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