Using the Beth–Uhlenbeck Approach to Describe the Kaon to Pion Ratio in a 2 + 1 Flavor PNJL Model

David Blaschke,Alexandra Friesen,Andrey Radzhabov,Yuri Kalinovsky

doi:10.3390/particles3010014

Abstract

The kaon to pion ratios are discussed in the framework of a 2 + 1 flavor PNJL model. In order to interpret the behavior of bound states in medium, the Beth–Uhlenbeck approach is used. It is shown that, in terms of phase shifts in the K + channel, an additional low-energy mode could appear as a bound state in medium, since the masses of the quark constituents are different. The comparison with experimental data for the ratios is performed and the influence of the anomalous mode to the “horn” effect in the K + / π + ratio is discussed.

Highlights

The asymptotic freedom feature of quantum chromodynamics (QCD) results in the behavior of quarks and gluons as point-like particles with rather weak interactions at high energy transfer
The most interesting region of the QCD phase diagram is subject to nonperturbative effects like bound state and condensate formation since the strong coupling constant is not a small parameter
The applicability of lattice QCD calculations is still limited to the low-density region of the QCD phase diagram

Summary

Introduction

The asymptotic freedom feature of quantum chromodynamics (QCD) results in the behavior of quarks and gluons as point-like particles with rather weak interactions at high energy transfer. For exploring bound state properties and thermodynamic parameters in the region of essentially nonperturbative QCD phase transition one can use effective models based on QCD symmetries. The parameters used for the numerical studies in this work are the bare quark masses m0(u,d) = 5.5 MeV and m0s = 138.6 MeV, the three-momentum cut-off Λ = 602 MeV and the scalar coupling constant GSΛ2 = 2.317. To this end we find the positions of the minima of the temperature derivative (the steepest descent) of the quark mass as the chiral order parameter dM/dT in the T − μ plane. The coupling to the Polyakov loop reduces the occupation of the phase space by quarks and the pseudocritical temperatures are higher than in the corresponding NJL model

Mass Spectrum for Mesons at Finite Temperature and Density

Kaon to Pion Ratio

Comparison with Experimental Data