Existence of the critical endpoint in the vector meson extended linear sigma model

Previously, a matrix model of the region near the transition temperature, in the "semi"-Quark Gluon Plasma, was developed for the theory of SU (3) gluons without quarks. In this paper we develop a a chiral matrix model applicable to QCD by including dynamical quarks with 2 + 1 flavors. This requires adding a nonet of scalar fields, with both parities, and coupling these to quarks through a Yukawa coupling, y. Treating the scalar fields in mean field approximation, the effective Lagrangian is computed by integrating out quarks to one loop order. As is standard, the potential for the scalar fields is chosen to be symmetric under the flavor symmetry of SU (3) L × SU (3) R × Z(3) A , except for a term linear in the current quark mass, m qk . In addition, at a nonzero temperature T it is necessary to add a new term, ∼ m qk T 2 . The parameters of the gluon part of the matrix model are identical to that for the pure glue theory without quarks. The parameters in the chiral matrix model are fixed by the values, at zero temperature, of the pion decay constant and the masses of the pions, kaons, η, and η . The temperature for the chiral crossover at T χ = 155 MeV is determined by adjusting the Yukawa coupling y. We find reasonable agreement with the results of numerical simulations on the lattice for the pressure and related quantities. In the chiral limit, besides the divergence in the chiral susceptibility there is also a milder divergence in the susceptibility between the Polyakov loop and the chiral order parameter, with critical exponent β − 1. We compute derivatives with respect to a quark chemical potential to determine the susceptibilities for baryon number, the χ 2n . Especially sensitive tests are provided by χ 4 − χ 2 and by χ 6 , which changes in sign about T χ . The behavior of the susceptibilities in the chiral matrix model strongly suggests that as the temperature increases from T χ , that the transition to deconfinement is significantly quicker than indicated by the measurements of the (renormalized) Polyakov loop on the lattice. * pisarski@bnl.gov † vskokov@bnl.gov 2

Section: Discussionmentioning

confidence: 86%

Chiral matrix model of the semi-QGP in QCD

Pisarski¹,

Skokov²

2016

“…[16] leads to the result R T > 1 for T > T c , which is another manifestation of the "negative susceptibility" problem discussed in Ref. [14,22]. Imposing the Haar measure to the potential [17,18] effectively restricts the Polyakov loop to the target region and thus improves the theoretical description.…”

Section: Polyakov Loop Susceptibility Ratios Within An Effectivementioning

confidence: 90%

Polyakov loop fluctuations in the presence of external fields

Szymański

Redlich

et al. 2018

We study the implications of the spontaneous and explicit Z(3) center symmetry breaking for the Polyakov loop susceptibilities. To this end, ratios of the susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop are computed within an effective model using a color group integration scheme. We show that the essential features of the lattice QCD results of these ratios can be successfully captured by the effective approach. Furthermore we discuss a novel scaling relation in one of these ratios involving the explicit breaking field, volume, and temperature.

“…Concerning the η − N interaction, despite experimental efforts [18,19], very little is known about its nature. In addition to the U A (1) anomaly, the interaction seems to be dictated by scalar meson exchange [6], and one is also interested in the role of various vector mesons [20,21].…”

Section: Introductionmentioning

confidence: 99%

Mesonic and nucleon fluctuation effects at finite baryon density

Fejős

2017

Mesonic and nucleon fluctuation effects are investigated in medium. We couple the nucleon field to the 2 + 1 flavor meson model and investigate the finite temperature and density behavior of the system, in particular, the axial anomaly function. Somewhat contrary to earlier expectations we find that it tends to strengthen at finite density. At lower temperatures nucleon density fluctuations can cause a relative difference in the UA(1) axial anomaly of about 20%. This has important consequences on the mesonic spectra, especially on the η − η system, as we observe no drop in the η mass as a function of the baryochemical potential, irrespective of the temperature. Based on the details of chiral symmetry restoration, it is argued that there has to be a competition between underlying QCD effects of the anomaly and fluctuations of the low energy hadronic degrees of freedom, and the fate of the UA(1) coefficient should be decided by taking into account both effects simultaneously.