Determination of the Wilson ChPT low energy constant c_2

TL;DR

This paper presents a straightforward method to determine the Wilson ChPT low energy constant c_2 by analyzing volume effects in 2-pion states using lattice QCD simulations, aiding in understanding discretization effects.

Contribution

It introduces a simple, computationally inexpensive approach to extract c_2 from lattice data, applicable as a routine check in Wilson fermion simulations.

Findings

c_2 values obtained from various lattice setups.

Method consistent with theoretical expectations.

Useful for assessing discretization effects in chiral extrapolations.

Abstract

Following a suggestion by Aoki and B\"ar, c2 can be extracted by analyzing volume effects in 2-pion states. To this end we consider renormalized ratios of four point to two point correlation functions. We present the results from various CLS lattices, with pion masses ranging from 280 to 450 MeV and lattice spacings of 0.07 fm and 0.08 fm. This low energy constant is useful to understand discretization effects in chiral extrapolations with Wilson fermions, especially for quantities which vanish in the chiral limit, like the pion mass. Since our procedure is computationally cheap and straightforward, it is recommended as a routine study for any Wilson-type simulation, as a check of discretization effects.