How Chiral Symmetry Breaking Affects the Spectrum of the Light-Heavy Mesons in the 't Hooft Model

TL;DR

This paper investigates how chiral symmetry breaking influences the spectrum of heavy-light mesons in a simplified 1+1 dimensional QCD model, revealing consistent effects across different gauges and formalisms.

Contribution

It demonstrates that chiral symmetry breaking impacts the meson spectrum similarly in both the rest frame and on the light cone within the 't Hooft model, despite different dynamical equations.

Findings

Spectrum results are identical in both gauges and formalisms.

Chiral symmetry breaking effects are evident from gap and Bethe--Salpeter equations.

Vacuum is trivial on the light cone, yet symmetry breaking effects are still manifest.

Abstract

We find the spectrum and wave functions of the heavy-light mesons in $(1 + 1)$-dimensional QCD in the 't Hooft limit, both in the rest frame, using the Coulomb (axial) gauge, and on the light cone. Our emphasis is on the effects of chiral symmetry breaking on the spectrum. While dynamical equations in both cases look different, the results for the spectrum are identical. The chiral symmetry breaking is clearly seen from the gap and Bethe--Salpeter equations in the laboratory frame. At the same time, while vacuum is trivial on the light cone (no chiral condensate), the effects of the spontaneous breaking of the chiral symmetry manifest themselves in the same way, as it follows from the coincidence of the spectra obtained from the laboratory-frame Bethe--Salpeter equation on the one hand, and the light-cone 't Hooft-type equation on the other.