Meson masses in large Nf QCD from the Bethe-Salpeter equation

TL;DR

This paper calculates meson masses in large Nf QCD using the Bethe-Salpeter and Schwinger-Dyson equations, revealing degenerate meson masses near the chiral phase transition, indicating chiral symmetry restoration.

Contribution

It introduces a novel approach to solving the Bethe-Salpeter equation directly in the time-like region for large Nf QCD, utilizing an analytic two-loop running coupling.

Findings

Scalar, vector, and axial-vector meson masses vanish at the chiral transition.

All meson masses become degenerate with the massless pseudoscalar meson.

The method allows solving the SD equation in the complex plane for the first time.

Abstract

We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector, and axial-vector bound states of quark and anti-quark in large Nf QCD with the improved ladder approximation in the Landau gauge. The quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for consistency with the chiral symmetry. Amazingly, due to the fact that the two-loop running coupling of large Nf QCD is explicitly written in terms of an analytic function, large Nf QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector, and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large Nf QCD.