Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order

TL;DR

This paper computes the partition function of partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order, revealing finite-volume effects on low-energy constants and spectral correlations relevant for lattice QCD.

Contribution

It provides a detailed calculation of the partition function at NLO in the epsilon regime using supersymmetry, including effects of imaginary chemical potential and comparison with random matrix theory.

Findings

Finite-volume corrections to low-energy constants are identical for quenched and unquenched cases.

Zero-momentum integral matches previous random matrix theory results.

Methodology enables improved lattice QCD simulations with minimized finite-volume effects.

Abstract

We calculate the partition function of partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order using the supersymmetry method in the formulation without a singlet particle. We include a nonzero imaginary chemical potential and show that the finite-volume corrections to the low-energy constants $\Sigma$ and $F$ for the partially quenched partition function, and hence for spectral correlation functions of the Dirac operator, are the same as for the unquenched partition function. We briefly comment on how to minimize these corrections in lattice simulations of QCD. As a side result, we show that the zero-momentum integral in the formulation without a singlet particle agrees with previous results from random matrix theory.