Chiral logs in twisted mass lattice QCD with large isospin breaking

TL;DR

The paper addresses the challenge of large isospin breaking in twisted-mass lattice QCD by computing pion masses and the decay constant to one loop in SU(2) WChPT within the Aoki/LCE regime at maximal twist. It demonstrates that chiral logs are modified by the mass splitting, with the charged-pion log tied to the neutral-meson mass and similar cross-logs appearing in $M_{\4$ and $f_\pi$, while finite-volume effects are enhanced when the neutral pion is lighter. The authors perform a detailed numerical analysis of ETM 2+1+1 data, finding that including the mass-splitting effects yields better fits and shifts in the extracted low-energy constants, notably $f$ and $\overline{l}_3$, with meaningful $O(a^2)$ corrections in a combined continuum-chiral extrapolation. They conclude that neglecting the splitting can bias chiral extrapolations and GL coefficient determinations, and they outline extensions to kaons and other observables as well as the need for more precise neutral-pion data to sharpen the fits.

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.