Chiral density wave in nuclear matter

Abstract

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...

Inhomogeneous quark condensate in compressed Skyrmion matter

“…There is a basic difference between this skyrmion prediction and the CDW phase discussed in Ref. [6]. First of all, in [6], the quark-antiquark condensate is the bona-fide order parameter indicating the onset of the Wigner phase, whereas it is not in the skyrmion description, where it is more like a "pseudo-gap".…”

“…The nucleon mass can be characterized by two components as m N = m 0 + M ( qq ), where M ( qq ) → 0 as qq → 0 and m 0 = 0. Here, m 0 resembles the chiral-invariant mass term in the parity-doubled nucleon model [6]. Furthermore, as will be mentioned later, parity doubling does take place in the hadron spectrum in a cold or hot dense medium.…”

“…Since then, the inhomogeneity of these condensates, now termed a chiral density wave(CDW), has been extensively studied in various different effective theory approaches modeling low-energy QCD; see, e.g., Refs. [5,6] and references therein.In this article, continuing our effort to understand hadronic matter at high densities, we approach this problem by putting skyrmions, representing nucleons, on a face-centered cubic (FCC) crystal lattice. This has the advantage of enabling one to describe, on the same footing, both the basic structure of the nucleon and the properties of nuclear matter, thereby probing the modification of the vacuum in which the nucleons are propagating.…”

“…Since then, the inhomogeneity of these condensates, now termed a chiral density wave(CDW), has been extensively studied in various different effective theory approaches modeling low-energy QCD; see, e.g., Refs. [5,6] and references therein.…”

“…Moreover, due to the parity invariance of the QCD vacuum, one normally has σ QCD = f π ∝ qq QCD and π a QCD ∝ qiτ a γ 5 q QCD = 0. However, in a medium, due to the interaction between the mesons and baryonic matter, both σ and π a could be nonzero and position dependent [1][2][3][4][5][6].…”