Exploring the Aoki regime

TL;DR

This paper calculates next-to-leading order corrections in Wilson and Staggered Chiral Perturbation Theory within the epsilon-regime, revealing differences in low energy constants' contributions and implications for phase boundaries and taste splitting.

Contribution

It provides the first detailed NLO corrections in WChPT and SChPT, highlighting differences in low energy constants' roles and their impact on physical observables.

Findings

NLO corrections in WChPT for SU(2) and U(N_f) at fixed index.

Finite-volume corrections to the Aoki phase boundary.

NLO corrections to taste splitting and the partition function in SChPT.

Abstract

We compute next-to-leading order (NLO) corrections in the \epsilon-regime of Wilson (WChPT) and Staggered Chiral Perturbation Theory (SChPT). A difference between the two is that in WChPT already at NLO, that is at O(\epsilon^2), new low energy constants (LECs) contribute, whereas in SChPT they only enter at O(\epsilon^4). We first determine the NLO corrections in WChPT for SU(2), and for U(N_f) at fixed index. This implies finite-volume corrections to the phase boundary between the Aoki phase and the Sharpe-Singleton scenario via corrections to the mean field potential. We also compute NLO corrections to the two-point function in the scalar and pseudo-scalar sector in WChPT. Turning to SChPT we determine the NLO corrections to the LECs and their effect on the taste splitting. Here the NLO partition function can be written as the leading order one with renormalized couplings, thus preserving the equivalence to staggered chiral random matrix theory at NLO for any number of flavors N_f. In WChPT this relation only appears to hold for SU(2).