Poincare covariant pseudoscalar and scalar meson spectroscopy in Wigner-Weyl phase

TL;DR

This paper investigates scalar and pseudoscalar meson properties in a chirally symmetric phase using Dyson-Schwinger and Bethe-Salpeter equations, revealing spacelike meson solutions independent of quark mass.

Contribution

It presents a novel analysis of meson spectra in Wigner-Weyl phase within a covariant framework, extending understanding beyond chiral symmetry breaking.

Findings

Meson solutions are spacelike with negative squared masses.

Meson masses and decay constants depend on current-quark mass in Wigner-Weyl phase.

Chiral condensate behavior is characterized in the symmetric phase.

Abstract

The coupled quark Dyson-Schwinger and meson Bethe-Salpeter equations in rainbow-ladder truncation for spin-0 mesons are solved in Wigner-Weyl phase in the chiral limit and beyond, retaining only the ultraviolet finite terms of the phenomenologically most successful Maris-Tandy interaction. This allows to reveal and discuss the scalar and pseudoscalar meson masses in a chirally symmetric setting without additional medium effects. Independent of the current-quark mass, the found solutions are spacelike, i.\,e.\ have negative squared masses. The current-quark mass dependence of meson masses, leptonic decay constants and chiral condensate are illustrated in Wigner-Weyl phase.