Analysis of the QCD spectrum and chiral symmetry breaking with varying quark masses

TL;DR

This paper investigates how the meson spectrum in QCD varies with quark mass, revealing two distinct branches—flux-tube and chiral symmetry breaking—and their convergence around 200 MeV, aligning with lattice data.

Contribution

It introduces a formalism for pseudoscalar mesons incorporating quark mass effects and describes the spectrum's two-branch structure with a unified propagator.

Findings

The spectrum has two branches: flux-tube and CSB.

CSB branch joins flux-tube branch near 200 MeV.

Results agree with recent lattice QCD data.

Abstract

The meson spectrum of QCD is studied in the framework of nonperturbative QCD as a function of varying quark masses $m_q$. It is shown, that the total spectrum consists of two branches: 1) the standard one, which may be called the flux-tube spectrum, depending approximately linearly on $m_q$ and 2) the chiral symmetry breaking (CSB) spectrum for pseudoscalar flavor nonsinglet (PS) mesons, with mass dependence $\sqrt{m_q}$. The formalism for PS mesons is derived from the QCD Lagrangian with $m_q$ corrections, and a unified form of the PS propagator was derived. It is shown, that the CSB branch of PS mesons joins to the flux-tube branch at around $m_q=200$ MeV. All these results are in close correspondence with recent numerical data on large lattices.