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In order to model pions of two-flavor QCD we consider a lattice field theoryinvolving two flavors of staggered quarks interacting strongly with U(1) gaugefields. For massless quarks, this theory has an $SU_L(2)\times SU_R(2) \timesU_A(1)$ symmetry. By adding a four-fermion term we can break the U_A(1)symmetry and thus incorporate the physics of the QCD anomaly. We can also tunethe pion decay constant F, to be small compared to the lattice cutoff bystarting with an extra fictitious dimension, thus allowing us to model lowenergy pion physics in a setting similar to lattice QCD from first principles.However, unlike lattice QCD, a major advantage of our model is that we caneasily design efficient algorithms to compute a variety of quantities in thechiral limit. Here we show that the model reproduces the predictions of chiralperturbation theory in the $\epsilon$-regime.

Modeling pion physics in the $\epsilon$-regime of two-flavor QCD using strong coupling lattice QED