Mass formula for 2 dimensional flavorful mesons

We analytically and numerically investigate the 't Hooft equations, the lowest order mesonic Light-Front Tamm-Dancoff equations for $\mathrm{S}\mathrm{U}({\mathrm{N}}_{\mathrm{C}})$ and $\mathrm{U}({\mathrm{N}}_{\mathrm{C}})$ gauge theories, generalized to flavor non singlet mesons. We find the wave function can be well approximated by new basis functions and obtain an analytic and an empirical formulae for the mass of the lightest bound state. Its value is consistent with the precedent results.