separated by sharp phase
transitions. There is also, potentially, a quark phase matching
hadronic K-condensation. (Phys. Rev. D60, 074014 (1999))
- R. Rapp, T. Schafer,
E. V. Shuryak and M. Velkovsky, hep-ph/9904353.High Density QCD and Instantons. Instantons generate strong non-perturbative
interactions between quarks. In the vacuum, these interactions lead to
chiral symmetry breaking and generate constituent quark masses on the
order of 300-400 MeV. The observation that the same forces also provide
attraction in the scalar diquark channel leads to the prediction that
cold quark matter is a color superconductor, with gaps as large as
$\sim$~100 MeV.(Ann als Phys. 280, 35 (2000)
- I.J.R. Aitchison, D.J.
Lee and G. Metikas, cond-mat/9905008.
Finite Temperature Time-Dependent Effective Theory For The Goldstone
Field In A BCS-Type Superfluid. We extend
to finite temperature the time-dependent effective theory for the
Goldstone field (the phase of the pair field) $ \theta $ which is
appropriate for a superfluid containing one species of fermions with
s-wave interactions, described by the BCS Lagrangian.
- J. B. Kogut, M. A.
Stephanov and D. Toublan, hep-ph/9906346.
On two-color QCD with baryon chemical potential. We study SU(2) color QCD with
even number of quark flavors. First, using QCD inequalities we show
that at finite baryon chemical potential mu,
condensation must occur in the channel with
scalar diquark quantum numbers. (Phys. Lett. B464, 183 (1999))
- G.W. Carter and D.
Diakonov, hep-ph/9905465. Chiral Symmetry
Breaking and Color Superconductivity in the Instanton Picture. The instanton approach to spontaneous chiral symmetry
breaking is reviewed, with emphasis on the connection to chiral random
matrix theory.
- E. Shuster and D. T.
Son, hep-ph/9905448. On finite-density QCD at large Nc. Deryagin, Grigoriev, and Rubakov (DGR) have shown that
in finite-density QCD at infinite Nc the Fermi surface is unstable with
respect to the formation of chiral waves
with wavenumber twice the Fermi
momentum, while the BCS instability
is suppressed. We show here that at large, but finite Nc, the DGR
instability
only occurs in a finite window of chemical potentials from above
Lambda_QCD
to mu_critical = exp(gamma ln^2 Nc + O(ln Nc ln ln Nc))Lambda_QCD,
where
gamma = 0.02173. Our analysis shows that, at least in the perturbative
regime,
the instability occurs only at extremely large Nc, Nc > 1000 Nf,
where
Nf is the number of flavors. We conclude that the DGR instability is
not
likely to occur in QCD with three colors, where the
ground state is expected to be a color superconductor. (Nucl. Phys.
B573, 434 (2000))
- D. K. Hong, hep-ph/9905523.Aspects
of high density effective theory in QCD.
We investigate the Cooper pair gap equation and find that the
color-flavor locking phase is energetically preferred at high density.
We also find the color-superconducting phase transition occurs in dense
quark matter when the chemical potential is larger than $250\pm
100~{\rm MeV}$ and the temperature is lower than 0.57 times the Cooper
pair gap in the leading order in the hard-dense-loop approximation.
(Nucl. Phys. B582, 451 (2000))
- D. K. Hong, V. A.
Miransky, I. A. Shovkovy and L. C. Wijewardhana, hep-ph/9906478.Schwinger-Dyson Approach to Color Superconductivity in
Dense QCD. The problem of color
superconductivity in dense QCD is reconsidered in the improved rainbow
approximation to the Schwinger-Dyson equation. The effect of the
unscreened magnetic modes of gluons on the value of the color
condensate is studied. In particular, it is shown that, at sufficiently
large values of the chemical potential, these modes lead to the
enhancement of the superconducting order parameter.(Phys. Rev.
D61, 056001 (2000), erratum ibid. D62, 059903 (2000))
- T. Schafer and F.
Wilczek, hep-ph/9906512.Superconductivity from perturbative one-gluon exchange
in high density quark matter. We study
color superconductivity in QCD at asymptotically large chemical
potential. In this limit, pairing is dominated by perturbative
one-gluon exchange. We derive the Eliashberg equation for the pairing
gap and solve this equation numerically. Taking into account both
magnetic and electric gluon exchanges, we find $\Delta\sim
g^{-5}\exp(-c/g)$ with $c=3\pi^2/\sqrt{2}$, verifying a recent result
by Son.
For chemical potentials that are of physical interest, $\mu< 1$ GeV,
the calculation ceases to be reliable quantitatively, but our results
suggest that the gap can be as large as 100 MeV. (Phys. Rev. D60,
114033 (1999))
- D. K. Hong, M. Rho and
I. Zahed, hep-ph/9906551.Qualitons At High Density.
In the color-flavor-locked (CFL) phase of the QCD superconductor we
show that baryons behave as qualitons (called "superqualitons") with
quantum numbers $B=(1{\rm
mod} 2)/3$, S=1/2 and Y=B. (Phys. Lett. B468, 261 (1999))
- R. D. Pisarski and D.
H. Rischke, nucl-th/9907041.Gaps and Critical Temperature for Color
Superconductivity. Because of a
logarithmic enhancement from soft, collinear magnetic gluons, in dense
quark matter the gap for a color superconducting condensate with spin
zero depends upon the QCD coupling constant g not as exp(-1/g^2), like
in BCS theory, but as exp(-1/g). (Phys. Rev. D61, 051501 (2000))
- J. Meyer, G. Papp,
H.-J. Pirner and T. Kunihiro, nucl-th/9908019.
Renormalization Group Flow Equation at Finite Density. For the linear sigma model with quarks we derive
renormalization group flow equations for finite temperature and finite
baryon density using the heat kernel cutoff. (Phys.Rev. C61 (2000)
035202)
- W. E. Brown, J. T. Liu
and H. Ren, hep-ph/9908248.On the Perturbative Nature of Color Superconductivity. We present a systematic derivation of the transition
temperature, T_C, from the QCD Lagrangian through study of the di-quark
proper vertex. (Phys. Rev. D61, 114012 (2000))
- S.D.H. Hsu and M.
Schwetz, hep-ph/9908310. Magnetic interactions, the renormalization
group and color superconductivity in high density
QCD. Investigation of the effects of
long range magnetic interactions on the RG evolution of local Cooper
pairing interactions near the Fermi surface in high density QCD
- F. Wilczek, hep-ph/9908480.
The recent excitement in high-density QCD.
Review of high-density QCD.
- A. Chodos, F. Cooper,
W. Mao, H. Minakata and A. Singh, hep-ph/9909296.
A two-dimensional model with chiral condensates and
Coopre pairs having QCD-like phase structure. Study of superconducting phases in a two-dimensional
model
- T. Schafer, hep-ph/9909574.Patterns
of Symmetry Breaking in QCD at High Baryon Density. We study the structure of QCD at very large
baryon density for an arbitrary number of flavors $N_f$. (Nucl. Phys.
B575, 269 (2000))
- R. D. Pisarski and D.
H. Rischke, nucl-th/9910056.Color superconductivity in weak coupling. We derive perturbatively the gap equations for a
color-superconducting condensate with total spin J=0 in dense
QCD. At zero temperature, we confirm the results of Son for
the dependence of the condensate on the coupling constant, and compute
the prefactor to leading logarithmic accuracy. (Phys.Rev. D61, 074017
(2000))
- I. A. Shovkovy and L.
C. Wijewardhana, hep-ph/9910225.On gap equations and color-flavor locking in cold
dense QCD with three massless flavors. The
superconductivity in cold dense
QCD with three massless flavors is analyzed in the framework of the
Schwinger-Dyson equation. The set of two coupled gap equations for the
color antitriplet, flavor antitriplet (bar{3},bar{3}) and the color
sextet, flavor sextet (6,6) order parameters is derived. It is shown
that the antitriplet-antitriplet gives the dominant contribution to the
color-flavor locked order parameter, while the sextet-sextet is small
but nonzero. (Phys. Lett. B470, 189 (1999))
- N. Evans, J.
Hormuzdiar, S. D. Hsu and M. Schwetz, hep-ph/9910313.On the QCD Ground State at High Density. We show that, as previously anticipated, in the two
flavor case the vacuum breaks SU(3) color to SU(2) and in the three
flavor case the vacua with color-flavor locking (CFL) have the
lowest energy. We identify a number of relatively flat directions in
the potential along which the pattern of gauge symmetry breaking
changes and parity is violated. We discuss possible phenomenological
consequences of our results. (Nucl. Phys. B581,391 (2000))
- B. Park, M. Rho, A.
Wirzba and I. Zahed, hep-ph/9910347.Dense QCD : Overhauser or BCS Pairing ? We discuss the Overhauser effect (particle-hole
pairing) versus the BCS effect (particle-particle or hole-hole pairing)
in QCD at large quark density. In weak coupling and to leading
logarithm accuracy, the pairing energies can be estimated exactly. For
a small number of
colors, the BCS effect overtakes the Overhauser effect, while for a
large number of colors the opposite takes place, in agreement with a
recent renormalization group argument.(Phys. Rev. D62,
034015 (2000))
- D. T. Son and M. A.
Stephanov, hep-ph/9910491.Inverse meson mass ordering in color-flavor-locking
phase of high density QCD. We derive the
effective Lagrangian for the low-energy massive meson excitations of
the color-flavor-locking (CFL) phase of QCD with 3 flavors of light
quarks.
We compute the decay constants, the maximum velocities, and the masses
of the mesons at large baryon chemical potential mu.(Phys. Rev. D61,
074012 (2000); erratum, ibid. D62, 059902
(2000), hep-ph/0004095.)
- M. Rho, A. Wirzba and
I. Zahed, hep-ph/9910550. Generalized Pions in Dense QCD. QCD superconductors in the color-flavor-locked (CFL)
phase sustain light Goldstone modes (that will be referred to as
generalized pions) that can be described as pairs of particle and/or
hole excitations around a gapped Fermi surface. (Phys. Lett. B473, 126
(2000))
- E.V. Shuryak, hep-ph/9911244. Scales and Phases of
Non-Perturbative QCD. The covered topic
include (i) discussion of the scales at which perturbative description
should be changed by the non-perturbative one. A number of various
examples are considered, leading to different scales, related to
instantons or confinement effects; (ii) Instanton vacuum as an
Instanton Liquid; (iii) The phase diagram of QCD at finite temperature
and density, and especially description of a recent progress in Color
Superconductivity. (lectures at UK Theory Institute, Swansea UK,
Sept.99; and XVII
School ``QCD: Perturbative or Non-perturbative?'' Lisbon, Portugal,
Oct.99)
- E.B. Gregory, S. Guo,
H. Kroger, Xiang-Qian Luo, hep-lat/9912054.
Hamiltonian lattice QCD at finite chemical potential. At sufficiently high temperature and density, quantum
chromodynamics (QCD) is expected to undergo a phase transition from the
confined phase to the quark-gluon plasma phase. In the Lagrangian
lattice formulation the Monte Carlo method works well for QCD at finite
temperature, however, it breaks down at
finite chemical potential. We develop a Hamiltonian approach to
lattice QCD at finite chemical potential and solve it in the case
of free quarks and in the strong coupling limit. (Phys. Rev. D62 (2000)
054508)
- W. E. Brown, J. T. Liu
and H. Ren, hep-ph/9912409.The Transition Temperature to the Superconducting
Phase of QCD at High Baryon Density. Based
on the dominant one-gluon-exchange interaction, both the transition
temperature and zero temperature gap have been determined to leading
order in the coupling, g. While the leading non-BCS behavior,
$T_C\sim\mu g^{-5}e^{-\kappa/g}$, is easily
obtained, the pre-exponential factor has proved more difficult to
evaluate. Focusing on the transition temperature, we present a
perturbative derivation of this factor, exact to leading order in g.
(Phys. Rev. D62, 054016 (2000))
- H. Heiselberg, hep-ph/9912419.
Color superconducting quark matter in neutron stars. Color superconductivity in quark matter is studied
for electrically
charge neutral neutron star matter in b-equilibrium.
- D. K. Hong, T. Lee and
D. Min, hep-ph/9912531. Meson Mass at Large Baryon Chemical Potential in Dense
QCD.We reexamine the quark mass induced
term in chiral Lagrangian in color-flavor locking phase in dense QCD,
and show that the meson mass term is determined by three independent
invariants under chiral-axial symmetry. (Phys. Lett. B477, 137
(2000))
- D. H. Rischke, nucl-th/0001040.Debye
screening and Meissner effect in a two-flavor color superconductor. I compute the gluon self-energy in a color
superconductor with two flavors of massless quarks, where condensation
of Cooper pairs breaks SU(3)_c to SU(2)_c.
(Phys. Rev. D62, 034007 (2000))
- C. Manuel and M. H.
Tytgat, hep-ph/0001095.Masses of the Goldstone modes in the CFL phase of QCD
at finite density. We construct the
U_L(3) x U_R(3) effective lagrangian which encodes the dynamics of the
low energy pseudoscalar excitations in the color-Flavor-Locking
superconducting phase of QCD at
finite quark density. We include the effects of
instanton-induced interactions and study the mass pattern
of the pseudoscalar mesons. A tentative comparison with the
analytical estimate for the gap suggests that some of these low energy
momentum modes are not stable for moderate values of the quark chemical
potential.(Phys. Lett. B479, 190 (2000))
- M. Rho, E. Shuryak, A.
Wirzba and I. Zahed, hep-ph/0001104.Generalized Mesons in Dense QCD. QCD superconductors in the color-flavor-locked (CFL)
phase support excitations (generalized mesons) that can be described as
pairs of particles or
holes (rather than particle-hole) around a gapped Fermi surface.(Nucl.
Phys. A676, 273(2000))
- O. Kiriyama, M.
Maruyama and F. Takagi, hep-ph/0001108.
Chiral phase transition at high temperature and density in the QCD-like
theory. The chiral
phase transition at finite temperature T and/or chemical
potential $\mu$ is studied using the QCD-like theory with a
variational approach. The ``QCD-like theory'' means the improved
ladder approximation with an infrared cutoff in terms of a modified
running coupling. The form of Cornwall-Jackiw-Tomboulis effective
potential is modified by the use of the Schwinger-Dyson equation for
generally nonzero current quark mass. (Phys.Rev. D62 (2000) 105008)
- J.B. Kogut, M.A.
Stephanov, D. Toublan, J.J.M. Verbaarschot, A. Zhitnitsky, hep-ph/0001171. QCD-like Theories at Finite
Baryon Density. We study QCD-like
theories with pseudoreal fermions at finite baryon density. Such
theories include two-color QCD with quarks in the
fundamental representation of the color group
as well as any-color QCD with quarks in the adjoint color
representation. (Nucl.Phys. B582 (2000) 477-513)
- G. Carter and D.
Diakonov, hep-ph/0001318.The Nonperturbative Color Meissner Effect in a
Two-Flavor Color Superconductor. In order
to analyze this effect at low quark density, when gaps are large and
generated nonperturbatively, we use instanton-induced quark
interactions augmented with gauge-invariant interactions between quarks
and perturbative gluons. The five gluon masses are found from the
static limit of the relevant polarization operators, in which
transversality is maintained via the Nambu-Goldstone modes of broken
color
symmetry. Working in the microscopic theory we calculate these masses
to one-loop order and estimate their density dependence.(Nucl. Phys.
B582, 571 (2000))
- K. Zarembo, hep-ph/0002123. Dispersion
Laws for Goldstone Bosons in a Color Superconductor. The effective action valid at energies and momenta
comparable to the gap is derived. Dispersion laws following from this
action are such that the energy of Goldstone bosons is always smaller
than the gap in the quasiparticle spectrum, and Goldstone bosons always
propagate without damping. (Phys. Rev. D62, 054003 (2000))
- S. R. Beane, P. F.
Bedaque and M. J. Savage, hep-ph/0002209.Meson Masses in High Density QCD. The low-energy effective theories for the two- and
three-flavor color-superconductors arising in the high density limit of
QCD are discussed. Using an effective field theory to describe quarks
near the fermi surface, we compute the masses of the pseudo-Goldstone
bosons that dominate the low-momentum dynamics of these systems. (Phys.
Lett. B483, 131 (2000))
- F. Sannino, hep-ph/0002277.A
Note on Anomaly Matching for Finite Density QCD. We note that the QCD phases at large finite density
respect 't Hooft anomaly matching conditions. Specifically the spectrum
of the light excitations possesses the correct quantum numbers required
to obey global anomaly constraints. We argue that 't Hooft constraints
can be used at finite density along
with non perturbative methods to help selecting
the correct phase. (Phys. Lett. B480, 280 (2000))
- Hiranmaya Mishra and
Jitendra C. Parikh, hep-ph/0003019.
Chiral symmetry breaking, color superconductivity
and quark matter phase diagram: a variational approach. We discuss in this note simultaneous existence of
chiral symmetry breaking and color superconductivity at finite
temperature and density in a Nambu-Jona-Lasinio type model. The
methodology involves an explicit construction of a variational ground
state and minimisation of the thermodynamic
potential. (Nucl. Phys. A679 (2001) 597-615)
- D. H. Rischke, nucl-th/0003063.Debye
screening and Meissner effect in a three-flavor color superconductor. I compute the gluon self-energy in a color
superconductor with three flavors of massless quarks. (Phys. Rev. D62,
054017 (2000))
- B. Vanderheyden and A.
D. Jackson, hep-ph/0003150. Random matrix model for chiral symmetry breaking and
color superconductivity in QCD at finite density. We consider a random matrix model which describes the
competition between chiral symmetry breaking and the formation of quark
Cooper pairs in QCD at finitedensity.(Phys. Rev. D62, 094010 (2000))
- M. Alford, hep-ph/0003185. Color superconductivity in
dense quark matter. I discuss recent
developments in our understanding of the
color-superconducting phases of cold, dense quark matter. I describe
the phase diagram as a function of density and the strange quark mass,
and outline some ideas about possible observational consequences of
these exotic phases. (proceedings of TMU-Yale symposium on the dynamics
of gauge fields)
- W. E. Brown, J. T. Liu
and H. Ren, hep-ph/0003199. Non-Fermi Liquid Behaviour, the BRST Identity in the
Dense Quark-Gluon Plasma and Color Superconductivity. Screening in the
plasma leads to novel behaviour, including a remarkable non-BCS scaling
of T_C, the transition temperature to the color superconducting phase.
Radiative corrections to one gluon exchange were previously considered
and found to affect T_C. In particular, the quark self-energy in a
plasma leads to non-Fermi liquid behaviour and suppresses T_C. However,
at the same time, the quark-gluon vertex was shown not to modify the
result at leading order. This dichotomy between the effects of the
radiative corrections at first appears rather surprising, as the BRST
identity connects the self-energy to the vertex corrections.
Nevertheless, as we demonstrate, there is in fact no contradiction with
the BRST identity, at least to leading log order. This
clarifies some of the previous statements on the importance of
the higher order corrections to the determination of T_C and the
zero temperature gap in color superconductivity. (Phys.Rev. D62,
054013 (2000))
- V. A. Miransky, I. A.
Shovkovy, L. C. R. Wijewardhana, hep-ph/0003327.
Diquark composites in the color superconducting
phase of two flavor dense QCD. We study
the Bethe-Salpeter equations for spin zero diquark composites in the
color superconducting phase of N_f=2 cold dense QCD. The explicit form
of the spectrum of the diquarks, containing an infinite tower of narrow
(at high density) resonances, is derived. (Nucl.Phys.Proc.Suppl. 102
(2001) 385-390)
- S. R. Beane, P. F.
Bedaque and M. J. Savage, nucl-th/0004013. Renormalization Group Improved Gap Equation for Color
Superconductors. The renormalization
group is used to resum leading logarithmic contributions of the form
alpha_s^{n+1} beta_0^n log^n (Delta/mu) to the gap equation appropriate
for high density QCD. The scale dependence of the strong coupling
constant alpha_s increases the gap by a factor of exp(33/16 (pi^2/4 -
1)) ~ 20 in the small coupling limit. (Nucl.Phys. A688 (2001) 931-938)
- C. Manuel, hep-ph/0005040. Dispersion
Relations in Ultradegenerate Relativistic Plasmas. The propagation of excitation modes in a relativistic
ultradegenerate plasma is modified by their interactions with the
medium. (Phys. Rev. D62, (6009))
- S.R. Beane and P. F.
Bedaque, nucl-th/0005052.How to Renormalize the Gap Equation in High
Density QCD. We discuss two technical
issues
related to the gap equation in high-density QCD:
i) how to obtain the asymptotic solution with well controlled
approximations, and ii) the renormalization of four-quark operators in
the high-density effective field theory. (Phys. Rev. D62, 117502 (2000))
- D. T. Son and M. A.
Stephanov, hep-ph/0005225. QCD at finite isospin density. QCD at finite isospin chemical potential mu_I
has no fermion sign problem and can be studied on the
lattice. We solve this theory analytically in two limits:
at low mu_I where chiral perturbation theory is applicable, and at
asymptotically high mu_I where perturbative QCD works. (Phys.Rev.Lett.
86 (2001) 592-595)
- Taekoon Lee, hep-ph/0005312. Chiral Vacuum Alignment in
Dense QCD. We discuss an
interesting possibility of nontrivial, quark-mass
induced chiral vacuum alignment in color-flavor locking phase of cold,
dense QCD. (Phys.Lett. B503 (2001) 307-312)
- J.T. Lenaghan, hep-ph/0005330. Influence of the U(1)_A
Anomaly on the QCD Phase Transition. The
SU(3)_{r} \times SU(3)_{\ell} linear sigma model is used to study the
chiral symmetry restoring phase transition of QCD at nonzero
temperature. The line of second order phase transitions separating the
first order and smooth crossover regions is located in the plane of
the strange and nonstrange quark masses. (Phys.Rev. D63 (2001) 037901).
- Chaejun Song, nucl-th/0006030. Dense Nuclear Matter: Landau
Fermi-Liquid Theory and Chiral Lagrangian with Scaling. The relation between the effective chiral Lagrangian
whose parameters scale according to Brown and Rho scaling("BR scaling")
and Landau Fermi-liquid theory for hadronic matter is discussed in
order to make a basis to describe the fluctuations under the extreme
condition relevant to neutron
stars. (Phys. Rept. 347 (2001) 289-371)
- T. Schafer, hep-ph/0006034. Quark
Hadron Continuity in QCD with one Flavor. We study QCD with one flavor at finite baryon density.
In the limit of very high baryon density the system is expected to be a
color superconductor. In the case of one
flavor, the order parameter is in a $\bar 3$ of color and has total
angular momentum one. (Phys. Rev. D62, 094007 (2000))
- S. D. Hsu, F. Sannino
and M. Schwetz, hep-ph/0006059. Anomaly Matching in Gauge Theories at Finite Matter
Density. We investigate the application of 't Hooft's anomaly matching
conditions to gauge theories at finite matter density. We show that the matching conditions constrain the
low-energy quasiparticle spectrum associated with possible realizations
of global symmetries. (Mod.Phys.Lett. A16 (2001) 1871-1880)
- D. K. Hong, hep-ph/0006105. Radiative
mass in QCD at high density. We show that
radiatively generated Majorana mass for antiquarks is same as the
Cooper-pair gap. (Phys. Rev. D62, 091501 (2000))
- C. Manuel, hep-ph/0006106. Lifetime
Effects in Color Superconductivity at Weak Coupling. Present computations of the gap of color
superconductivity in weak coupling assume that the quarks which
participate in the condensation process are infinitely long-lived.
However, the quasiparticles in a plasma are characterized by having a
finite lifetime.
(Phys. Rev. D62, 114008 (2000))
- T. Schafer, nucl-th/0007021. Kaon Condensation in High Density Quark
Matter. We point out that the problem of
kaon condensation in dense hadronic matter can be addressed in
perturbative QCD. Indeed, perturbative calculations suggest that
negative kaons are condensed in high density quark matter if the
electroweak interaction is taken into account. (Phys.Rev.Lett. 85
(2000) 5531-5534)
- M. A. Nowak, M. Rho,
A. Wirzba and I. Zahed, hep-ph/0007034. Pi0 -> Gamma Gamma in Dense QCD. We analyze the generalized process
$\tilde\pi^0\to\tilde{\gamma}\tilde{\gamma}$ in the weak coupling limit
and show that it is related to the recently suggested
Wess-Zumino-Witten (WZW) term. In dense QCD, the radiative decay of the
generalized pion is constrained by geometry and vanishes at large
density. (Phys.Lett. B497 (2001) 85-90)
- Mannque Rho, nucl-th/0007073. Physics of dense and superdense matter. Review of dense QCD. (KIAS International Workshop on
Astrophysics, Seoul, Korea, 24-27 May 2000)
- W. Mao, F. Cooper, A.
Singh and A. Chodos, hep-ph/0007244.Dynamics of the chiral phase transition at finite
chemical potential. Study of the chiral
phase in the Gross Neveu model in the large N limit
- V. Schon and M. Thies,
hep-th/0008175. 2D model field theories at finite temperature and
density. Study of 2D models. Contribution
to the Festschrift in honor of Boris Ioffe, edited by M. Shifman
- R. Rapp, E.
Shuryak and I. Zahed, hep-ph/0008207. A chiral crystal in cold QCD matter at intermediate
densities? The analogue of Overhauser
(particle-hole) pairing in electronic systems (spin-density waves with
non-zero
total momentum $Q$) is analyzed in finite-density QCD for 3 colors
and 2 flavors, and compared to the color-superconducting BCS ground
state (particle-particle pairing, $Q$=0). Employing medium-modified
instanton-induced 't Hooft interactions, as applicable around
$\mu_q\simeq 0.4$ GeV (or 4 times nuclear
saturation density), we find the 'chiral
crystal phase' to be competitive with the color superconductor.
(Phys.Rev. D63
(2001) 034008)
- Andreas Wirzba, nucl-th/0009002. Cooper-Mesons in the
Color-Flavor-Locked Superconducting Phase of Dense QCD. QCD superconductors in the color-flavor-locked (CFL)
phase sustain excitations (``Cooper'' mesons) that can be described as
pairs of particles or holes around a gapped Fermi surface. In weak
coupling and to leading logarithm accuracy the masses, decay constants
and form factors of the scalar, pseudoscalar, vector and axial-vector
excitations, which explicitly are of finite
size, can be calculated exactly. (invited talk for Bologna
2000)
- A. Chodos, F. Cooper,
W. Mao, H. Minakata and A. Singh, hep-ph/0009019.A
two-dimensional model with chiral condensates and Coopre pairs having
QCD-like phase structure. Generalization
of the original Gross-Neveu model from U(N) to O(N) leading to pair
condensation. )Presented at TMU-Yale Symposium on Dynamics of
Gauge Fields: An External Activity of APCTP, Tokyo, Japan, 13-15 Dec
1999)
- V. A. Miransky, I. A.
Shovkovy and L. C. Wijewardhana, hep-ph/0009129.
Diquarks in cold dense QCD with
two flavors. We derive and
analyze the Bethe-Salpeter equations for spin zero
diquarks in the color superconducting phase of cold dense
QCD with two massless flavors. (Phys. Rev.D62, 085025 (2000))
- D. Boyanovsky and H.
J. de Vega, hep-ph/0009172. Non-Fermi
Liquid Aspects of Cold and Dense QED and QCD: Equilibrium and
Non-Equilibrium. Infrared divergences from
the exchange of dynamically screened magnetic gluons (photons) lead to
the breakdown of the Fermi liquid description of the normal state of
cold and dense
QCD and QED. We implement a resummation of these divergences via the
renormalization group to obtain the spectral density, dispersion
relation, widths and wave function renormalization of single
quasiparticles near the Fermi surface. (Phys.Rev. D63 (2001) 034016)
- V. A. Miransky, I. A.
Shovkovy and L. C. Wijewardhana, hep-ph/0009173.
Bethe-Salpeter equation
for diquarks in color-flavor locked phase of
cold dense QCD. The Bethe-Salpeter
equations for diquarks with the quantum numbers of
the Nambu-Goldstone bosons are analyzed in the color-flavor locked
phase of cold dense QCD with three quark flavors.
(Phys.Rev. D63 (2001) 056005)
- T. Grandou, hep-ph/0009351.
Puzzling aspects of hot quantum fields. Some
intriguing points of finite temperature quantum field theory are
considered. (Proceedings of the 5th workshop on QCD,
Villefranche-sur-Mer, 3-8 January 2000)
- E. Babaev, cond-mat/0009438. Aspects of topology of condensates and knotted
solitons in two-band superconductors.
Discussion of type-II superconductors with two flavors
of Cooper pairs. (Animations of knotted solitons by Hietarinta and Salo
are available at this http URL)
- I.A. Shovkovy, nucl-th/0010021. The Spectrum of Diquark
Composites in Cold Dense QCD. The
Bethe-Salpeter equations for spin zero diquark composites in the color
superconducting phase of $N_f=2$ and $N_f=3$ cold dense QCD are
studied. The explicit form of the spectrum of the diquarks with the
quantum numbers
of the (pseudo-) Nambu-Goldstone bosons is derived. (Int.J.Mod.Phys.
A16S1C (2001) 1271-1273)
- T. Schaefer and E.
Shuryak, nucl-th/0010049. Phases of QCD
at High Baryon Density. We review recent
work on the phase structure of QCD at very high baryon density. We
introduce the phenomenon of color
superconductivity and discuss how the quark masses and chemical
potentials determine the structure of the superfluid quark
phase. (Lect.Notes Phys. 578 (2001) 203-217)
- J.V. Steele, nucl-th/0010066.
Effective field theory power counting at finite density. Power counting for finite density theory is studied.
- R.J. Furnstahl, H.-W.
Hammer and Negussie Tirfessa, nucl-th/0010078.
Field Redefinitions at Finite Density. The
apparent dependence of nuclear matter observables on off-shell
properties of the two-nucleon potential is re-examined in the context
of the effective field theory (EFT) approach. (Nucl. Phys. A689 (2001)
846-868)
- Nguyen Van Hieu, hep-ph/0010154. Functional Integral Method
in the Theory of Color Superconductivity.
We propose to study the superconducting pairing of quarks with the
formation of the diquarks as well as the quark-antiquark pairing in QCD
by means of the functional integral technique. ( Invited talk given at
the International Conference on Physics at Extreme Energy - Rencontres
du Vietnam IV, Hanoi 19-25 July 2000)
- D.K. Hong, H.K. Lee,
M.A. Nowak and M. Rho, hep-ph/0010156. Neutrino interactions in color-flavor-locked dense
matter. Determination of the relevant electro-weak interactions in the
CFL phase. Implications about the cooling
of neutron stars.
- C. Manuel and M.
Tytgat, hep-ph/0010274. Sum Rules in the CFL Phase of QCD at finite density. We study the asymmetry between the vector current and
axial-vector current correlators in the colour-flavour locking (CFL)
phase
of QCD at finite density. Using Weinberg's sum rules, we compute
the decay constant $f_\pi$ of the Goldstone modes and find agreement
with previous derivations. (Phys.Lett. B501 (2001) 200-208)
- O. Philipsen, hep-lat/0011019. Static correlation lengths
in QCD at high temperature and finite density. A brief review is given of the sign problem in
finite density lattice QCD and various attempts to overcome it.
(Nucl.Phys.Proc.Suppl. 94 (2001) 49-60)
- D. K. Hong, S.-T. Hong
and Y.-J. Park, hep-ph/0011027. Bosonization of QCD at high density. We describe the color-flavor locking (CFL) color
superconductor in terms of bosonic variables, where the gaped quarks
are realized as solitons, so-called superqualitons. We then show that
the ground state of the CFL color superconductor is a $Q$-matter, which
is the lowest energy state for a given fixed
baryon number. (Phys.Lett. B499 (2001) 125-134)
- J. Hosek, hep-ph/0011033. On Superfluid Phases of Cold
Deconfined QCD Matter at Moderate Baryon Density. We present an overview of the arguments which lead to
the picture that at low temperatures the
QCD matter not far above a critical confinement-deconfinement density
exists in one of several distinct superfluid phases exhibiting the
quantum behavior on macroscopic scales. (talk given at Les Rencontres
de Physique de la Vallee d'Aoste, February 27 - March 4, 2000, La
Thuile, Italy)
- J. Hosek, hep-ph/0011034.
Anisotropic color superconductor. We
argue that the QCD matter not far above a critical
confinement-deconfinement baryon density and low temperatures can
develop spontaneously the condensates of spin-one quark Cooper pairs.
Depending upon their color these condensates characterize two distinct
anisotropic color-superconducting phases. For
them we derive the generic form of the quasiquark
dispersion laws and the gap equation. (talk given at
ICHEP 2000 in parallel session "High Energy Heavy Ion
Collisions", July 27)
- Xiang-Qian Luo, E.B. Gregory, Shuo-Hong Guo and H.
Kroger, hep-ph/0011120. QCD at Finite Density.
At sufficiently high temperature and density, quantum chromodynamics
(QCD) predicts phase transition from the hadronic phase to the
quark-gluon plasma phase. (Proceedings of the International Workshop on
Nonperturbative Methods and Lattice QCD, World Scientific (2001)
138-149)
- Kei Iida and G. Baym, hep-ph/0011229.The superfluid phases of
quark matter: Ginzburg-Landau theory and color neutrality. We apply Ginzburg-Landau theory to determine BCS
pairing in a strongly-coupled uniform superfluid of three-flavor
massless quarks in flavor equilibrium. (Phys.Rev. D63 (2001) 074018)
See also hep-ph/0108149,
hep-ph/0204124
- D. Ebert, K.G.
Klimenko and H. Toki, hep-ph/0011273.Chromagnetic catalysis of color superconductivity in a
(2+1)-dimensional NJL model. Influence of
a constant chromomagnetic field on the formation of color
superconductivity is studied. (Phys.Rev. D64 (2001) 014038)
- D.T. Son and M.A.
Stephanov, hep-ph/0011365. QCD at finite isospin density: from pion to
quark-antiquark condensation. Study od QCD
at finite isospin chemical
potential. (Phys.Atom.Nucl. 64 (2001) 834-842; Yad.Fiz. 64 (2001)
899-907)
- D.H. Rischke, D.T. Son
and M.A. Stephanov, hep-ph/0011379. Asymptotic deconfinement in high density QCD. We discuss QCD with two light flavors at large baryon
chemical potential mu. Color superconductivity leads to partial
breaking of the color SU(3) group. We show that
the infrared physics is governed by the gluodynamics of the remaining
SU(2) group with an exponentially soft confinement scale
Lambda_QCD' Delta*exp[-a*mu/(g*Delta)], where Delta<<mu is the
superconducting gap, g is the strong coupling, and a=0.81...
(Phys.Rev.Lett.87:062001,2001)
- J. Baacke, D. Cormier,
H. J. de Vega and K. Heitmann, hep-ph/0011395.
Dynamics of O(N) chiral supersymmetry at finite energy density. We consider an O(N) version of
a massive, interacting, chiral supersymmetry model solved exactly in
the large N limit. We demonstrate that the system approaches a stable
attractor at high energy densities, corresponding to a non-perturbative
state for which the relevant field
quanta are massless. (Phys. Lett. B520 (2001) 317-321)
- M.B. Hecht, C.D.
Roberts and S.M. Schmidt, nucl-th/0012023.
Diquarks and Density. We describe aspects
of the role that diquark
correlations play in understanding baryon structure and interactions.
(Lect.Notes Phys. 578 (2001) 218-234)
- D.T. Son, M.A.
Stephanov, A.R. Zhitnitsky, hep-ph/0012041. Domain walls of high-dProceedings of the
International Workshop on Nonperturbative Methods and Lattice QCD,
World Scientific (2001) 138-149ensity QCD. We
show that in very dense quark matter there must
exist metastable domain walls where the axial U(1) phase of the
color-superconducting condensate changes by 2pi. The decay rate of the
domain walls is exponentially suppressed and we compute it
semiclassically. We give an estimate of the critical chemical
potential above which our analysis is under
theoretical control. (Phys.Rev.Lett. 86 (2001) 3955-3958)
- Yasuo Umino, hep-ph/0012071. Equation of state of
strongly coupled Hamiltonian lattice QCD at finite density. We calculate the equation of state of strongly
coupled Hamiltonian lattice QCD at finite density by constructing a
solution to the equation of motion corresponding to an effective
Hamiltonian using Wilson fermions.
- V.M. Lotkev, R.M.
Quick and S.G. Sharapov, cond-mat/0012082. Phase fluctuations and pseudogap phenomena. Review of superconducting phase fluctuations.
(Phys.Rept. 349 (2001) 1-123)
- K. Splittorff, D.T.Son
and M.A. Stephanov, hep-ph/0012274. QCD-like Theories at Finite Baryon and Isospin
Density. We use 2-color QCD as a model to
study the effects of simultaneous presence of chemical potentials for
isospin charge, $\mu_I$, and for baryon number,
$\mu_B$. (Phys.Rev. D64 (2001) 016003)
- J. Berges and C.
Wetterich, hep-ph/0012311. Higgs description of two-flavor QCD vacuum. Higgs description of the QCD vacuum in the limit of
two-quark flavors. (Phys.Lett. B512 (2001) 85-90)
- G.E. Brown, Mannque
Rho, nucl-th/0101015. The Fate of Hadron
Masses in Dense Matter: Hidden Local Symmetry and Color Flavor Locking.
The notion that hadron masses scale
according to the scaling of the quark condensate in hadronic matter,
partly supported by a number of
observations in finite nuclei, can be interpreted in terms of
Harada-Yamawaki's ``vector manifestation" (VM) of
chiral symmetry.
- Y. Kim, Young-Ho Song
and Dong-Pil Min, hep-ph/0101189. Meson exchange effect on color superconductivity. Effects of pion and gluon exchanges on the formation
of two-flavor superconductivity at moderate density, m < 1 GeV. (Phys.Rev. D64 (2001) 014026)
- J.A. Oller, hep-ph/0101204. Chiral Lagrangians at finite
density. The effective SU(2) chiral
Lagrangian with external sources is given in the presence of
non-vanishing nucleon densities by calculating the in-medium
contributions of the chiral pion-nucleon Lagrangian. (Phys.Rev. C65
(2002) 025204)
- F. Gastineau, R.
Nebauer and J. Aichelin, hep-ph/0101289.
Thermodynamics of the 3-flavor NJL model : chiral symmetry breaking and
color superconductivity.Employing an
extended three flavor version
of the NJL model we discuss in detail the phase diagram of
quark matter. The presence of quark as well as of diquark condensates
gives raise to a rich structure of the phase diagram.
- C.Wetterich, hep-ph/0102248. Phase transition between
three- and two-flavor QCD?
Spontaneous breaking of color is investigated for
the vacuum of QCD$_2$ with two light flavors of quarks. We classify
possible colored quark-antiquark, diquark and gluon condensates that
are compatible with a spectrum of integer charged states and conserved
isospin and baryon number.
- D.H. Rischke, nucl-th/0103050.
Gluon self-energy in a two-flavor color superconductor. The energy and momentum dependence of the gluon
self-energy is investigated in a color superconductor with two flavors
of massless quarks. The presence of a color-superconducting quark-quark
condensate modifies the gluon self-energy for energies which are of the
order of the gap parameter. (Phys.Rev. D64 (2001) 094003)
- D.T. Son, M.A.
Stephanov, A.R. Zhitnitsky, hep-ph/0103099.
Instanton interactions in dense-matter QCD.
A Coulomb gas representation of dense-matter QCD is derived from a dual
transformation of the low-energy effective Lagrangian. The point-like
charges Q=+1,-1 of the gas are identified with the instantons and
anti-instantons of such topological charges. An instanton repels
another instanton with the same force as it attracts an anti-instanton,
in
contrast to the semiclassical interaction. (Phys.Lett. B510 (2001)
167-172)
- V.A. Miransky, G.W.
Semenoff, I.A. Shovkovy and L.C.R. Wijewardhana, hep-ph/0103227. Color superconductivity and nondecoupling phenomena
in 2+1 dimensional QCD. Study of
superconductivity in 2+1 dimensional QCD. (Phys.Rev. D64 (2001) 025005)
- V.P. Gusynin and I.A.
Shovkovy, hep-ph/0103269. Carlson-Goldman modes in the color superconducting
phase of dense QCD. Prediction of the
gapless Carlson-Godman modes in the CFL
phase. (Phys.Rev. D64 (2001) 116005)
- D.T. Son, M.A.
Stephanov, cond-mat/0103451. Domain walls of relative phase in two-component
Bose-Einstein condensates. We consider a
system of two interpenetrating Bose-Einstein
condensates of atoms in two different hyperfine spin states. We show
that in the presence of a small coupling drive between the two spin
levels, there exist domain walls across which the relative phase of the
two condensates changes by 2pi. We give
the physical interpretation of such walls. (Phys.Rev. A65 (2002) 063621)
- J.B. Kogut, D. Toublan
and D.K. Sinclair, hep-lat/0104010.
Diquark Condensation at Nonzero Chemical Potential and Temperature. SU(2) lattice gauge theory with four flavors of
quarks is studied at nonzero chemical potential $\mu$ and temperature
$T$ by computer simulation and Effective Lagrangian techniques.
(Phys.Lett. B514 (2001) 77-87)
- D.H. Rischke, nucl-th/0104071. Remarks on the
extraction of freeze-out parameters. I
review the extraction of kinetic and chemical freeze-out parameters
from experimental data, with particular emphasis on the underlying
assumptions and the validity of the conclusions. (Nucl.Phys. A698
(2002) 153-163)
- P. F. Bedaque and T.
Schaefer, hep-ph/0105150. High Density
Quark Matter under Stress. We study the
effect of SU(3) flavor breaking on high density quark matter.
We discuss, in particular, the effect a non-zero electron chemical
potential and a finite strange quark mass. We argue that these
perturbations trigger pion or kaon condensation. (Nucl.Phys. A697
(2002) 802-822)
- D.F. Litim and C.
Manuel, hep-ph/0105165. Photon
Self-Energy in a Color Superconductor. In
a color superconductor the diquark
condensates break spontaneously both the color and ordinary
electromagnetism, leaving a remanining rotated U(1) symmetry unbroken.
The gauge interactions associated to this rotated
symmetry may be considered as the in-medium electromagnetism. We
compute the in-medium photon self-energy in the presence of diquark
condensates at high baryonic density and weak coupling. (Phys.Rev. D64
(2001) 094013)
- O. Kiriyama, S. Yasui,
H. Toki, hep-ph/0105170. Color
superconductivity at finite density and temperature with flavor
asymmetry. Color superconductivity of QCD
at finite density, temperature and flavor asymmetry is studied within
an approximation which the interaction is modeled upon four--fermion
interactions. (Int.J.Mod.Phys. E10 (2001) 501-510)
- A. Rebhan, hep-ph/0105183.
Thermal gauge firld theories. Review of
real and imaginary time formalisms of thermal field
theory. (Lectures delivered at the 40th Schladming Winter School on
``Dense Matter'', Lect. Notes Phys. 583 (2002) 161-208)
- N. Van Hieu, hep-ph/0105286.
Functional integral method in quantum theory of composite particles and
quasiparticles. Functional integral
methods for bound states. (Lectures at the 7-th International School in
Theoretical Physics, Hanoi 23 December 2000-05 January 2001)
- N. Van Hieu, hep-ph/0105343.
Functional approach in the theory of color superconductivity. Study of superconductivity with functional methods.
(Phys.Part.Nucl. 33 (2002) 37-51; Fiz.Elem.Chast.Atom.Yadra 33 (2002)
72-100)
- Z. Fodor and S.D.
Katz, hep-lat/0106002. Lattice
determination of the critical point of QCD at finite T and mu. Based on universal arguments it is believed that
there is a critical point (E) in QCD on the temperature (T) versus
chemical potential (\mu) plane, which is of extreme
mportance for heavy-ion experiments. Using finite size
scaling and a recently proposed lattice method to study QCD at finite
\mu we determine the location of E in QCD with n_f=2+1 dynamical
staggered quarks with semi-realistic masses on
$L_t=4$ lattices. Our result is T_E=160 \pm 3.5 MeV and \mu_E=725 \pm
35 MeV. For the critical temperature at \mu=0 we obtained T_c=172 \pm 3
MeV. (JHEP 0203 (2002) 014)
- B.O. Kerbikov, hep-ph/0106324.
Anderson theorem for color superconductor.
Derivation of the Ginsburg-Landau functional for system with diverse
condensates and proof of the Anderson theorem
- F. Karsch, E.
Laermann, Ch. Schmidt, hep-lat/0107020. The Chiral Critical Point in 3-Flavour QCD. We determine the second order endpoint of the line of
first order phase transitions, which occur in the light quark
mass regime of 3-flavour QCD at finite temperature, and analyze
universal properties of this chiral critical point. (Phys.Lett.
B520 (2001) 41-49)
- J.T. Lenaghan, F.
Sannino and K. Splittorff, hep-ph/0107099.
The Superfluid and Conformal Phase Transitions of Two-Color QCD. The phase structure of two-color QCD is examined as a
function of the chemical potential and the number of light quark
flavors. We consider effective
Lagrangians for two-color QCD containing the Goldstone excitations,
spin-one particles and negative intrinsic parity terms. We discuss
the possibility of a conformal phase transition and the enhancement of
the global symmetries as the number of flavors is increased.
(Phys.Rev. D65 (2002) 054002)
- D. Kharzeev, E. Levin,
nucl-th/0108006. Manifestations of high density QCD in the first RHIC
data. We derive a simple analytical
scaling function which embodies the predictions of high density QCD on
the energy, centrality, rapidity, and atomic number dependences of
hadron multiplicities in nuclear collisions. Both centrality and
rapidity dependences of hadron multiplicity in $Au-Au$ collisions as
measured at RHIC at $\sqrt{s}= 130 {GeV}$ are
well described
in this approach. (Phys.Lett. B523 (2001) 79-87)
- S. Mallik, hep-th/0108139. Scattering amplitude and
shift in self-energy in medium. Two simple
proofs are presented for the first order virial expansion of the
self-energy of a particle moving through a medium, characterised by
temperature and/or chemical potential(s). One is based on the virial
expansion of the self-energy operator itself, while the other is on the
analysis of its Feynman diagrams in configuration space. (Eur.Phys.J.
C24 (2002) 143-147)
- Kei Iida and G. Baym, hep-ph/0108149. Superfluid phases of quark
matter, II: Phenomenology and sum rules.
We derive sum rules for a uniform, isotropic superfluid quark-gluon
plasma with massless quarks, first laying out the phenomenological
equations obeyed by a color superconductor in
terms of macroscopic observables such as the superfluid mass and baryon
densities, and the electric and magnetic gluon masses, and then
expressing these quantities in terms of equilibrium
correlation functions. (Phys.Rev. D65 (2002) 014022)
- Masayasu Harada,
Satoshi Takagi, hep-ph/0108173. Phase
Transition in Dense QCD with the Schwinger-Dyson Equation. We investigate the phase structure of dense QCD using
the Schwinger-Dyson equation (SDE) with the improved ladder
approximation in the Landau gauge. We use the gluon propagator
with the electric mode corrected by Debye screening and the magnetic
mode corrected by Landau damping. (Prog.Theor.Phys. 107 (2002) 561-596)
- V. P. Gusynin, I. A.
Shovkovy, hep-ph/0108175. Collective modes of color-flavor locked phase of
dense QCD at finite temperature. A
detailed analysis of collective modes that couple to either vector or
axial color currents in color-flavor locked phase of color
superconducting dense quark matter at finite temperature is presented.
Among the realm of collective modes, including the plasmons and the
Nambu-Goldstone bosons, we also reveal the
gapless Carlson-Goldman modes, resembling the scalar Nambu-Golstone
bosons. (Nucl.Phys. A700 (2002) 577-617)
- V. A. Miransky, I. A.
Shovkovy, hep-ph/0108178. Spontaneous
Symmetry Breaking with Abnormal Number of Nambu-Goldstone Bosons and
Kaon Condensate.
We describe a class of relativistic models incorporating finite density
of matter in which spontaneous breakdown of continuous symmetries leads
to a lesser number of Nambu-Goldstone bosons than that required by the
Goldstone theorem. (Phys.Rev.Lett. 88 (2002) 111601)
- T. Schaefer, D.T. Son,
M.A. Stephanov, D. Toublan, J.J.M. Verbaarschot, hep-ph/0108210.
Kaon Condensation and Goldstone's Theorem.
We consider QCD at a nonzero chemical potential for
strangeness. At a critical value of the chemical potential equal to the
kaon mass, kaon condensation occurs through a continuous phase
transition. We show that, when the isospin
symmetry is exact in the Lagrangian, a Goldstone boson with a
dispersion relation $E \sim p^2$ appears in the kaon condensed phase.
At the same time, the number of the Goldstone bosons is less than the
number of broken generators. (Phys.Lett. B522 (2001) 67-75)
- Hiroaki Abuki, Tetsuo
Hatsuda and Kazunori Itakura, hep-ph/0109013.
Structural Change of Cooper Pairs and Momentum-dependent Gap in Color
Superconductivity.
The two-flavor color superconductivity is studied over a wide
range of baryon density with a single model. We pay a special attention
to the spatial-momentum dependence of the gap and to the
spatial-structure of Cooper pairs. (Phys.Rev. D65 (2002) 074014)
- T. Schaefer, nucl-th/0109029. Strange Goings on in Quark
Matter. We review recent work on how the
superfluid state of three flavor quark matter is affected by non-zero
quark masses and chemical potentials. (Proceedings of 6th Workshop on
Non-Perturbative QCD, Paris, France, 5-9 Jun 2001)
- K. Langfeld, hep-lat/0109033. Confinement versus color
superconductivity: a lattice investigation.
High density YM-theory is addressed by means of an effective theory
where a Higgs type field corresponds to the diquark order parameter.
The effective Higgs theory mimics the Cooper instability at the Fermi
surface. (contribution to 'Statistical QCD', Bielefeld, August 26-30,
2001)
- S. Hands, hep-lat/0109034. Lattice Matter. I review recent developments in the study of strongly
interacting field theories with non-zero chemical potential mu. In
particular I focus on (a) the determination of the QCD critical
endpoint in the (mu,T) plane; (b) superfluid condensates in Two Color
QCD; and (c) Fermi
surface effects in the NJL model. Some remarks are made concerning the
relation of superconductivity with the sign problem.
(Nucl.Phys.Proc.Suppl. 106 (2002) 142-150)
- T. Schaefer, hep-ph/0109052. Mass Terms in
Effective Theories of High Density Quark Matter. We study the structure of mass terms in the effective
theory for quasi-particles in QCD at high baryon density. To
next-to-leading order in the $1/p_F$ expansion we find two types of
mass terms, chirality conserving two-fermion operators and chirality
violating four-fermion operators. In the effective chiral theory
for Goldstone modes in the color-flavor-locked
(CFL) phase the former terms correspond to effective chemical
potentials, while the latter lead to Lorentz invariant mass terms. We
compute the masses of Goldstone bosons in the CFL phase, confirming
earlier results by Son and Stephanov
as well as Bedaque and Sch\"afer. We show that to leading order in
the coupling constant $g$ there is no anti-particle gap contribution to
the mass of Goldstone modes, and that our results are independent of
the choice of gauge. (Phys.Rev. D65 (2002) 074006)
- M. Buballa, M. Oertel,
hep-ph/0109095. Color-Flavor Unlocking
and Phase Diagram with Self-Consistently Determined
Strange Quark Masses. The phase diagram of
strongly interacting matter at non-zero temperature and baryon chemical
potential is calculated
within a 3-flavor NJL-type quark model with realistic quark masses. The
model exhibits spontaneous chiral symmetry
breaking as well as diquark condensation in the two-flavor
color-superconducting phase and in the color-flavor locked phase. We
investigate the color-flavor unlocking phase transition, taking into
account self-consistently calculated effective
quark masses. We find that it is mainly triggered by a first order
phase transition with respect to the strange quark mass. It takes place
at much higher values of the chemical potential than
the transition to the hadronic phase such that we find a relatively
large region in the phase diagram where the two-flavor
color-superconductor seems to be the most favored state. (Nucl.Phys.
A703 (2002) 770-784)
- C.M. Varma, cond-mat/0109409. Higgs Boson in Superconductors. Superfluid helium, describable by a two-component
order parameter, exhibits only the Bogolubov mode with energy $\to 0$
at long wavelengths, while a Lorentz-invariant theory with a
two-component order parameter exhibits a finite energy mode at long
wavelengths (the Higgs Boson), besides the above mass-less mode.
- Qun Wang and D.H.
Rischke, nucl-th/0110016. How the quark
self-energy affects the color-superconducting gap. We consider color superconductivity with two flavors
of massless quarks which form Cooper pairs with total spin zero. We
solve the gap equation
for the color-superconducting gap parameter to
subleading order in the QCD coupling constant $g$ at zero temperature.
At this order in $g$, there is also
a previously neglected contribution from the real part of the quark
self-energy to the gap equation. Including this contribution leads to a
reduction of the color-superconducting gap parameter $\f_0$ by a factor
$b_0'=\exp \big[ -(\p ^2+4)/8 \big]\simeq 0.177$. On the other hand,
the BCS relation $T_c\simeq 0.57\f_0$ between $\f_0$ and the transition
temperature $T_c$ is shown to remain valid after taking into account
corrections from the
quark self-energy. The resulting value for $T_c$ confirms a result
obtained previously with a different method. Phys.Rev. D65 (2002)
054005)
- Mei Huang, Pengfei
Zhaung, Weiqin Chao, hep-ph/0110046.
Massive Quark Propagator in the Color-superconducting Phase. A more general expression for the
quark propagator including both chiral and diquark
condensates has been derived by using energy projectors. This makes it
possible to study the phase transition from hadron phase to color
superconductivity phase in the moderate baryon density region by using
Feynman diagrammatic method
or Green-function method.
- P.F. Bedaque, nucl-th/0110049.
Charged kaon condensation in high density quark matter. We show that at asymptotically high densities the
``color-flavor-locked + neutral kaon condensate'' phase of QCD develops
a {\it charged} kaon condensate through the Coleman-Weinberg mechanism.
At densities achievable in neutron stars a charged kaon condensate
forms only for some (natural) values of the low energy constants
describing the low-lying excitations of the ground state. (Phys.Lett.
B524 (2002) 137-143)
- E.V.Shuryak, hep-ph/0110130. The QCD Phase Diagram,
Equation of State, and Heavy Ion Collisions.
After some historic remarks and a brief summary of recent theoretical
news about the QCD phases, we
turn to the issue of freeze-out in heavy ion collisions. (Invited talk
at "Statistical QCD", Bielefeld, Sept.2001)
- B.O. Kerbikov, hep-ph/0110197. Color Superconducting State
of Quarks. An introductory review of
physics of color superconducting state
of matter is presented. Comparison with superconductivity in electron
systems reveals difficulties involved in formulating color
superconductivity theory at moderately ultra-nuclear density.
- Youngman Kim, Dong-Pil
Min and Mannque Rho, hep-ph/0110223. Kaon
Condensation and Enforced Charge Neutrality
of the Color-Flavor Locked Phase. We
investigate the influence of charged kaon
condensation in hadronic sector on the formation of the electron-free
charge neutral quark matter of equipartition of three light flavors,
i.e., a phenomenon called ``enforced electrical neutrality" of the
color-flavor locked (CFL) phase.
- P. Amore, M. C. Birse,
J.A. McGovern and N.R. Walet, hep-ph/0110267. Colour superconductivity in finite systems. In this paper we study the effect of finite size on
the two-flavour colour superconducting state. As well as restricting
the quarks to a box, we project onto states of good baryon number and
onto colour singlets, these being necessary restrictions on any
observable ``quark nuggets''. We find that whereas finite size alone
has a significant effect for very small boxes, with the superconducting
state often being destroyed, the effect of projection is to restore it
again. The infinite-volume limit is a good approximation even for quite
small systems. (Phys.Rev. D65 (2002) 074005)
- A. Rebhan, hep-ph/0111341. Hard thermal loops and QCD
thermodynamics. These lectures give an
introduction to thermal perturbation theory, hard thermal loops, and
their use in a nonperturbative, approximately self-consistent
resummation of the thermodynamical potentials of quantum
chromodynamics. (Lectures given
at the NATO Advanced Study Institute ``QCD perspectives on hot and
dense matter'', August 6-18, 2001, in Carg\`ese, Corsica, France)
- I.A. Shovkovy, hep-ph/0110352.
Collective modes in color superconducting matter. The properties of plasmons, Nambu-Goldstone bosons
and gapless Carlson-Goldman collective modes in color-flavor locked
phase of color superconducting dense quark matter at finite temperature
are reviewed. A possibility of a kaon condensation with an abnormal
number of the NG bosons is also discussed. (Int.J.Mod.Phys. A17 (2002)
904-913)
- R.D. Pisarski, D.H.
Rischke, nucl-th/0111070. Gauge
invariance of the color-superconducting gap on the mass shell. The gap parameter for color superconductivity is
expected to be a gauge invariant quantity, at least on the appropriate
mass shell. Computing the gap to subleading order in the QCD coupling
constant, g, we show that the prefactor of the exponential in 1/g is
gauge dependent off the mass shell, and independent of gauge on the
mass shell. (Proceedings of the Conference on Statistical QCD,
Bielefeld, August
26 - 30, 2001)
- D.T. Son, M.A.
Stephanov, hep-ph/0111100. Pion
Propagation near the QCD Chiral Phase Transition.
We point out that, in analogy with spin waves in antiferromagnets, all
parameters describing the real-time propagation of soft pions at
temperatures below the QCD chiral phase
transition can be expressed in terms of static correlators. This
allows, in principle, the determination of the soft
pion dispersion relation on the lattice. Using scaling and universality
arguments, we determine the critical behavior of the parameters of pion
propagation. We predict that when the
critical temperature is approached from below, the pole mass of the
pion drops despite the growth of the pion screening mass.
This fact is attributed to the decrease of the pion velocity near
the phase transition. (Phys.Rev.Lett. 88 (2002) 202302)
- Mei Huang, Pengfei
Zhaung, Weiqin Chao, hep-ph/0112124. Massive quark
propagator
and competition between chiral and diquark condensate. The Green-function approach has been extended to the
moderate baryon density region in the framework of an extended
Nambu--Jona-Lasinio model, and the
thermodynamic potential with both chiral and diquark condensates has
been evaluated by using the massive quark propagator. (Phys.Rev. D65
(2002) 076012)
- K.B.W. Buckley, hep-ph/0112144. Classical stability of
U(1)_A domain walls in dense matter QCD.
It was recently shown that there exists metastable U(1)_A domain wall
configurations in high-density QCD (\mu >> 1 GeV). In the
following we will assess the stability of such non-trivial field
configurations
at intermediate densities (\mu < 1 GeV). The existence of such
configurations at intermediate densities could have interesting
consequences for the physics of neutron stars with high core
density. (Phys.Rev. D65 (2002) 125011)
- Tadafumi Ohsaku, cond-mat/0112456. BCS and generalized BCS
superconductivity in relativistic quantum field theory. I. formulation. We investigate the BCS and generalized BCS theories
in the relativistic quantum
field theory. We select the gauge freedom as U(1), and introduce a
BCS-type effective attractive interaction. (Phys.Rev. B65 (2002)
024512). See also cond-mat/0201292
- T. Schafer, nucl-th/0201031. Superdense Matter. We review recent work on
the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity
and discuss the use of weak coupling methods. We study the phase
structure as a function of the number of flavors and their masses. We
also introduce effective theories that describe low energy excitations
at high baryon density. Finally, we study the possibility of kaon
condensation at very large baryon density. (Talk at ICPAQGP, Jaipur,
India, Nov. 26-30, 2001)
- T. Schafer, hep-ph/0201189. Instanton Effects in QCD at
High Baryon Density. We
study instanton effects in QCD at very high baryon density. In this
regime instantons are suppressed by a large power of
$(\Lambda_{QCD}/\mu)$, where $\Lambda_{QCD}$ is the QCD scale parameter
and $\mu$ is the baryon chemical potential.
- Tadafumi Ohsaku, cond-mat/0201292. BCS and Generalized BCS Superconductivity in
Relativistic Quantum Field Theory. II. Numerical Calculations. We solve numerically various types of the gap
equations developed in the relativistic BCS and generalized BCS
framework, presented in part I of this paper. See also cond-mat/0112456
- M. Sadzikowski and M.
Tachibana, hep-ph/0201223. Andreev
reflection at QGP/CFL interface. In this
letter we address the question of the phenomena of
Andreev reflection between the cold quark-gluon plasma phase
and CFL color superconductor. We show that there are two different
types of reflections connected to the structure of the
CFL phase. We also calculate the probability current at the
interface and we show that it vanishes for energy of scattering quarks
below the superconducting gap.
- M. Oertel and M.
Buballa, hep-ph/0202098. Color-Flavor
(Un)locking. The structure of the phase
diagram of strongly interacting matter at moderate
densities is calculated within a 3-flavor NJL-type quark model
with realistic quark masses. We focus on the influence of the
selfconsistently determined effective strange quark mass on the
color-flavor unlocking phase transition. (proceedings of the workshop
"Ultrarelativistic heavy ion collisions", Hirschegg 2002)
- C.P. Hofmann, cond-mat/0202153. Ferromagnets and
antiferromagnets in the effective Lagrangian perspective. Nonrelativistic systems exhibiting collective
magnetic behavior are analyzed within the framework of effective
Lagrangians. The method, which formulates the
dynamics of the system in terms of Goldstone bosons, allows to
investigate the consequences of spontaneous symmetry breaking from a
unified point of view. (Contributed Talk at 8th Mexican Workshop on
Particles and Fields, Zacatecas, Mexico, 14-20 Nov 2001)
- R. A. Schneider, T.
Renk and W. Weise, hep-ph/0202180.
Quasiparticles in QCD thermodynamics and applications. We propose a novel quasiparticle interpretation of
the equation of state of deconfined QCD at finite temperature. Using
appropriate thermal masses, we introduce
a phenomenological
parametrization of the onset of confinement in the vicinity of the
phase transition. (Talk given at the International Workshop XXX on
Gross Properties of Nuclei and Nuclear Excitations, Hirschegg, Austria)
- Deog Ki Hong, Stephen
D.H. Hsu, hep-ph/0202236. Positivity of High Density Effective Theory. We show that the effective field theory of low energy
modes in dense QCD has positive Euclidean path integral measure. The
complexity of the measure of QCD at finite chemical
potential can be ascribed to modes which are irrelevant to the dynamics
at sufficiently high density. Rigorous inequalities follow at
asymptotic density. Lattice simulation of dense QCD should be possible
using the quark determinant calculated in the effective theory.
- K.B.W. Buckley and
A,R. Zhitnitsky, hep-ph/0204064.
Superconducting K strings in high density QCD. Recently it has been argued that the ground
state of high density QCD is likely be a combination of
the CFL-phase along with condensation of the K^0 field. This state
spontaneously breaks a global U(1)_Y symmetry, therefore
one would expect the formation of U(1)_Y global strings. (JHEP
0208 (2002) 013)
- M. Buballa, J. Hosek, M. Oertel, hep-ph/0204275.
Anisotropic admixture in color-superconducting quark matter.
The analysis of color-superconducting
two-flavor deconfined quark matter at moderate densities
is extended to include a particular spin-1 Cooper pairing of
those quarks which do not participate in the standard spin-0 diquark
condensate: (i) Due to the peculiar form of the gap equation,
exhibiting spontaneous breakdown of rotational symmetry, the
corresponding gap parameter Delta' is extremely sensitive to
details of the effective interaction and to the chemical potential.
(ii) The critical temperature of the anisotropic component is
approximately given by the relation T_c'\simeq Delta'(T=0)/3. (iii) In
the chiral limit the gas of anisotropic Bogolyubov-Valatin quasiquarks
becomes effectively gapless and two-dimensional. Consequently, its
specific heat depends quadratically on temperature. (iv) All
collective Nambu-Goldstone excitations of the anisotropic phase have a
linear dispersion law and the whole system remains a superfluid.
- Kei Iida and G. Baym, hep-ph/0204124.
Superfluid phases of quark matter. III. Supercurrents and vortices. We study, within Ginzburg-Landau theory, the
responses of three-flavor superfluid quark-gluon plasmas
to external magnetic fields and rotation, in both the color-flavor
locked
and isoscalar color-antitriplet diquark phases
near the critical temperature. (Phys.Rev. D66 (2002) 014015)
- D.T. Son, hep-ph/0204199. Low-Energy Quantum Effective
Action for Relativistic Superfluids. We
consider relativistic superfluids where the
U(1) baryon symmetry is spontaneously broken. Using the formalism of
the quantum effective action, we show that the low-energy dynamics of
the superfluid Goldstone boson
is completely determined by the equation of state.
- D.T. Son, M.A. Stephanov, hep-ph/0204226. Real-time pion propagation
in finite-temperature QCD. We argue that
in QCD near the chiral limit, at all temperatures below
the chiral phase transition, the dispersion relation of soft pions can
be expressed entirely in terms of three temperature-dependent
quantities: the pion screening mass, a pion decay constant, and
the axial isospin susceptibility. The definitions of these quantities
are given in terms of equal-time (static) correlation functions. Thus,
all three quantities can be determined directly by lattice methods. The
precise meaning of the Gell-Mann--Oakes--Renner relation at
finite temperature is given.
- M. Buballa, M. Oertel,
hep-ph/0205027. Color
superconductivity in two- and three-flavor systems at moderate
densities. Basic features of color
superconductivity are reviewed, focusing on the regime of ``moderate
densities'', which is not accessible by perturbation theory. We discuss
the standard picture of two- and three flavor color superconductors and
study the color-flavor unlocking phase transition within an NJL-type
model. (Proceedings of the NATO Advanced Research Workshop on
Confinement, Topology, and other Non-Perturbative Aspects of QCD, Stara
Lesna, Slovakia, Jan 21-27, 2002)
- D.H. Rischke and I.A.
Shovkovy, nucl-th/0205080. Longitudinal
gluons and Nambu-Goldstone bosons in a two-flavor color superconductor.
In
a two-flavor color superconductor, the SU(3)_c gauge
symmetry is spontaneously broken by diquark condensation. The
Nambu-Goldstone excitations of the diquark condensate mix with the
gluons associated with the broken generators of the original gauge
group. It is shown how one can decouple these modes with a particular
choice of 't Hooft gauge.
- V.A. Miransky, I.A.
Shovkovy, hep-ph/0205348. Magnetic
catalysis and anisotropic confinement in QCD. The expressions for dynamical masses
of quarks in the chiral limit in QCD in a strong magnetic field are
obtained. (Phys. Rev. D 66 (2002) 045006)
- T.D. Fugleberg, hep-ph/0206033. General Quasiparticle
Propagator and Mass Dependence in Degenerate Color Superconductivity. The general quasiparticle propagator in dense quark
matter is derived for equal
mass quarks. Specialized to an NJL model, this propagator includes one
new condensate, $\Delta_3$, in addition to the usual CFL condensate,
$\Delta_1$.
- Mei Huang, Pengfei
Zhuang and Weiqin Chao, hep-ph/0207008. Charge Neutrality Effects on 2-flavor Color
Superconductivity. The effect of electric
and color neutrality on 2-flavor color superconductivity has been
investigated. It has been found that the effect of the charge eutrality
on a 2-flavor quark system is very different from that on a 3-flavor
system.
- E. Gubankov,
hep-ph/0208015. Color
superconductivity
from magnetic interaction induced by flow equations. Using flow equations, we derive an effective
quark-quark interaction and obtain the coupled set of gap equations for
the condensates of the CFL phase of massless N_f=3 dense QCD. We find
two different sources of the infrared cutoff in magnetic interaction.
When the penetration depth of the magnetic field inside the
superconductor is less than the coherence length of quark-quark bound
state, our results
for the gap agree with those of Son. In the other case, we obtain
parametric enhancement of the gap on the coupling constant.
- M. Sadzikowski and
Motoi Tachibana, hep-ph/0208037. Andreev
reflection in superconducting QCD. In this
paper we discuss the phenomenon of the Andreev reflection
of quarks at the interface between the 2SC and the Color-Flavor-Locked
(CFL) superconductors appeared in QCD at asymptotically high densities.
We also give the general introduction to the Andreev reflection in the
condensed matter systems as well as the review
of this subject in high density QCD.
- F. Cooper and V.M.
Savage, hep-ph/0208057. Dynamics of the
chiral phase transition in the 2+1 dimensional Gross-Neveu model. The phase diagram of the Gross-Neveu (G-N) model in
2+1 dimensions as a function of
chemical potential and temperature has a simple curve
separating the broken symmetry and unbroken symmetry phases, with
chiral symmetry being restored both at high temperature and high density.
- E. Gubankova, hep-ph/0209033. Diquark interaction and gaps for color
superconductivity. Using flow equations,
we derive an effective quark-quark interaction and obtain the coupled
set of gap equations for the condensates of the CFL phase of massless
$N_f=3$ dense QCD. The formalism developed here enables one to
consider more general case of nonzero $s$-quark mass.
- Kazunori Itakura, hep-ph/0209081.
Structure change of Cooper pairs in color superconductivity. Crossover
from BCS to BEC? We discuss a
possibility of transition from color superconductivity of the standard
BCS type at high density, to Bose-Einstein Condensation (BEC) of Cooper
pairs at lower density. Examining two-flavor QCD over a wide range of
baryon density, we found the size of a Cooper pair becomes small enough
to be comparable to the averaged quark-quark distance at lower density.
We also consider the same problem in two-color QCD.
- Tadafumi Ohsaku, cond-mat/0209352
(+ Figs). Superconductivity in
(2+1)-dimensional Relativistic Quantum Field Theory. We investigate the superconductivity in
(2+1)-dimensional relativistic quantum field theory. We employ the
massless Gross-Neveu model as a model Lagrangian. By using this model,
we study the superconductivity and superconducting instability. Our
investigation is strongly related to the
superconductivity in (2+1)-dimensional two-band systems.
- A. Schmitt,
Qun Wang and D.K. Rischke, nucl-th/0209050.
Study of color SC for N_f=1,2,3. The leading order for
the gap equation is the same in all cases. Various cases
are studied in a unified way and T_c is evaluated.
- M. D'Elia, M.P. Lombardo, hep-lat/0209146. Finite density QCD via
imaginary chemical potential. We study
QCD at nonzero temperature and baryon density in the framework of the
analytic continuation from
imaginary chemical potential. We carry out simulations of QCD with four
flavor of staggered fermions, and reconstruct the phase diagram
in the temperature-imaginary \mu plane. We consider ans\"atze for
the analytic continuation of the critical line and other observables
motivated both by theoretical considerations and mean field
calculations in four fermion models and random matrix theory. We
determine
the critical line, and the analytic continuation of the chiral
condensate, up to \mu_B approx. 500 MeV. The results are in qualitative
agreement with the predictions of model field theories, and consistent
with a first order chiral transition. The correlation between the
chiral transition and the deconfinement transition observed at \mu=0
persists at nonzero density.
- I. Zakout, H.R. Jaqaman, W. Greiner,
hep-ph/0209342. Numerical solution of
the color superconductivity gap in a weak coupling constant. We present the numerical solution of the full gap
equation in a weak coupling constant $g$. It is found that the standard
approximations to derive the gap equation to the leading order of
coupling constant are essential for a secure numerical evaluation of
the logarithmic singularity with a small coupling constant. The
approximate integral gap equation with a very small $g$ should be
inverted to a soft integral equation to smooth the logarithmic
singularity near the Fermi surface. The full gap equation is solved for
a rather large coupling constant $g\ge 2.0$. The approximate and soft
integral gap equations are solved for small $g$ values. When their
solutions are extrapolated to larger $g$ values, they coincide the full
gap equation solution near the Fermi surface. Furthermore, the
analytical solution matches the numerical one up to the order one O(1).
Our results confirm the previous estimates that the gap energy is of
the order tens to 100 MeV for the chemical potential $\mu\le 1000$ MeV.
They also support the
validity of leading approximations applied to the full gap equation to
derive the soft integral gap equation and its analytical solution near
the Fermi surface.
- Andrew W. Steiner, Sanjay Reddy,
Madappa Prakash, hep-ph/0205201.
Color-Neutral Superconducting Quark Matter. We investigate the consequences of enforcing local
color neutrality on the color superconducting phases of quark
matter by utilizing the Nambu-Jona-Lasinio model supplemented by
diquark and the t'Hooft six-fermion interactions. In neutrino free
matter at zero temperature, color neutrality guarantees that the
number densities of u, d, and s quarks in the Color-Flavor-Locked (CFL)
phase will be equal even with physical current quark masses. Electric
charge neutrality follows as a consequence and without the presence of
electrons. In contrast, electric charge neutrality in the less
symmetric 2-flavor superconducting (2SC) phase with ud
pairing requires more electrons than the normal quark phase. The free
energy density cost of enforcing color and electric charge neutrality
in the CFL phase is lower than that in the 2SC phase, which favors the
formation of the CFL phase. With increasing temperature and neutrino
content, an unlocking transition occurs from the CFL phase to the 2SC
phase with the order of the transition depending on the temperature,
the quark and lepton number chemical potentials. The astrophysical
implications of this rich structure in the phase diagram, including
estimates of the effects from Goldstone bosons in the CFL phase, are
discussed.
- Prashanth Jaikumar, Ismail Zahed, hep-ph/0209249. Scalar-isoscalar excitation
in dense quark matter. We study the spectrum of
scalar-isoscalar excitations in the color-flavor locked phase of dense
quark matter. The sigma meson in this phase appears as a four-quark
state (of diquark and anti-diquark) with a well-defined mass and
extremely small width, as a consequence of it's small coupling to two
pions. The quark particle/hole degrees of freedom also contribute
significantly to the correlator just above the threshold 2\Delta where
\Delta is the superconducting gap.
- Bang-Rong Zhou, hep-th/0210023. Critical analyses of order
parameter and phase transitions at high density in Gross-Neveu and
Nambu-Jona-Lasinio model. Based on gap
equations and
effective potentials derived from them we have analyzed
behaviors of dynamical fermion mass near critical chemical potentials
in four-fermion interaction models and proven that the symmetry
restoring phase transitions at high density are second
order in time-space dimension D=2 Gross-Neveu (GN) model when
temperature is high and in D=3 GN model and D=4 Nambu-Jona-Lasinio
(NJL) model when temperature is finite. However, when temperature goes
to zero the phase transition will be first order in D=2 and
D=3 GN model and still second order in D=4 NJL model. The researches
not only reproduce the known most essential results in D=2 and D=3
GN model and further strengthen the conclusion in D=4 NJL model,
but also indicate that the gap equations alone are fully effective
for critical analyses of second order even some first order phase
transitions, and after combined with the derived effective potentials,
are also effective for critical analyses of general first order phase
transitions.
- M. Sadzikowski, hep-ph/0210065. Non-uniform chiral boundary
between normal and superconducting phases. We
show that the superconducting 2SC phase at
high density and normal chiraly broken quark phase at low density is
separated by the mixed non-uniform phase along the baryon density
line.
- F. Neumann, M. Buballa, M. Oertel, hep-ph/0210078. Mixed phases of color
superconducting quark matter. We examine
electrically and color neutral quark matter in beta-equilibrium
focusing on the possibility of mixed phases between different color
superconducting phases. To that end we apply the Gibbs criterion to
ensure phase equilibrium and discuss the external conditions under
which these mixed phases can occur. Neglecting surface and Coulomb
effects we find a
rich structure of different mixed phases with up to four components,
including 2SC and CFL matter as well as more ``exotic'' components,
like a phase with us- and ds-pairing but without ud-pairing.
Preliminary estimates indicate, however, that the mixed phases become
unstable if surface and Coulomb effects are included.
- M.G. Alford, J.A. Bowers, J.M.
Cheyne, G.A. Cowan, hep-ph/0210106.
Single color and single flavor color superconductivity. We survey the non-locked color-flavor-spin channels
for quark-quark (color superconducting) condensates in QCD, using an
NJL model. We also study isotropic quark-antiquark (mesonic)
condensates. We make mean-field estimates of the strength and sign of
the self-interaction of each condensate, using four-fermion
interaction vertices based on known QCD interactions. For the
attractive
quark pairing channels, we solve the mean-field gap equations to
obtain the size of the gap as a function of quark density. We also
calculate the dispersion relations for the quasiquarks, in order
to see how fully gapped the spectrum of fermionic excitations will
be. We use our results to specify the likely pairing patterns in
neutral quark matter, and comment on possible phenomenological
consequences.
- S. Takagi, hep-ph/0210227.
Phase Structure of Hot and/or Dense QCD with the Schwinger-Dyson
Equation. We investigate the phase
structure of hot and/or dense QCD using the Schwinger-Dyson equation
(SDE) with the improved ladder approximation in the Landau gauge. We
show that the phase transition from the two-flavor color
superconducting (2SC) phase to the quark-gluon plasma (QGP) phase is of
second order, and that the scaling properties of the Majorana mass gap
and the diquark condensate are consistent with the mean field scaling.
We examine the effect of antiquark contribution, and find that setting
the antiquark Majorana mass equal to the quark one is a good
approximation in the medium
density region. We also study the effect of the Debye screening mass of
gluon, and find that neglection of it moves the critical
lines to the higher temperature and higher chemical potential
region.
- C. Manuel, S. Mrowczynski, hep-ph/0206209. QCD effective actions from
the solutions of the transport equations. We
solve the collisionless transport equations of a quark-gluon plasma
interacting through mean chromodynamic fields. The system is assumed to
be translation invariant in
one or more space-time directions. We present exact solutions that
hold if the vector gauge fields in the direction of the translation
invariance commute with their covariant derivatives. We also
solve the equations perturbatively when the commutation condition
is relaxed. Further, we derive the color current and the associated
effective action. For the static quasi-equilibrium system, our
results reproduce the full one-loop effective action of QCD in the
presence of constant background fields, where the above mentioned
commutation condition is satisfied.
- I.A. Shovkovy, P.J. Ellis, hep-ph/0211049. Optically opaque
color-flavor locked phase inside compact
stars. The contribution of thermally
excited electron-positron pairs to the bulk properties of the
color-flavor locked quark phase inside compact stars is examined. The
presence of these pairs causes the photon mean free path
to be much smaller than a typical core radius ($R_{0} \simeq
1$ km) for all temperatures above 25 keV so that the photon
contribution
to the thermal conductivity is much smaller than that of the
NG bosons. We also find that the electron and positron contributions to
the total thermal energy of the quark core is considerably smaller than
the contribution of the NG bosons and photons. These electron-positron
pairs dominate the electrical conductivity since their masses are
considerabley smaller than those of the lightest charged pseudo-NG
bosons.
- G. Lugones, J. E. Horvath, hep-ph/0211070 +Figs..
Color-flavor locked strange matter. We analyze
how the CFL states in dense matter work in the direction of enhancing
the parameter space for absolutely stable phases (strange matter). We
find that the "CFL strange matter" phase can be the true ground state
of
hadronic matter for a much wider range of the parameters of the
model (the gap of the QCD Cooper pairs $\Delta$, the strange quark
mass $m_s$ and the Bag Constant $B$) than the state without any
pairing,
and derive a full equation of state and an accurate analytic
approximation to the lowest order in $\Delta$ and $m_{s}$ which may be
directly used for applications. The effects of pairing on the equation
of state are found to be small (as previously expected) but not
negligible and may be relevant for astrophysics. (Phys. Rev. D
66, 074017 (2002))
- K. Splittorff, J.T. Lenaghan, J.
Wirstam, hep-ph/0211086. Fluctuation
Induced Critical Behavior at Non-Zero Temperature and Chemical
Potential. The presence of a chemical potential
explicitly breaks Lorentz invariance and may additionally break other
internal symmetries. This introduces new subtleties in the
determination of the critical properties of field theories at nonzero
temperature. In this article, we discuss the occurrence of
phase transitions in relativistic systems as a function of both
chemical potential and temperature. We find that the
$\epsilon$-expansion at nonzero chemical potential is not affected by
the explicit breaking of Lorentz invariance but is sensitive to the
breaking of additional symmetries by the chemical potential. We derive
effective three dimensional theories at criticality and study the
effect of the chemical potential on the fixed point structure of the
$\beta$-functions within several different contexts: first for a scalar
field theory with a global U(1) symmetry, then for the chiral phase
transition in QCD with two colors and two flavors, and finally, we
consider QCD with three colors at nonzero baryon and isospin chemical
potential.
- H. Müther, A. Sedrakian, hep-ph/0212317.
Breaking rotational symmetry in two-flavor color superconductors. The color superconductivity under flavor asymmetric
conditions relevant to the compact star phenomenology is studied within
the Nambu-Jona-Lasinio model. We focus on the effect of the deformation
of the Fermi surfaces on the pairing properties
and the energy budget of the superconducting state. We find that
at finite flavor asymmetries the color superconducting BCS state is
unstable towards spontaneous quadrupole deformation of the Fermi
surfaces of the $d$ and $u$ quarks into ellipsoidal form. The ground
state of
the phase with deformed Fermi surfaces corresponds to a superposition
of prolate and oblate deformed Fermi ellipsoids of $d$ and $u$ quarks.
- F. Sannino, hep-ph/0301035.
Anomaly Matching and Low Energy Theories at High Matter Density. I provide new arguments supporting the validity of the
t'Hooft anomaly conditions at non zero quark chemical potential. These
constraints strengthen the quark-hadron continuity scenario. Finally I
review the 2SC effective Lagrangian for color superconductivity.
- D. Blaschke, M. K. Volkov,
V.L.Yudichev, hep-ph/0301065.
Coexistence of color superconductivity and chiral symmetry breaking
within the NJL model. The phase diagram for
quark matter is investigated within a simple Nambu--Jona-Lasinio model
without vector correlations. It is found that the phase structure in
the temperature--density plane depends sensitively on the
parametrization of the model. We present two schemes of parametrization
of the model where within the first one a first order phase transition
from a phase with broken chiral symmetry to a color superconducting
phase
for temperatures below the triple point at T_t= 55 MeV occurs whereas
for the second one a second order phase transition for temperatures
below T_t = 7 MeV is found. In the latter case, there is also a
coexistence phase of broken chiral symmetry with color
superconductivity, which is a new finding within this class of models.
Possible consequences for the phenomenology of the QCD phase transition
at high baryon densities are discussed.
- A. Schmitt, Qun Wang, D. H. Rischke,
nucl-th/0301090. Electromagnetic
Meissner effect in spin-one color superconductors. It is shown that
color-superconducting quark matter, where quarks of the same flavor
form Cooper pairs with spin one, exhibits an electromagnetic Meissner
effect. This is in contrast to spin-zero color superconductors where
Cooper pairs consist of
quarks with different flavors.
- I. Shovkovy, Mei Huang, hep-ph/0302142. Gapless two-flavor color
superconductor. A new, gapless two-flavor color
superconducting phase that appears under conditions of local charge
neutrality and beta-equilibrium is revealed. In this phase, the
symmetry of the ground state is the same as in the conventional
two-flavor color superconductor. In the low-energy spectrum of this
matter, however, there are only two gapped fermionic quasiparticles,
and the rest four quasiparticles are gapless. The origin and the basic
properties of the gapless two-flavor color superconductor are
discussed. This phase is a natural candidate for quark matter in cores
of compact star
- D. K. Hong, T. Lee, Dong-Pil Min,
D. Seo, C. Song, hep-ph/0303181. Higher
order corrections to Color superconducting gaps. We
find a (nonlocal) gauge where the wavefunction renormalization constant
does not get any corrections for all momenta in the hard-dense loop
approximation. In this gauge, we solve the Schwinger-Dyson equations
for the diquark condensate in dense QCD to calculate the Cooper
pair gap. We determine not only the exponent but also the prefactor of
the gap in a gauge independent way. We find that the higher order
corrections increase the gap only by about 1.6 times to the leading
order gap at Coulomb gauge.
- T. Brauner,
J. Hosek, R. Sykora, hep-ph/0303230.
Color superconductor with a color-sextet condensate.We analyze
color superconductivity of one massive flavor quark matter at moderate
baryon density with a spin-zero color-sextet condensate. The most
general Higgs-type ground-state expectation value of the order
parameter implies complete breakdown of the SU(3)xU(1) symmetry.
However, the lowest
order calculations in both the effective bosonic description and a
fermionic NJL-type model favor an enhanced SO(3) symmetry of the ground
state.
- E.Nakano, T.Maruyama, T.Tatsumi, hep-ph/0304223.
Spin Polarization and Color Superconductivity in Quark Matter. A coexistent phase of spin polarization and color
superconductivity in high-density QCD is investigated using a
self-consistent mean-field method at zero temperature. The axial-vector
current stemming from
the Fock exchange term of the one-gluon-exchange interaction has a
central role to cause spin polarization. The magnitude of spin
polarization
is determined by the coupled Schwinger-Dyson equation with a
superconducting gap function. As a significant feature the Fermi
surface is deformed
by the axial-vector self-energy and then rotational symmetry is
spontaneously broken. The gap function is also taken to be anisotropic
in accordance with the deformation. As a result of numerical
calculation, it is found
that spin polarization barely conflicts with color superconductivity,
but
almost coexists with it.
- Ji-Sheng Chen, Jia-Rong Li,
Peng-Fei Zhuang, nucl-th/0209043.
Dispersion relation of rho meson in hot/dense nuclear matter. The dispersion relation of $\rho$ meson in both time-
and space-like regimes in hot and dense nuclear medium is analyzed
and compared with $\sigma $ meson based on the quantum hadrodynamics
model. The pole and screening masses of $\rho $ and $\sigma$ are
discussed.
The behavior of screening mass of $\rho$ is different from that of
$\sigma$ due to different Dirac- and Fermi-sea contributions at finite
temperature and density.
- A. Kryjevski, hep-ph/0305173.
Charge Neutrality of the Color-Flavor Locked Phase from the Low Energy
Effective Theory. We investigate the issue of
charge neutrality of the CFL$K^0$ phase of dense quark matter using the
low energy effective theory of high density QCD. We show that the local
electric and color charge neutrality of the ground state in a
homogeneous color superconducting medium follows from its dynamics. We
also consider the situation of a spatially inhomogeneous medium, such
as may be found in a neutron star core. We find that spatial
inhomogeneity results in the generation of electric fields, and
positrons may be present in the ground state. We estimate the
concentration of positrons in the ground state to be
$n_{e^+}\sim{10^2}{cm}^{-3}$ and consider their influence on the
opacity of the medium with respect to the modified photon.
- A. Vuorinen, hep-ph/0305183.
The pressure of QCD at finite temperatures and chemical potentials. The perturbative expansion of the pressure of hot QCD
is computed here to order g^6ln(g) in the presence of finite quark
chemical potentials. In this process all two- and three-loop
one-particle irreducible vacuum diagrams of the theory are evaluated at
arbitrary T and mu, and these results are then used to analytically
verify the outcome of an old order g^4 calculation of Freedman and
McLerran for the zero-temperature pressure. The results for the
pressure and the different quark number susceptibilities at high T are
compared with recent lattice simulations showing excellent agreement
especially for the chemical potential dependent part of the pressure.
- Y. Nishida, K. Fukushima, T.
Hatsuda, hep-ph/0306066. Thermodynamics
of strong coupling 2-color QCD with chiral and diquark condensates.
2-color QCD (quantum chromodynamics with N_c=2) at finite temperature T
and chemical potential \mu is revisited in the strong coupling limit on
the lattice with staggered fermions. The phase structure in the space
of T, \mu, and the quark mass m is elucidated with the use of the mean
field approximation and the 1/d expansion (d being the number of
spatial dimensions). We put special emphasis on the interplay among the
chiral condensate <\bar{q}q>, the diquark condensate <qq>,
and the quark density <q^{\dagger}q> in the T-\mu-m space. Simple
analytic formulae are also derived without assuming \mu nor m being
small. Qualitative comparisons are made between our results and those
of recent Monte-Carlo simulations in 2-color QCD. Contribution
to the Hidenaga Yamagishi Commemorative volume of Physics Reports,
edited
by E. Witten and I. Zahed
- Hiroaki Abuki, hep-ph/0306074.
Color Superconductivity in Schwinger-Dyson Approach -- Strange Quark
Mass and Color-Flavor Unlocking Line --. Phase
structure and phase transitions in dense QCD are studied
using the Schwinger-Dyson (SD) method in the improved ladder
approximation. We construct the Cornwall-Jackiw-Tomboulis (CJT)
effective potentials at finite temperature for two types of pairing
ansatz, namely the Color-Flavor locking (CFL) state and the two flavor
superconducting (2SC) state. Strong coupling effects at low densities,
such as the off-Fermi surface and antiquarks contribution to the
pairing gap due to the large effective coupling, make the gap, critical
temperature and those ratio deviate from those weak coupling values.
Nevertheless, the ratio of the physical quantity for the CFL and that
for the 2SC does not differ so much from the weak coupling value, as
long as the pairing interaction is taken to be the same for the both
cases. As a consequence, the CFL state always dominates over 2SC state
and the
critical temperatures to quark-gluon plasma (QGP) from both states
coincides
in the chiral limit. The energy gain in the CFL state relative to the
2SC
state gets smaller towards the critical line dividing (mu, T) plane
into
the QGP and CFL phases, and thus small perturbations can remove the
degeneracy
of these critical lines. As one of such perturbations, the effect of
the
strange quark mass m_s on the quark-pairing is examined. In particular,
using
a simple kinematical criterion, we discuss the behaviour of the
``color-flavor unlocking line'' on which the CFL phase turns into the
2SC phase, against the variation of m_s.
- Amruta Mishra, Hiranmaya Mishra, hep-ph/0306105. Chirral symmetry breaking,
color superconductivity and color neutral quark matter: a variational
approach. We investigate the vacuum realignment
for chiral symmetry breaking and color superconductivity at finite
density
in Nambu-Jona-Lasinio model in a variational method. The treatment
allows
us to investigate simultaneous formation of condensates in quark
antiquark
as well as in diquark channels. The methodology involves an explicit
construction
of a variational ground state and minimisation of the thermodynamic
potential.
Color and electric charge neutrality conditions are imposed through
introduction
of appropriate chemical potentials. Color and flavor dependent
condensate
functions are determined through minimisation of the thermodynamic
potential.
The equation of state is calculated. Simultaneous existence of a mass
gap
and superconducting gap is seen in a small window of quark chemical
potential
within the model when charge neutrality conditions are not imposed.
Enforcing
color and electric charge neutrality conditions gives rise to existence
of gapless superconducting modes depending upon the magnitude of the
gap
and the difference of the chemical potentials of the condensing
quarks.
- M. Sadzikowski, hep-ph/0306114. Superconducting phase
transition in the Nambu - Jona-Lasinio model. The
Nambu - Bogoliubov - de Gennes method is applied to the problem of
superconducting QCD. The effective quark-quark interaction is described
within the framework of the Nambu - Jona-Lasinio model. The details of
the phase diagram are given as a function of the strength of the
quark-quark coupling constant $G^{\prime}$. It is find that there is no
superconducting phase transition when one uses the relation between the
coupling constants $G^{\prime}$ and $G$ of the Nambu - Jona-Lasinio
model which follows from the Fierz transformation. However, for other
values of $G^{\prime}$ one can find a rich phase structure containing
both the chiral and the superconducting phase transitions.
- D.N. Voskresensky, nucl-th/0306077. Fluctuations of the
Color-superconducting Order Parameter in Heated and Dense Quark Matter.
Fluctuations of the color superconducting
order parameter in dense quark matter at finite temperatures are
investigated in terms
of the phenomenological Ginzburg - Landau approach. Our estimates show
that fluctuations of the di-quark gap may strongly affect some of
thermodynamic quantities even far below and above the critical
temperature. If the critical temperature of the di-quark phase
transition were rather high one could
expect a manifestation of fluctuations of the di-quark gap in the
course
of heavy ion collisions.
- T. Schaefer, hep-ph/0307074.
Hard Loops, Soft Loops, and High Density Effective Field Theory. We study several issues related to the use of
effective field
theories in QCD at large baryon density. We show that the power
counting is
complicated by the appearance of two scales inside loop integrals. Hard
dense
loops involve the large scale $\mu^2$ and lead to phenomena such as
screening
and damping at the scale $g\mu$. Soft loops only involve small scales
and
lead to superfluidity and non-Fermi liquid behavior at exponentially
small
scales. Four-fermion operators in the effective theory are suppressed
by
powers of $1/\mu$, but they get enhanced by hard loops. As a
consequence their
contribution to the pairing gap is only suppressed by powers of the
coupling
constant, and not powers of $1/\mu$. We determine the coefficients of
four-fermion
operators in the effective theory by matching quark-quark scattering
amplitudes.
Finally, we introduce a perturbative scheme for computing corrections
to
the gap parameter in the superfluid phase.
- T. D . Cohen, hep-ph/0307089.
Functional integrals for QCD at nonzero chemical potential and zero
density. In a Euclidean space functional
integral treatment of the free energy of QCD, a chemical potential
enters only through the
functional determinant of the Dirac operator which for any flavor is
$\dslash
+ m - \mu_f \gamma_0$ (where $\mu_f$ is the chemical potential for the
given
flavor). Any nonzero $\mu$ alters all of the eigenvalues of the Dirac
operator
relative to the $\mu=0$ value, leading to a naive expectation that the
determinant is altered and which thereby alters the free energy.
Phenomenologically,
this does not occur at T=0 for sufficiently small $\mu$, in
contradiction
to this naive expectation. The problem of how to understand this
phenomenological behavior in terms functional integrals is solved for
the case of an isospin chemical through the study of the spectrum of
the operator $\gamma_0 (\dslash + m)$.
- M. Huang, I. Shovkovy, hep-ph/0307273. Gapless color
superconductivity at zero and at finite temperature. We present a detailed study of the recently proposed
gapless color superconductivity in neutral two-flavor quark matter in
beta-equilibrium at zero as well as at finite temperature.
We clarify the nature of the fermionic quasiparticles, and discuss the
physical
properties of this gapless phase of quark matter. The appearance of two
"secondary"
spin-1 condensates in the gapless ground state is pointed out. The
gluon
screening properties are also discussed. It is found that finite
temperature
properties of the gapless color superconductor are rather unusual. One
of
the most striking results is that the ratio of the critical temperature
to
the gap at zero temperature is not a universal number. Moreover, this
ratio
could become arbitrarily large at some values of the coupling constant.
In
addition, the value of the gap parameter is not a monotonic function of
temperature,
although the phase transition is a second order phase transition. In an
extreme
case, in fact, a nonzero finite temperature gap can appear even if its
zero
temperature value is vanishing.
- A.D. Jackson, F. Sannino, hep-ph/0308182. Duality in the Color
Flavor Locked Spectrum.
We analyze the spectrum of the massive states for the color flavor
locked
phase (CFL) of QCD. We show that the vector mesons have a mass of the
order of
the color superconductive gap $\Delta$. We also see that the
excitations
associated with the solitonic sector of the CFL low energy theory have
a mass
proportional to $F^2_{\pi}/\Delta$ and hence are expected to play no
role for
the physics of the CFL phase for large chemical potential. Another
interesting
point is that the product of the soliton mass and the vector meson mass
is
independent of the gap. We interpret this behavior as a form of
electromagnetic
duality in the sense of Montonen and Olive. Our approach for
determining the
properties of the massive states is non-perturbative in nature and can
be
applied to any theory with multiple scales.
LOFF papers
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Ovchinnikov. Inhomogeneous state of superconductors. (JETP 20, 762 (1965))
- M. R. Norman, cond-mat/9306051. Existence of the LOFF
State in Superconducting UPd_2Al_3. In a recent Letter, Gloos et al
have suggested that the heavy fermion superconductor, UPd_2Al_3, has a
transition in magnetic field from
the normal state to an inhomogeneous superconducting state, known as
the LOFF state, followed at lower fields by a first order phase
transition to the usual flux lattice state.
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Larkin-Ovchinnikov-Fulde-Ferrell state in quasi-one-dimensional
superconductors. The properties of a
quasi-one-dimensional (quasi-1D) superconductor with {\it an open Fermi
surface} are expected to be unusual in a magnetic field. On the one
hand, the quasi-1D structure of the Fermi surface strongly favors the
formation of a non-uniform state Larkin-Ovchinnikov-Fulde-Ferrell
(LOFF) state) in the presence of a magnetic field
acting on the electron spins.
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Kachkachi, cond-mat/9611153. Generalized
Ginzburg-Landau theory for non-uniform FFLO superconductors. We derive a generalized Ginzburg-Landau (GL)
functional near the tricritical point in the (T,H)-phase diagram for
the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state, in
1,2, and 3 dimensions. (Phys. Lett. A 225 (1997) 341-348)
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state in two-dimensional superconductors. Nonuniform
superconducting state due to strong
spin magnetism is studied in two-dimensional type-II superconductors
near the second order phase transition line between the normal
and the superconducting states. The optimum spatial structure of the
orderparameter is examined in systems with cylindrical symmetric Fermi
surfaces. It is found that states with two-dimensional structures have
lower free energies than the traditional one-dimensional solutions, at
low temperatures and high magnetic fields.
- A. Sedrakian and U.
Lombardo, nucl-th/9907076. Thermodynamics
of n-p condensate in asymmetric nuclear matter. We study the neutron-proton pairing in nuclear matter
as a function of isospin asymmetry at finite temperatures and the
saturation density using realistic nuclear
forces and Brueckner-renormalized single particle spectra.
(Phys. Rev. Lett. 84, 602 (2000))
- U. Klein, D. Rainer
and H. Shimahara, cond-mat/9909124. Interplay of Fulde-Ferrell-Larkin-Ovchinnikov and
Vortex states in two-dimensional Superconductors. Clean superconductors with weakly coupled conducting
planes have been suggested as promising candidates for observing the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We consider here a
layered superconductor in a
magnetic field of arbitrary orientation with respect to the conducting
plane. In this case there is competition of spin-pair-breaking and
orbital-pair-breaking effects.
- P. F. Bedaque, hep-ph/9910247. Color Superconductivity in
Asymmetric Matter. The influence of
different chemical potential for different flavors on color
superconductivity is analyzed. It is found that there is a first order
transition as the asymmetry grows. This transition proceeds through the
formation of bubbles of
low density, flavor asymmetric normal phase inside a high density,
superconducting phase with a gap {\it larger} than the one
found in the symmetric case. (Nucl.Phys. A697 (2002) 569-577)
- Kun Yang and D. F.
Agterberg, cond-mat/9912364. Josephson Effect in Fulde-Ferrell-Larkin-Ovchinnikov
Superconductors. Due to the difference in
the momenta of the superconducting order parameters, the Josephson
current in a Josephson junction between a
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor and a
conventional BCS superconductor is suppressed. (Phys. Rev. Lett. 84,
4970 (2000))
- S. Manalo,and U.
Klein, cond-mat/0006327. Has the FFLO
state been observed in the organic superconductor? We compare the theoretical anisotropic upper critical
field $H_{C}(\Theta,T)$ of a quasi-two-dimensional d-wave
superconductor
with recent $H_{c2}$ data for the layered organic superconductor
$\kappa-(BEDT-TTF)_2Cu(NCS)_2$. We find agreement both with regard to
the angular and the temperature dependence of $H_{C}$. This supports
the suggestion that the Fulde-Ferrell-Larkin-Ovchinnikov state (FFLO
state) exists in this material for exactly plane-parallel orientation
of the magnetic field.
- D. F. Agterberg and
Kun Yang, cond-mat/0006344. Ginzburg-Landau theory of
Fulde-Ferrell-Larkin-Ovchinnikov states in unconventional singlet
superconductors with impurities. We
derive the Ginzburg-Landau theory of unconventional singlet
superconductors in the presence of a Zeeman field and impurities, in
order to examine the resulting Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
phases.(J. Phys.: Condens. Matter 13, 9259 (2001))
- R. Combescot, cond-mat/0007191.
BCS superfluidity in ultracold gases with unequal atomic populations. We consider the existence of a BCS superfluid phase in
$^{6}$Li due to the pairing of two hyperfine states with unequal number
of atoms.(Europhys. Lett. {\bf 55}, 150 (2001))
- A. Sedrakian, nucl-th/0008052. Spatially inhomogeneous
condensate in asymmetric nuclear matter.
We study the isospin singlet pairing in asymmetric nuclear matter with
nonzero total momentum of the condensate Cooper pairs. The
quasiparticle excitation spectrum is fourfold split compared to the
usual BCS spectrum of the symmetric, homogeneous matter. (Phys.Rev. C63
(2001) 025801)
- M. G. Alford, J. A.
Bowers and K. Rajagopal, hep-ph/0008208. Crystalline color superconductivity. In the case of
pairing between species of quarks with differing
chemical potentials, for suitable values of the differences between
chemical potentials, Cooper pairs with nonzero total momentum are
favored, as was first realized by Larkin, Ovchinnikov, Fulde and
Ferrell (LOFF). Condensates of this
sort spontaneously break translational and rotational invariance,
leading to gaps which vary periodically in a crystalline pattern.
(Phys.Rev.D63:074016,2001)
- J. A. Bowers, J.
Kundu, K. Rajagopal and E. Shuster, hep-ph/0101067.
A Diagrammatic approach to
crystalline color superconductivity. Derivation
of the gap equation through the Schwinger-Dyson equation and
Nambu-Gorkov propagator. (Phys.Rev. D64 (2001) 014024)
- R. Casalbuoni, R.
Gatto, M. Mannarelli and G. Nardulli, hep-ph/0101326,
Effective Field Theory for the Crystalline Colour Superconductive Phase
of QCD. Effective lagrangian for the LOFF
phase. Anisotropic dispersion relation
for the phonon. (Phys.Lett. B511 (2001) 218-228)
- M. Holland, S. J. J.
M. F. Kokkelmans, M. L. Chiafolo and R. Walser, cond-mat/0103479. Resonance superfluidity
in a quantum degenerate Fermi gas. We
consider the superfluid phase transition that arises when a Feshbach
resonance pairing occurs in a dilute Fermi gas. We apply our theory to
consider a specific resonance in potassium-40, and find that for
achievable experimental conditions, the transition to a superfluid
phase is possible at the high critical temperature of about 0.5 T_F.
(Phys. Rev. Lett. 87, 120406 (2001))
- A. K. Leibovich, K.
Rajagopal and E. Shuster, hep-ph/0104073. Opening the crystalline color superconductivity
window. The window for the LOFF phase is
re-evaluated using one-gluon exchange interaction. (Phys.Rev. D64
(2001) 094005)
- J. Singleton, J.A.
Symington, M.-S. Nam, A. Ardavan, M. Kurmoo and P. Day, cond-mat/0105335. Observation of the Fulde-Ferrell-Larkin-Ovchinnikov
state in the quasi-two-dimensional organic superconductor
$\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$. Single
crystals of the layered organic type II
superconductor, $\kappa$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$, have been
studied in magnetic fields of up to 33 T and at temperatures between
0.5 K and 11 K using a compact differential susceptometer. When the
magnetic field lies precisely in the quasi-two-dimensional planes of
the material, there is strong evidence for a phase transition from the
superconducting mixed state into a Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) state, manisfested as a change in the rigidity of the vortex
system.(J. Phys. Condens. Matter Volume
12 L641 (2000))
- D.K. Hong and Y. J.
Sohn, hep-ph/0107003. Critical couplings in Crystalline Color
superconductivity. Solving the
Schwinger-Dyson equations, we analyze the pairing of quarks in
asymmetric quark matter where quarks have different chemical
potentials. We show that in the asymmetric quark matter a
crystalline color-superconducting gap opens when the quark coupling is
stronger than a critical value.
- R. Casalbuoni, R.
Gatto, M. Mannarelli and G. Nardulli, hep-ph/0107024,
Effective gluon interactions in
the Colour Superconductive Phase of two flavor
QCD. Evaluation of the two- three- and
four- point functions of the gluons in the 2SC phase. (Phys.Lett. B524
(2002) 144-152)
- F. Schreck, L.
Khaykovich, K. L. Corwin, G. Ferrari, T. Bourdel, J. Cubizolles and C.
Salomon, cond-mat/0107442. A quasi-pure Bose-Einstein condensate immersed in
a Fermi sea. We report the observation of
co-existing Bose-Einstein condensate and Fermi gas in a magnetic trap.
With a very small fraction of thermal atoms, the 7Li condensate is
quasi-pure and in thermal contact with a 6Li Fermi gas. The lowest
common temperature is 0.28 muK = 0.2(1) T_C =
0.2(1) T_F where T_C is the BEC critical temperature and T_F the Fermi
temperature. (Phys. Rev. Lett. {\bf 87}, 080403
(2001))
- K. Rajagopal, hep-ph/0109135.
Crystalline Color Superconductivity. We
give an
introduction crystalline color superconductivity, arguing that it is
likely to occur wherever quark matter in which color-flavor locking
does not occur is found.(AIP Conf.Proc. 602 (2001) 339-351;
Nucl.Phys. A702). (2002)
25-38)
- J. Singleton, N.
Harrison, C.H. Mielke, J. Schlueter and A.M. Kini, cond-mat/0109363.
A statistical model for the
intrinsically broad superconducting to normal transition in
quasi-two-dimensional crystalline organic metals. Although quasi-two-dimensional organic superconductors
such as $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ seem to be very clean
systems, with apparent quasiparticle mean-free paths of several
thousand \AA, the superconducting transition
is intrinsically broad (e.g $\sim 1$ K wide for $T_c \approx 10$ K).
We propose that this
is due to the extreme anisotropy of these materials, which greatly
exacerbates the statistical effects of spatial variations in the
potential experienced by the quasiparticles.
- K. Ohwa, hep-ph/0111074. Crystalline ground state in
chiral Gross-Neveu and Cooper pair models
at finite densities. We study the
possibility of spatially non-uniform ground state in (1+1)-dimensional
models with quartic fermi interactions at finite fermion densities by
introducing chemical potential \mu. We examine the chiral Gross-Neveu
model and the Cooper pair model as toy models of the chiral symmetry
breaking and the difermion pair condensates which are presumed to exist
in QCD. (Phys.Rev. D65 (2002)
085040)
- G. Nardulli, hep-ph/0111178, Effective theory for QCD in the LOFF phase. Review of the LOFF phase (Copenhagen 2001, eConf
C010815:104-109, 2002)
- D.K. Hong, hep-ph/0112028.
Crystalline Color Superconductivity in Dense Matter. In this talk I discuss a recently proposed color
superconducting phase of asymmetric quark matter where the up and down
quark have different chemical potential, being in chemical equilibrium
with electrons. Using Schwinger-Dyson equations derived from an
effective theory of low-energy quasiparticles, a
critical coupling for LOFF phase is estimated
for both the case
of an effective four Fermi interaction and Landau-damped
one gluon exchange. (eConf C010815 (2002) 116-124)
- T.D. Fugleberg, hep-ph/0112162. Color Superconductivity with
Non-Degenerate Quarks. In
dense quark matter, the response of the color superconducting gaps to a
small variation, $\delta\mu$, in the chemical potential of the strange
quark was studied.
- J. Kundu and, K.
Rajagopal, hep-ph/0112206.Mass induced
crystalline color superconductivity. The
LOFF phase is obtained by allowing a quark with non zero mass.
(Phys.Rev.D65:094022,2002)
- A. M. Dyugaev, I.D.
Vagner and P. Wyder, cond-mat/0112286. Nuclear ferromagnetism induced
Fulde-Ferell-Larkin-Ovchinnikov state. We
present a theoretical study of the influence of the nuclear
ferromagnetism on superconductivity in the presence of the
electron-nuclear spin interaction. It is demonstrated that in some
metals, e.g. Rh, W, the BCS condensate imbedded in a matrix of
ferromagneticaly ordered nuclear spins should manifest the FFLO
(Fulde-Ferel-Larkin-Ovchinniov) state.
- Prashanth Jaikumar,
Ralf Rapp, Ismail Zahed, hep-ph/0112308.
Photon and dilepton emission rates from high density quark matter. We compute the rates of real and virtual photon
(dilepton) emission from
dense QCD matter in the color-flavor locked (CFL) phase, focusing on
results at moderate densities (3-5 times the nuclear
saturation density) and temperatures $T\simeq80$ MeV. (
Phys.Rev. C65 (2002) 055205)
- R. Casalbuoni, R.
Gatto, M. Mannarelli and G. Nardulli, hep-ph/0201059,
Anisotropy Parameters for the
Effective Description of Crystalline Color Superconductors. The parameters of the effective lagrangian describing
the LOFF phase are evaluated. (Phys.Rev. D66 (2002) 014006)
- H. Won and K. Maki, cond-mat/0201124.
Fulde-Ferrell-Larkin-Ovchinnikov state in d-wave superconductors. The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can
be found in layered d-wave superconductors such as high $T_c$ cuprates
and $\kappa$-(ET)$_2$ salts in a planar magnetic field.
- A. Serquis, X. Y.
Liao, Y. T. Zhu, J. Y. Coulter, J. Y. Huang, J. O. Willis, D. E.
Peterson, F. M. Mueller, N. O. Moreno, J. D. Thompson, S. S. Indrakanti
andV. F. Nesterenko, cond-mat/0201486.
The influence of microstructures and crystalline defects on the
superconductivity of MgB2. This work
studies the influence of microstructures and crystalline defects on the
superconductivity of
MgB2, with the objective to improve its flux pinning. (Journal of
Applied Physics, Vol. 92, No. 1, pp. 351--356, 1 July
2002)
- I. Giannakis, J. T.
Liu and Hai-cang Ren, hep-ph/0202138.
Angular Momentum Mixing in Crystalline Color Superconductivity. In crystalline color superconductivity, quark pairs
form at non-zero total momentum. This crystalline order potentially
enlarges the domain
of color superconductivity in cold dense quark matter. We present a
perturbative calculation of the parameters governing the crystalline
phase and show that this is indeed the case.
Nevertheless, the enhancement is modest, and to lowest order is
independent of the strength of the color interaction.
- R. Combescot and C.
Mora, cond-mat/0203031. Transition to Fulde-Ferrel-Larkin-Ovchinnikov phases
near the tricritical point : an analytical study. We explore analytically the nature of the transition
to the Fulde-Ferrel-Larkin-Ovchinnikov superfluid phases in the
vicinity of the tricritical point, where
these phases begin to appear. We make use of an expansion of the free
energy up to an overall sixth order, both in order parameter amplitude
and in wavevector.
- H. Shimahara, cond-mat/0203109.
Fulde-Ferrell-Larkin-Ovchinnikov State and Field-Induced
Superconductivity in an Organic Superconductor.
An experimental phase diagram of the
field-induced superconductivity in the lambda-(BETS)_2FeCl_4 compound
is theoretically reproduced by a combination of the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state and the Jaccarino-Peter
mechanism.
- P. Goddard, S.W.
Tozer, J. Singleton, A. Ardavan, A. Abate and M. Kurmoo, cond-mat/0203357. Superconductivity,
incoherence and Anderson localization in the crystalline organic
conductor. The conducting properties of
the pressure-induced, layered organic superconductor
(BEDT-TTF)_3Cl_2.2H_20 have been studied at 13.5 and 14.0 kbar using
low temperatures, high magnetic fields and two-axis rotation.
- J. A. Bowers and K.
Rajagopal, hep-ph/0204079.The
crystallography of color superconductivity. Calculation of the crystalline structure minimizing
the free energy in the LOFF phase
- V. Barzykin and L.P.
Gor'kov, cond-mat/0204480. Inhomogeneous stripe (LOFF) phase revisited for
surface superconductivity. We address 2D surface
superconductivity in high magnetic fields parallel to the
surface. The account for spin-orbit
interaction
at the surface changes properties of inhomogeneous superconducting
Larkin-Ovchinnikob-Fulde-Ferrel state that develops above fields given
by the paramagnetic criterion. Strong spin-orbit significantly broadens
the range of existence of the LOFF phase resulting in appearance, on
the surface,
of periodic superconducting stripes running along the field direction.
- M.Mannarelli, hep-ph/0205098.Effective
description of the LOFF phase of QCD. We present
an effective field theory for the crystalline color superconductivity
phase of QCD. It
is kown that at high density and at low temperature QCD
exhibits a transition to a color superconducting phase
characterized by energy gaps in the fermion spectra. Under specific
circumstances the gap parameter has a crystalline pattern, breaking
translational and rotational invariance.(Talk at the Giselda Meeting,
Frascati (Roma), 14-18 Jan 2001
- Ken'ichi Takahashi,
Toshiyuki Atsumi, Nariaki Yamamoto, Mingxiang Xu, Hideaki Kitazawa and
Takekazu Ishida, cond-mat/0205010. Superconducting anisotropy and evidence for intrinsic
pinning in single crystalline MgB$_2$. We
examine the superconducting anisotropy $\gamma_c = (m_c /
m_{ab})^{1/2}$ of a metallic high-$T_c$ superconductor MgB$_2$ by
measuring the magnetic torque of a single crystal. The anisotropy
$\gamma_c$ does not depend sensitively on the applied magnetic field at
10 K. We obtain the anisotropy parameter $\gamma_c =
4.31 \pm 0.14$.
- R. Casalbuoni, R.
Gatto and G. Nardulli, hep-ph/0205219, Crystalline Color Superconductivity: Effective
Lagrangian and Phonon Dispersion Law. Effective
lagrangian for the cubic crystalline phase of QCD.
- M. A. Tanatar, T.
Ishiguro, H. Tanaka and H. Kobayashi, cond-mat/0205239.
Fulde-Ferrell-Larkin-Ovchinnikov
state observed via thermal conductivity in quasi-two-dimensional
organic superconductor $\lambda$-(BETS)$_2$GaCl$_4$. The thermal conductivity kappa of the
quasi-two-dimensional (Q2D) organic superconductor lambda-(BETS)_2
GaCl_4 was studied in the magnetic field H applied parallel to the Q2D
plane. The phase diagram determined from this bulk measurement shows
notable dependence on the sample quality.
- M. Angst, R. Puzniak,
A. Wisniewski, J. Roos, H. Keller and J.Karpinski, cond-mat/0206407. Comment on
"Superconducting anisotropy and evidence for intrinsic pinning in
single crystalline (Comment on PRB 66, 012501 (2002) (cond-mat/0205010). In
a recent paper [Phys. Rev. B 66, 012501 (2002)], torque data measured
on a MgB2 single crystal in fields from 10 to 60 kOe at 10 K were
presented. The authors obtained the anisotropy gamma by fitting a
theoretical expression to the data and concluded that the anisotropy is
field independent gamma \approx 4.3. They also reported the observation
of "intrinsic pinning", which they take as experimental evidence for
the occurence of superconductivity in the
boron layers. In this comment, we discuss the range of validity of the
theoretical expression used by the authors and show that the conclusion
of a field independent anisotropy does not hold.
- R. Casalbuoni, E.
Fabiano, R. Gatto, M. Mannarelli and G. Nardulli, hep-ph/0208121.
Phonons and gluons in the
crystalline color superconducting phase of QCD. The High Density Effective Theory formalism is used to
calculate the low energy properties of the phonons and gluons in the
Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of two-flavor QCD.
Calculations are done for the phonons of the cubic crystal and of the
gluons for the cube and for the
single plane wave.
- W.V. Liu and F.
Wilczek, cond-mat/0208052. Interior Gap
Superfluidity. We propose a new state of
matter in which the pairing interactions
carve out a gap within the interior of a large Fermi ball,
while the exterior surface remains gapless. This defines a system which
contains both a superfluid and a normal Fermi liquid
simultaneously, with both gapped and gapless quasiparticle excitations.
This state can be realized at weak coupling. We predict that a cold
mixture of two species of fermionic atoms with different mass will
exhibit this state. For electrons in appropriate solids, it would
define a material that is simultaneously superconducting and metallic.
- M. Houzet, A. Buzdin, L. Bulaevskii, M.
Maley, cond-mat/0205041.
New superconducting phases in field-induced organic superconductor
lambbda-(BETS)2FeCl4. We derive the parallel
upper critical field, Hc2, as a function of the temperature T in
quasi-2D organic compound lambda-(BETS)2FeCl4, accounting for the
formation of the nonuniform LOFF state. To further check the 2D LOFF
model we propose to study the Hc2(T) curve at low T in tilted fields,
where the vortex state is described by the high Landau level functions
characterized by the index n. We predict a cascade of first order
transitions between vortex phases with different n, between
phases with different types of the symmetry at given n and the change
of the superconducting transition from the second order to the first
order as FeCl4 ions are replaced partly by GaCl4 ions.
- E. Gubankova,
W. V. Liu, F. Wilczek, hep-ph/0304016.
Breached pairing superfluidity: Possible realization in QCD. We
propose a wide universality class of gapless superfluids, and analyze a
limit that might be realized in quark matter at intermediate densities.
In the breached pairing color superconducting phase heavy $s$-quarks,
with a small Fermi surface, pair with light $u$ or $d$ quarks. The
groundstate has a superfluid and a normal Fermi component
simultaneously. We expect a second order phase transition, as a
function of increasing density,
from the breached pairing phase to the conventional color-flavor locked
(CFL) phase.
- C. Mora, R. Combescot, cond-mat/03065765. Nature of the
Fulde-Ferrell-Larkin-Ovchinnikov
phases at low temperature in 2 dimensions. We
investigate,
mostly analytically, the nature of the Fulde-Ferrell-
Larkin-Ovchinnikov
superfluid phases for an isotropic two-dimensional superconductor,
which
is relevant for the experimental observation of these phases. We show
that
there is, in the low temperature range, a cascade of transitions toward
order
parameters with ever increasing complexity.