Meson mass differences in two dimensional gauged four-Fermi models

We quantitatively analyze the meson mass inequality relations of two dimensional gauged four-Fermi models in the large N limit. The class of models we study includes the 't Hooft model and the chiral and nonchiral Gross-Neveu models as special points in the space of field theories. Cases in which the chiral symmetry is spontaneously or explicitly broken are both studied. We study the meson mass differences quantitatively and define a susceptibility which allows us to systematically analyze these quantities. In the generalized Gross-Neveu model limit, we derive an analytic expression for this susceptibility. Even though no analytic proof of the validity of the classic mass inequality exists for the generic case, the mass difference is found to have the standard sign throughout most of the parameter space. We point out that the difference might have the opposite sign in certain cases.