Interpolation between the epsilon and p regimes

TL;DR

This paper introduces a new computational scheme in chiral perturbation theory that smoothly interpolates between the epsilon and p regimes, improving finite volume effect estimates in lattice QCD.

Contribution

A novel interpolation method in chiral perturbation theory that maintains infra-red finiteness and accurately captures finite volume effects across regimes.

Findings

Derived a two-point pseudoscalar correlator with a constant term

Demonstrated the scheme's ability to smoothly connect epsilon and p regimes

Provided tools for precise finite volume effect estimation in lattice QCD

Abstract

We reconsider chiral perturbation theory in a finite volume and develop a new computational scheme which smoothly interpolates the conventional epsilon and p regimes. The counting rule is kept essentially the same as in the p expansion. The zero-momentum modes of Nambu-Goldstone bosons are, however, treated separately and partly integrated out to all orders as in the epsilon expansion. In this new scheme, the theory remains infra-red finite even in the chiral limit, while the chiral-logarithmic effects are kept present. We calculate the two-point function in the pseudoscalar channel and show that the correlator has a constant contribution in addition to the conventional hyperbolic cosine function of time t. This constant term rapidly disappears in the p regime but it is indispensable for a smooth convergence of the formula to the epsilon regime result. Our calculation is useful to precisely estimate the finite volume effects in lattice QCD simulations on the pion mass Mpi and kaon mass MK, as well as their decay constants Fpi and FK.