The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential

TL;DR

This paper advances chiral perturbation theory calculations at NNLO by incorporating a small imaginary chemical potential, analyzing finite-volume effects, and exploring optimal lattice geometries to reduce non-universal corrections.

Contribution

It provides the first detailed NNLO finite-volume corrections in chiral perturbation theory with imaginary chemical potential, including non-universal effects and lattice geometry optimization.

Findings

Finite-volume corrections to low-energy constants are quantified.

Optimal lattice geometries can minimize finite-volume effects.

A detailed calculation of the massless sunset diagram at finite volume is presented.

Abstract

We discuss chiral perturbation theory for two and three quark flavors in the epsilon expansion at next-to-next-to-leading order (NNLO) including a small imaginary chemical potential. We calculate finite-volume corrections to the low-energy constants $\Sigma$ and $F$ and determine the non-universal modifications of the theory, i.e., modifications that cannot be mapped to random matrix theory (RMT). In the special case of two quark flavors in an asymmetric box we discuss how to minimize the finite-volume corrections and non-universal modifications by an optimal choice of the lattice geometry. Furthermore we provide a detailed calculation of a special version of the massless sunset diagram at finite volume.