On mass spectrum in 't Hooft's 2D model of mesons

TL;DR

This paper develops an analytic method to study meson mass spectra in 't Hooft's 2D QCD model, providing large-n expansions and sum rules, with potential applicability to general quark masses.

Contribution

The paper introduces a systematic analytic approach for solving 't Hooft's integral equation, including large-n expansion and sum rules, for meson masses in 2D QCD.

Findings

Large-n expansion for meson masses derived

Exact sum rules established for the spectrum

Method applicable to general quark masses

Abstract

We study 't Hooft's integral equation determining the meson masses M_n in multicolor QCD_2. In this note we concentrate on developing an analytic method, and restrict our attention to the special case of quark masses m_1=m_2=g/\sqrt{\pi}. Among our results is systematic large-n expansion, and exact sum rules for M_n. Although we explicitly discuss only the special case, the method applies to the general case of the quark masses, and we announce some preliminary results for m_1=m_2.