Connecting Lattice QCD with Chiral Perturbation Theory at Strong Coupling

TL;DR

This paper investigates the detection of chiral singularities in lattice QCD at strong coupling, demonstrating consistency with chiral perturbation theory predictions at very small quark masses using a novel algorithm.

Contribution

It connects lattice QCD results with chiral perturbation theory at strong coupling, highlighting the need for very small quark masses and higher order terms for accurate description.

Findings

Chiral condensate, pion mass, and decay constant match ChPT predictions at small quark masses.

Detection of power-like singularities is feasible at finite temperature in the broken phase.

Larger quark masses used in typical simulations do not reveal the predicted singularities.

Abstract

We study the difficulties associated with detecting chiral singularities predicted by chiral perturbation theory (ChPT) in lattice QCD. We focus on the physics of the remnant O(2) chiral symmetry of staggered fermions in the strong coupling limit using the recently discovered directed path algorithm. Since it is easier to look for power-like singularities as compared to logarithmic ones, our calculations are performed at a fixed finite temperature in the chirally broken phase. We show that the behavior of the chiral condensate, the pion mass and the pion decay constant, for small masses, are all consistent with the predictions of ChPT. However, the values of the quark masses that we need to demonstrate this are much smaller than those being used in dynamical QCD simulations. We also need to use higher order terms in the chiral expansion to fit our data.