Locating the critical endpoint of QCD: Mesonic backcoupling effects

Pascal J Gunkel,Christian S Fischer

doi:10.1103/physrevd.104.054022

Pascal J Gunkel, Christian S Fischer

Open Access

https://doi.org/10.1103/physrevd.104.054022

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Abstract

We study the effects of pion and sigma meson backcoupling on the chiral order parameters and the QCD phase diagram and determine their effect on the location of the chiral critical endpoint. To this end, we solve a coupled set of truncated Dyson-Schwinger equations for Landau gauge quark and gluon propagators with ${N}_{\mathrm{f}}=2+1$ dynamical quark flavors and explicitly backcoupled mesons. The corresponding meson bound-state properties and the quark-meson Bethe-Salpeter vertices are obtained from their homogeneous Bethe-Salpeter equation. We find chiral-restoration effects of the pion and/or sigma meson backcoupling and observe a (small) shift of the critical endpoint towards smaller chemical potentials. The curvature of the chiral crossover line decreases. Our results indicate that the location of the critical endpoint in the phase diagram is mainly determined by the microscopic degrees of freedom of QCD (in contrast to its critical properties).

Highlights

The phase structure of QCD at finite chemical potential is probed in heavy-ion-collision experiments at Relativistic Heavy Ion Collider/Brookhaven National Laboratory [1] and High Acceptance Di-Electron Spectrometer (FAIR Phase-0) [2], as well as the future Compressed Baryonic Matter/Facility for Antiproton and Ion Research experiment [3]
Functional approaches, i.e., approaches via DysonSchwinger equations (DSE) and/or the functional renormalization group (FRG), do in principle allow for a mapping of the whole QCD phase diagram but inherently depend on
The new element that is different from previous finitetemperature studies within the DSE framework is the quark-meson loop appearing in the quark DSE. It arises from a specific diagram in the DSE for the quark-gluon vertex that involves a four-quark kernel in pole approximation, shown in the left diagram of Fig. 2

Summary

INTRODUCTION

The phase structure of QCD at finite chemical potential is probed in heavy-ion-collision experiments at Relativistic Heavy Ion Collider/Brookhaven National Laboratory [1] and High Acceptance Di-Electron Spectrometer (FAIR Phase-0) [2], as well as the future Compressed Baryonic Matter/Facility for Antiproton and Ion Research experiment [3]. Theoretical approaches to QCD agree with each other that no such CEP may be found in the region of the temperature–baryon-chemical-potential plane ðT; μBÞ with μB=T < 2.5 This region is excluded by recent studies on the lattice; see, e.g., Refs. Due to the inherent complementarity of truncations in the DSE and FRG frameworks, it is highly desirable to complement these studies by a corresponding one in the DSE approach. This is the purpose of the present work.

TRUNCATION

Z DXðPÞ q

EFFECT ON THE CHIRAL ORDER PARAMETERS

EFFECT ON THE QCD CHIRAL PHASE DIAGRAM

Findings

CONCLUSIONS AND OUTLOOK