Mass inequalities 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, the chiral and non-chiral Gross-Neveu models as special points in the space of field theories. Cases where the chiral symmetry is spontaneously or explicitly broken are both studied. We study the meson mass inequality quantitatively and define a susceptibility which allows us to systematically analyze the inequality. 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 inequality is found to be positive throughout most of the parameter space. We point out that the inequality might be negative in certain cases.