New spectrum and condensate in two dimensional QCD

TL;DR

This paper numerically evaluates the boson mass and condensate in two-dimensional QCD, revealing finite boson mass at the massless limit, agreement with large N_c predictions, and insights into light cone methods and chiral symmetry breaking.

Contribution

It provides a detailed numerical analysis of the boson mass and condensate in 2D QCD, clarifying the validity of light cone methods and the nature of chiral symmetry breaking.

Findings

Boson mass remains finite at the massless limit.

Condensate values match 1/N_c expansion predictions.

Light cone prescription is valid for QED2 but not for QCD2.

Abstract

The boson mass and the condensate in two dimensional QCD with $SU(N_c)$ colors are numerically evaluated with the Bogoliubov vacuum. It is found that the boson mass is finite at the massless limit, and it is well described by the phenomenological expression $ {\cal M}_{N_c}={2\over 3}\sqrt{{N_cg^2\over{3\pi}}} $ for large $N_c$. Also, the condensate values agree very well with the prediction by the $1/N_c$ expansion. The validity of the naive light cone method is examined, and it turns out that the light cone prescription of the boson mass with the trivial vacuum is accidentally good for QED$_2$. But it is not valid for QCD$_2$. Further, at the massless fermion limit, the chiral symmetry is spontaneouly broken without anomaly, and the Goldstone theorem does not hold for QCD$_2$.