Inhomogeneous quark condensate in compressed Skyrmion matter

Abstract

The inhomogeneous quark condensate, responsible for dynamical chiral symmetry breaking in cold nuclear matter, is studied by putting skyrmions onto the face-centered cubic crystal and treating the skyrmion matter as nuclear matter. By varying the crystal size, we explore the effect of density on the local structure of the quark-antiquark condensate. By endowing the light vector mesons ρ and ω with hidden local symmetry and incorporating a scalar meson as a dilaton of spontaneously broken scale symmetry, we uncover the intricate interplay of heavy mesons in the local structure of the quark condensate in dense baryonic matter described in terms of skyrmion crystal. It is found that the inhomogeneous quark density persists to as high a density as ∼ 4 times nuclear matter density. The difference between the result from the present approach and that from the chiral density wave ansatz is also discussed.PACS numbers: 11.30. Qc,11.30.Rd,12.39.Dc While the observation of the Higgs boson is considered to account for the masses of "elementary constituents" of visible matter, i.e., quarks and leptons, the bulk of the mass of the proton, the constituents of which are three light quarks, i.e., two up quarks and one down quark, remains more or less unexplained. The quark masses account for only < ∼ 1% of the proton mass. This is in marked contrast to the next scale hadron, the nucleus. The mass of a nucleus of mass number A is given almost entirely, say, ∼ 98%, by the sum of the masses of A nucleons. It is generally accepted, although not proven rigorously, that the nucleon mass arises from the nonperturbative dynamics of strong interactions encoded in QCD. What is involved is quark confinement and chiral symmetry spontaneously broken by the vacuum. It is not established but generally believed that the two are related. It is easier to address the latter in effective theories, so we will focus on it in what follows.In QCD, the order parameter of the chiral symmetry breaking is the pion decay constant f π and, in terms of the fundamental QCD quantities, the quark condensates, typically the two-quark condensate qq . The two-quark condensate in cold or hot dense matter has been studied for a long time. In Refs. [1, 2] it was found that in neutron matter at the neutron star density, both the σ (the isoscalar component of the chiral four-vector) and pion condensates exist and because of the chiral invariance of the system, these two condensates are linked to each other through a chiral rotation. Later, the approach put forward in Ref.[1] was investigated in more detail, and it was found that both condensates, σ and the pion, * harada@hken.phys.nagoya-u.ac.jp † hyunkyu@hanyang.ac.kr ‡ yongliangma@jlu.edu.cn § mannque.rho@cea.fr could depend on the position; that is, the condensates are inhomogeneous [3]. In a phenomenological model with nucleons as explicit degrees of freedom which are put on a crystal lattice, Pandharipande and Smith found that in solid neutron matter, given an enhanced attractive tensor force, which is stronger...

Pseudoconformal structure in dense baryonic matter

“…What takes place in the changeover here, loosely called transition throughout this paper, is not a bona fide Landau-Ginzburg-type phase transition since it involves no local order parameter. At the transition we are concerned with, what corresponds to Σ ≡ qq -called quark condensate -goes to zero when space-averaged, Σ → 0, but is not zero locally, bearing inhomogeneity [19]. Thus the vanishing of Σ does not signal chiral symmetry restoration.…”

“…To move towards a chiral symmetric Gell-Mann-Lévy (GML)-type linear sigma model, we do the field reparameterizations Z = U χf π /f χ = s + i τ · π, defining the scalar s, and write (19) composed of two parts, one that is regular, L reg , and the other that is singular, L sing , as tr(ZZ † ) ≡ κ 2 = 2 s 2 + π a 2 → 0. 10 The singular part that arises solely from the scale invariant part of the original Lagrangian (19) takes the form L sing = (g vρ − g A ) A 1/tr ZZ † 9 To simply the notations, we do not affix * to the parameters to indicate IDDs. 10 It is worth pointing out that this limiting process is equivalent to dialing ζ to 0 to go from a nonlinear sigma model to scalesymmetric theory via a linear sigma model as was done with (10) discussed above.…”

Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions: Topological Structure of Dense Matter

“…To give an idea, n 1/2 in massive compact stars comes in [8] at ∼ 3n 0 . The condensate, however, is non-zero locally, thereby supporting a chiral density wave in skyrmion crystal [35]. This seems to be the case in general as observed in various models [36].…”

“…There is an indication that the sheet structure of the stack of lasagnes could give a consistent density profile of even finite nuclei [45]. In fact, there seems little doubt that an inhomogeneity is favored in dense matter at non-asymptotic densities [35,36]. Thus, it could be considered robust.…”

Fractionized Skyrmions in Dense Compact-Star Matter

“…Although the bilinear quark condensate vanishes on average, it is non-zero locally and has a chiral-density-wave structure. 26 There is parity-doubling although pions are still present. This picture is also arrived at using a renormalization-group technique used in Ref: 25 with the continuum Lagrangian.…”