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

TL;DR

This paper presents a lattice field theory model with strong coupling U(1) gauge fields and staggered quarks that effectively reproduces low-energy pion physics in the epsilon-regime, offering computational advantages over traditional lattice QCD.

Contribution

The authors introduce a novel lattice model that incorporates chiral symmetry breaking and anomaly effects, enabling efficient simulation of pion physics in the epsilon-regime from first principles.

Findings

Model reproduces chiral perturbation theory predictions in the epsilon-regime.

Allows tuning of pion decay constant to be small compared to lattice cutoff.

Provides an efficient computational framework for low-energy QCD phenomena.

Abstract

In order to model pions of two-flavor QCD we consider a lattice field theory involving two flavors of staggered quarks interacting strongly with U(1) gauge fields. For massless quarks, this theory has an $SU_L(2)\times SU_R(2) \times U_A(1)$ 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 tune the pion decay constant F, to be small compared to the lattice cutoff by starting with an extra fictitious dimension, thus allowing us to model low energy 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 can easily design efficient algorithms to compute a variety of quantities in the chiral limit. Here we show that the model reproduces the predictions of chiral perturbation theory in the $\epsilon$-regime.