Chiral and isospin breaking in the two-flavor Schwinger Model

The Schwinger model with two massive fermions is a nontrivial theory for which no analytical solution is known. The strong coupling limit of the theory allows for different semiclassical approximations to extract properties of its low-lying spectrum. In particular, analytical results exist for the fermion condensate, the fermion mass dependence of the pseudoscalar meson mass or its decay constant. These approximations, nonetheless, are not able to quantitatively predict isospin breaking effects in the light spectrum, for example. In this paper we use lattice simulations to test various analytical predictions, and study isospin breaking effects from nondegenerate quark masses. We also introduce a low-energy effective field theory based on a nonlinear $\sigma$ model with a dilaton field, which leads to the correct fermion mass dependence of the pion mass, the correct $\sigma$-to-$\pi$ mass ratio and a prediction of the isospin breaking effects, which we test numerically.