Chiral logs in twisted mass lattice QCD with large isospin breaking

TL;DR

This paper calculates pion properties in twisted mass lattice QCD considering large isospin breaking, revealing significant modifications in chiral logs and improving fits to lattice data.

Contribution

It introduces a modified chiral perturbation theory accounting for large pion mass splitting in twisted mass lattice QCD.

Findings

Modified chiral logarithms involving neutral pion mass

Better fits to lattice data with new formulas

Implications for extracting low-energy constants

Abstract

The pion masses and the pion decay constant are calculated to 1-loop order in twisted mass Wilson chiral perturbation theory, assuming a large pion mass splitting and tuning to maximal twist. Taking the large mass splitting at leading order in the chiral expansion leads to significant modifications in the chiral logarithms. For example, the result for the charged pion mass contains a chiral logarithm that involves the neutral pion mass instead of the charged one. Similar modifications appear in the results for the neutral pion mass and the decay constant. These new results are used in fits to lattice data obtained recently by the European twisted mass collaboration. The data can be fitted well, in general better than with the standard chiral perturbation theory expressions that ignore the mass splitting. The impact on the extraction of low-energy couplings is briefly discussed.