[Show abstract][Hide abstract] ABSTRACT: An increasing number of model results suggests that chiral symmetry is broken
inhomogeneously in a certain window at intermediate densities in the QCD phase
diagram. This could have significant effects on the properties of compact
stars, possibly leading to new astrophysical signatures. In this contribution
we discuss this idea by reviewing recent results on inhomogeneous chiral
symmetry breaking under an astrophysics-oriented perspective. After introducing
two commonly studied spatial modulations of the chiral condensate, the chiral
density wave and the real kink crystal, we focus on their properties and their
effect on the equation of state of quark matter. We also describe how these
crystalline phases are affected by different elements which are required for a
realistic description of a compact star, such as charge neutrality, the
presence of magnetic fields, vector interactions and the interplay with
color-superconductivity. Finally, we discuss possible signatures of
inhomogeneous chiral symmetry breaking in the core of compact stars,
considering the cases of mass-radius relations and neutrino emissivity
explicitly.
[Show abstract][Hide abstract] ABSTRACT: We investigate the effects of isospin asymmetry on inhomogeneous chiral
symmetry breaking phases within the two-flavor NJL model. After introducing a
plane-wave ansatz for each quark-flavor condensate, we find that, as long as
their periodicities are enforced to be equal, a non-zero isospin chemical
potential shrinks the size of the inhomogeneous phase. The asymmetry reached in
charge neutral matter is nevertheless not excessively large, so that an
inhomogeneous window is still present in the phase diagram. Lifting the
constraint of equal periodicities alters the picture significantly, as the
inhomogeneous phase survives in a much larger region of the phase diagram.
[Show abstract][Hide abstract] ABSTRACT: We study the beahviour of the dual quark condensate $\Sigma_1$ in the
Nambu-Jona-Lasinio (NJL) model and its nonlocal variant. In quantum
chromodynamics $\Sigma_1$ can be realted to the breaking of the center symmetry
and is therefore an (approximate) order parameter of confinement. The
deconfinement transition is then signaled by a strong rise of $\Sigma_1$ as a
function of temperature. However, a similar behaviour is also seen in the NJL
model, which is known to have no confinement. Indeed, it was shown that in this
model the rise of $\Sigma_1$ is triggered by the chiral phase transition. In
order to shed more light on this issue, we calculate $\Sigma_1$ for several
variants of the NJL model, some of which have been suggested to be confining.
Switching between "confining" and "non-confining" models and parametrizations
we find no qualitative difference in the behaviour of $\Sigma_1$, namely, it
always rises in the region of the chiral phase transition. We conclude that
without having established a relation to the center symmetry in a given model,
$\Sigma_1$ should not blindly be regarded as an order parameter of confinement.
[Show abstract][Hide abstract] ABSTRACT: A quark-meson-diquark plasma is considered within the PNJL model for
dynamical chiral symmetry breaking and restoration in quark matter. Based on a
generalized Beth-Uhlenbeck approach to mesons and diquarks we present the
thermodynamics of this system including the Mott dissociation of mesons and
diquarks at finite temperature. A striking result is the suppression of the
diquark abundance below the chiral restoration temperature by the coupling to
the Polyakov loop, because of their color degree of freedom. This is understood
in close analogy to the suppression of quark distributions by the same
mechanism. Mesons as color singlets are unaffected by the Polyakov-loop
suppression. At temperatures above the chiral restoration mesons and diquarks
are both suppressed due to the Mott effect, whereby the positive resonance
contribution to the pressure is largely compensated by the negative scattering
contribution in accordance with the Levinson theorem.
Physical Review D 12/2014; 91(12). DOI:10.1103/PhysRevD.91.125040 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The chiral condensate, which is constant in vacuum, may become spatially
modulated at moderately high densities and temperatures, where in the
traditional picture of the QCD phase diagram a first-order chiral phase
transition occurs. We review the current status of this idea, which originally
dates back to Migdal's pion condensation, but recently received new momentum by
studies on the nature of the chiral critical point and by the conjecture of a
quarkyonic-matter phase. We discuss how these nonuniform phases emerge in
generalized Ginzburg-Landau analyses as well as in specific calculations, both
within effective models and in Dyson-Schwinger or large-$N_c$ approaches to
QCD. Questions about the most favored shape of the modulations and in
particular its dimension, and about the effects of nonzero isospin chemical
potential, strange quarks, color superconductivity, and external magnetic
fields, will be adressed as well.
Progress in Particle and Nuclear Physics 06/2014; 81. DOI:10.1016/j.ppnp.2014.11.001 · 3.66 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Inhomogeneous chiral-symmetry breaking phases at non-vanishing chemical
potential and temperature are studied within a two-flavor quark-meson model in
the chiral limit. The analysis is performed beyond the standard mean-field
approximation by taking into account the Dirac-sea contributions of the quarks.
Compared with the case where the Dirac sea is neglected, we find that the
inhomogeneous phase shrinks, but in general does not disappear. It is shown
within a Ginzburg-Landau analysis that the Lifshitz point of the inhomogeneous
phase coincides with the tricritical point if the ratio between sigma-meson and
constituent quark mass in vacuum is chosen to be $m_\sigma/M = 2$,
corresponding to the fixed mass ratio in the Nambu--Jona-Lasinio model. In the
present model, however, this ratio can be varied, offering the possibility to
separate the two points. This is confirmed by our numerical calculations, which
demonstrate a strong sensitivity of the size of the inhomogeneous phase on
$m_\sigma$. Finally, we uncover a general instability of the model with respect
to large wave numbers of the chiral modulations, which calls for further
improvements beyond the present approximation.
Physical Review D 03/2014; 90(1). DOI:10.1103/PhysRevD.90.014033 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The recent measurement of two solar mass pulsars has initiated an intense
discussion on its impact on our understanding of the high-density matter in the
cores of neutron stars. A task force meeting was held from October 7-10, 2013
at the Frankfurt Institute for Advanced Studies to address the presence of
quark matter in these massive stars. During this meeting, the recent
oservational astrophysical data and heavy-ion data was reviewed. The
possibility of pure quark stars, hybrid stars and the nature of the QCD phase
transition were discussed and their observational signals delineated.
Journal of Physics G Nuclear and Particle Physics 02/2014; 41(12). DOI:10.1088/0954-3899/41/12/123001 · 2.78 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The formation of inhomogeneous chiral condensates in QCD matter at nonzero
density and temperature is investigated for the first time with Dyson-Schwinger
equations. We consider two massless quark flavors in a so-called chiral density
wave, where scalar and pseudoscalar quark condensates vary sinusoidally along
one spatial dimension. We find that the inhomogeneous region covers the major
part of the spinodal region of the first-order phase transition which is
present when the analysis is restricted to homogeneous phases. The triple point
where the inhomogeneous phase meets the homogeneous phases with broken and
restored chiral symmetry, respectively, coincides, within numerical accuracy,
with the critical point of the homogeneous calculation. At zero temperature,
the inhomogeneous phase seems to extend to arbitrarily high chemical
potentials, as long as pairing effects are not taken into account.
Physics Letters B 08/2013; 727(1-3). DOI:10.1016/j.physletb.2013.10.050 · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An important first step in the program of hadronization of chiral quark
models is the bosonization in meson and diquark channels. This procedure is
presented at finite temperatures and chemical potentials for the SU(2) flavor
case of the NJL model with special emphasis on the mixing between scalar meson
and scalar diquark modes which occurs in the 2SC color superconducting phase.
The thermodynamic potential is given the Beth-Uhlenbeck form which allows a
detailed discussion of bound state dissociation in hot, dense matter (Mott
effect) in terms of the in-medium scattering phase shift of two-particle
correlations. It is shown for the case without meson-diquark mixing that the
phase shift can be separated into a continuum and a resonance part. In the
latter, the Mott transition manifests itself by a change of the phase shift by
\pi\ in accordance with the Levinson theorem, when a bound state transforms to
a resonance in the scattering continuum. The question of a selfconsistent
quasiparticle picture is discussed as a preparation for the second step in the
hadronization program: the introduction of baryons and "integrating out" the
diquark fields.
Annals of Physics 05/2013; 348. DOI:10.1016/j.aop.2014.06.002 · 2.10 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate the phases of dense QCD matter at finite temperature with
Dyson-Schwinger equations for the quark propagator for N_f=2+1 flavors. For the
gluon propagator we take a fit to quenched lattice data and add quark-loop
effects perturbatively in a hard-thermal-loop--hard-dense-loop approximation.
We consider 2SC and CFL-like pairing with chiral up and down quarks and massive
strange quarks and present results for the condensates and the phase diagram.
We find a dominant CFL phase at chemical potentials larger than 500-600 MeV. At
lower values of the chemical potential we find a 2SC phase, which also exists
in a small band at higher temperatures for larger chemical potentials. With
values of 20-30 MeV, the critical temperatures to the normal phase turn out to
be quite small.
European Physical Journal A 03/2013; 49(8). DOI:10.1140/epja/i2013-13096-5 · 2.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The existence and the properties of self-bound quark matter in the NJL model
at zero temperature are investigated in mean-field approximation, focusing on
inhomogeneous structures with one-dimensional spatial modulations. It is found
that the most stable homogeneous solutions which have previously been
interpreted as schematic quark droplets are unstable against formation of a
one-dimensional soliton-antisoliton lattice. The solitons repel each other, so
that the minimal energy per quark is realized in the single-soliton limit. The
properties of the solitons and their interactions are discussed in detail, and
the effect of vector interactions is estimated. The results may be relevant for
the dynamics of expanding quark matter.
[Show abstract][Hide abstract] ABSTRACT: We investigate the phase structure of the Nambu-Jona-Lasinio model at zero temperature, allowing for a two-dimensional spatial dependence of the chiral condensate. Applying the mean-field approximation, we consider various periodic structures with rectangular and hexagonal geometries, and minimize the corresponding free energy. We find that these two-dimensional chiral crystals are favored over homogeneous phases in a certain window in the region where the phase transition would take place when the analysis was restricted to homogeneous condensates. It turns out, however, that in this regime they are disfavored against a phase with a one-dimensional modulation of the chiral condensate. On the other hand, we find that square and hexagonal lattices eventually get favored at higher chemical potentials. Although stretching the limits of the model to some extent, this would support predictions from quarkyonic-matter studies.
[Show abstract][Hide abstract] ABSTRACT: We study the Gaussian fluctuations of the two-flavor, meson-diquark bosonized NJL model for two and three colors at the color superconducting phase transition. The analysis is based on analytical properties of the polarization matrix. Pionic fluctuations are shown to be stabilised in the 2SC phase compared to the two-color result where they are right on threshold.
[Show abstract][Hide abstract] ABSTRACT: We show that the CJT thermodynamic potential of dynamical quark models with a
quark propagator represented by complex conjugate mass poles inevitably
exhibits thermodynamic instabilities. We find that the minimal coupling of the
quark sector to a Polyakov loop potential can strongly suppress but not
completely remove such instabilities. This general effect is explicitly
demonstrated in the framework of a covariant, chirally symmetric, effective
quark model.
[Show abstract][Hide abstract] ABSTRACT: A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/N{sub c} expansion scheme. It is found that the 1/N{sub c} corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/N{sub c} expansion breaks down and a nonperturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition region.
[Show abstract][Hide abstract] ABSTRACT: We investigate inhomogeneous chiral symmetry breaking phases in the phase diagram of the two-flavor Nambu-Jona-Lasinio model, concentrating on phases with one-dimensional modulations. It is found that the first-order transition line in the phase diagram of homogeneous phases gets completely covered by an inhomogeneous phase which is bordered by second-order transition lines. The inhomogeneous phase turns out to be remarkably stable when vector interactions are included.
[Show abstract][Hide abstract] ABSTRACT: The properties of strongly interacting matter are probed in ultra-relativistic heavy-ion collisions. In the context of measurements of the elliptic flow at RHIC and the LHC the shear viscosity is of particular interest. In this presentation we discuss recent results for η/sη/s in hadronic matter at vanishing baryo-chemical potential within kinetic theory. Using the Nambu Jona-Lasinio model, special attention is paid to effects arising from the restoration of spontaneously broken chiral symmetry with increasing temperature.
Progress in Particle and Nuclear Physics 04/2012; 67(2):348–352. DOI:10.1016/j.ppnp.2011.12.042 · 3.66 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate the phase structure of the Nambu--Jona-Lasinio model at zero
temperature, allowing for a two-dimensional spatial dependence of the chiral
condensate. Applying the mean-field approximation, we consider various periodic
structures with rectangular and hexagonal geometries, and minimize the
corresponding free energy. We find that these two-dimensional chiral crystals
are favored over homogeneous phases in a certain window in the region where the
phase transition would take place when the analysis was restricted to
homogeneous condensates. It turns out, however, that in this regime they are
disfavored against a phase with a one-dimensional modulation of the chiral
condensate. On the other hand, we find that square and hexagonal lattices
eventually get favored at higher chemical potentials. Although stretching the
limits of the model to some extent, this would support predictions from
quarkyonic-matter studies.
[Show abstract][Hide abstract] ABSTRACT: We investigate the shear viscosity of a pion gas in relativistic kinetic
theory, using the Nambu-Jona-Lasinio model to construct the pion mass and the
pi-pi interaction at finite temperature. Whereas at low temperatures the
scattering properties and, hence, the viscosity are in agreement with
lowest-order chiral perturbation theory, we find strong medium modifications in
the crossover region. Here the system is strongly coupled and the scattering
lengths diverge, similarly as for ultra-cold Fermi gases at a Feshbach
resonance. As a consequence, the ratio eta/s is found to be strongly reduced as
compared to calculations without medium-modified masses and scattering
amplitudes. However, the quantitative results are very sensitive to the details
of the applied approximations.
European Physical Journal A 02/2012; 48(10). DOI:10.1140/epja/i2012-12142-2 · 2.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The properties of strong-interaction matter are probed in ultra-relativistic
heavy-ion collisions. In the context of measurements of the elliptic flow at
RHIC and the LHC the shear viscosity is of particular interest. In this
presentation we discuss recent results for eta/s in hadronic matter at
vanishing baryo-chemical potential within kinetic theory. Using the
Nambu-Jona-Lasinio model, special attention is paid to effects arising from the
restoration of spontaneously broken chiral symmetry with increasing
temperature.