Determining low-energy constants in partially quenched Wilson chiral perturbation theory

TL;DR

This paper proposes methods to separately determine low energy constants in partially quenched Wilson chiral perturbation theory, which are crucial for understanding lattice QCD spectral properties.

Contribution

The paper introduces novel techniques to independently calculate three low energy constants in the theory, enhancing the analysis of lattice Dirac operator spectra.

Findings

Methods to extract LECs W'_6, W'_7, W'_8 from correlation functions.

Ability to distinguish different LEC combinations in spectral density.

Framework applicable to partially quenched lattice QCD studies.

Abstract

In the low energy effective theory describing the partially quenched extension of two light Wilson fermions, three low energy constants (LECs) appear in terms proportional to a^2 (a being the lattice spacing). We propose methods to separately calculate these LECs, typically called W'_6, W'_7 and W'_8. While only one linear combination of these constants enters into physical quantities, different combinations enter into the description of the spectral density and eigenvalue distributions of the lattice Dirac operator and its Hermitian counterpart. Thus it is useful to be able to determine the LECs separately. Our methods require studying certain correlation functions for either two or three pion scattering, which are accessible only in the partially quenched extension of the theory.