Meson mass spectrum in QCD${}_2$ 't Hooft's model

Abstract

We study the spectrum of meson masses in large $N_c$ QCD${}_2$ governed by celebrated 't Hooft's integral equation. We generalize analytical methods proposed by Fateev, Lukyanov and Zamolodchikov to the case of arbitrary, but equal quark masses $m_1=m_2.$ Our results include analytical expressions for spectral sums and systematic large-$n$ expansion. We also study the spectral sums in the chiral limit and the heavy quark limit and find a complete agreement with known results.

Comments: 29 pages and 1 figure, v3: typos corrected