Inspired by recent work on inhomogeneous chiral condensation in cold, dense quark matter within models featuring quark degrees of freedom, we investigate the chiral density-wave solution in nuclear matter at zero temperature and nonvanishing baryon number density in the framework of the so-called extended linear sigma model (eLSM). The eLSM is an effective model for the strong interaction based on the global chiral symmetry of quantum chromodynamics (QCD). It contains scalar, pseudoscalar, vector, and axial-vector mesons as well as baryons. In the latter sector, the nucleon and its chiral partner are introduced as parity doublets in the mirror assignment. The eLSM simultaneously provides a good description of hadrons in vacuum as well as nuclear matter ground-state properties. We find that an inhomogeneous phase in the form of a chiral density wave is realized, but only for densities larger than 2.4ρ0, where ρ0 is the nuclear matter ground-state density.PACS numbers: 12.39. Fe,11.10.Wx,11.30.Qc,21.65.Cd Introduction: The spontaneous breaking of chiral symmetry in the QCD vacuum is a nonperturbative phenomenon which has to be reflected in low-energy hadronic theories, see e.g. Refs. [1][2][3]. The order parameter of chiral symmetry breaking is the chiral condensate, denoted as qq ∼ σ , which contributes to hadronic masses and is responsible for the mass splitting of so-called chiral partners, i.e., hadrons with the same quantum numbers except for parity and G-parity.At sufficiently large temperature and density, it is expected that the spontaneously broken chiral symmetry is (at least partially) restored. Lattice-QCD calculations [4,5] show that, for values of the quark masses realized in nature, this so-called chiral transition is cross-over along the temperature axis of the QCD phase diagram. Along the density axis, lattice-QCD calculations are not yet available (for realistic quark masses), but phenomenological models [6,7] indicate that chiral symmetry restoration may occur through a first-order phase transition.An interesting possibility is that the effective potential is minimized by an order parameter which varies as a function of spatial coordinate. Such inhomogeneous phases were already suggested in the pioneering works of Ref. [8][9][10][11][12][13][14][15][16][17][18][19]. In particular, the chiral condensate may assume the form of the so-called chiral-density wave where not only the chiral condensate σ but also the expectation value of the neutral pion field is nonvanishing, π 3 = 0. However, the problem of the aforementioned approaches was that, without nucleon-nucleon tensor forces, inhomogeneous chiral condensation took place already in the nuclear matter ground state, in contradiction to experimental findings.More recently, inhomogeneous phases were studied in the framework of the (1+1)-dimensional Gross-Niveau model [21,22], where it was indeed found that a spatially varying order parameter minimizes the effective potential at high density. In Ref. [23,24], the authors coined the phrase "quark...

We use a numerical method, the finite-mode approach, to study inhomogeneous condensation in effective models for QCD in a general framework. Former limitations of considering a specific ansatz for the spatial dependence of the condensate are overcome. Different error sources are analyzed and strategies to minimize or eliminate them are outlined. The analytically known results for 1 + 1 dimensional models (such as the Gross-Neveu model and extensions of it) are correctly reproduced using the finite-mode approach. Moreover, the NJL model in 3 + 1 dimensions is investigated and its phase diagram is determined with particular focus on the inhomogeneous phase at high density.

We investigate the implications of a tetraquark field on chiral symmetry restoration at nonzero temperature. In order for the chiral phase transition to be cross-over, as shown by lattice QCD studies, a strong mixing between scalar quarkonium and tetraquark fields is required. This leads to a light ($\sim0.4$ GeV), predominantly tetraquark state, and a heavy ($\sim1.2$ GeV), predominantly quarkonium state in the vacuum, in accordance with recently advocated interpretations of spectroscopy data. The mixing even increases with temperature and leads to an interchange of the roles of the originally heavy, predominantly quarkonium state and the originally light, predominantly tetraquark state. Then, as expected, the scalar quarkonium is a light state when becoming degenerate in mass with the pion as chiral symmetry is restored at nonzero temperature.Comment: 4 pages, 2 figure

We study the large-Nc behavior of the critical temperature Tc for chiral symmetry restoration in the framework of the Nambu-Jona-Lasinio (NJL) model and the linear σ-model. While in the NJL case Tc scales as N 0 c and is, as expected, of the same order as ΛQCD (just as the deconfinement phase transition), in the σ-model the scaling behavior reads Tc ∝ N 1/2 c . We investigate the origin of the different scaling behavior and present two improvements of the σ-model: (i) a simple, phenomenologically motivated temperature dependence of the parameters and (ii) the coupling to the Polyakov loop. Both approaches lead to the scaling Tc ∝ N 0 c .PACS numbers: 11.30. Rd ,11.15.Pg, 11.10.Wx, 11.30.Qc Although quantum chromodynamics (QCD) is a theory for quarks and gluons, in the vacuum they are confined inside hadrons. It is, however, expected that at sufficiently high temperature and/or density a phase transition to a deconfined gas of interacting quarks and gluons takes place [1,2]. Moreover, it is also expected that this deconfinement phase transition is related to the so-called chiral phase transition: chiral symmetry is broken in the vacuum and restored in a hot and/or dense medium, see Ref.[3] and the lattice simulations of Refs. [4,5].The precise connection between the deconfinement and the chiral phase transition is not yet clear. This is also due to the fact that both transitions can only be precisely defined in limiting situations which are not realized in nature. Namely, in the context of pure Yang-Mills theory (QCD with infinitely heavy quarks) the Polyakov loop is the order parameter for the deconfinement phase transition [6]: the expectation value of the Polyakov loop vanishes for low T and µ (confined matter) and approaches unity in the deconfined phase. On the other hand, in the limit of zero quark masses the QCD Lagrangian is invariant under chiral transformations. The chiral condensate qq is the order parameter for the chiral phase transition: it is nonzero in the vacuum, decreases for increasing T and µ, and vanishes in the chirally restored phase. Nature is somewhere in between: the quark masses are neither infinite nor zero. The chiral condensate and the Polyakov loop are therefore only approximate order parameters.Since QCD cannot be directly solved, various methods are used to perform explicit calculations. Besides the already mentioned lattice simulations, effective models containing quark degrees of freedom only, such as the NJL model [7][8][9][10], and purely hadronic models, such as the linear σ-model [11,12], have been used to study the thermodynamics of QCD. Both approaches cannot describe the deconfinement phase transition: the degrees of freedom of NJL models are deconfined quarks at all temperatures and densities, while linear σ-models feature hadronic degrees of freedom in which quarks are always confined. However, in both approaches the critical temperature for the chiral phase transition is in agreement with recent lattice studies.In order to amend these problems, generalizations of th...

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