Pseudo-scalar mesons at finite temperatures from a Dyson-Schwinger-Bethe-Salpeter approach

Sergey Dorkin,Burkhard Kämpfer,Leonid Kaptari,S Bondarenko,V Burov,A Malakhov

doi:10.1051/epjconf/201920408005

Abstract

The truncated Dyson-Schwinger–Bethe-Salpeter equations are employed at non-zero temperature. The truncations refer to a rainbow-ladder approximation augmented with an interaction kernel which facilitates a special temperature dependence. At low temperatures,T →0, we recover a quark propagator from the Dyson-Schwinger (gap) equation smoothly interpolating to theT= 0 results. Utilizing that quark propagator we evaluate the Bethe-Salpeter vertex function in the pseudo-scalarqq̅channel for the lowest boson Matsubara frequencies and find a competition ofqq̅bound states and quasi-free two-quark states atT=O(100 MeV).

Highlights

The description of mesons as quark-antiquark bound states within the framework of the Bethe-Salpeter (BS) equation with momentum dependent quark mass functions, determined by the Dyson-Schwinger (DS) equation, is able to explain successfully many spectroscopic data, such as meson masses, electromagnetic properties of pseudoscalar mesons and their radial excitations, and other observables [1,2,3,4,5,6,7,8,9,10,11,12,13]
Utilizing that quark propagator we evaluate the BetheSalpeter vertex function in the pseudo-scalar qqchannel for the lowest boson Matsubara frequencies and find a competition of qqbound states and quasi-free two-quark states at T = O (100 MeV)
The main ingredients here are the full quark-gluon vertex function and the dressed gluon propagator, which are entirely determined by the running coupling and the bare quark mass parameters

Summary

Introduction

The description of mesons as quark-antiquark bound states within the framework of the Bethe-Salpeter (BS) equation with momentum dependent quark mass functions, determined by the Dyson-Schwinger (DS) equation, is able to explain successfully many spectroscopic data, such as meson masses, electromagnetic properties of pseudoscalar mesons and their radial excitations, and other observables [1,2,3,4,5,6,7,8,9,10,11,12,13]. We treat the bound states within the BS formalism within the same approach as the one used in solving the DS equation, i.e. with the rainbow truncation and Alkofer-Watson-Weigel (AWW) interaction kernel [12]

Truncated Dyson-Schwinger and Bethe-Salpeter equations in vacuum

Partial decomposition of the BS vertex function

Angular integration

Results

Summary