Comparison of the mixed-fermion-action Effects using different fermion and gauge actions with 2+1 and 2+1+1 flavors

TL;DR

This study calculates the low-energy constant  in mixed-action chiral perturbation theory using 2+1+1-flavor gauge ensembles, revealing the dominant influence of fermion action and negligible charm quark loop effects.

Contribution

It provides the first detailed comparison of mixed-fermion-action effects across different fermion and gauge actions with 2+1 and 2+1+1 flavors.

Findings

Fermion action has the dominant impact on 

Gauge action has a secondary but measurable effect

Charm quark loops are negligible within current uncertainties

Abstract

The leading-order low-energy constant $\Delta_{\rm mix}$ in mixed-action chiral perturbation theory is calculated using $2+1+1$-flavor gauge ensembles with HISQ fermions and a tadpole-improved Symanzik gauge action at four lattice spacings $a \in [0.048, 0.111]$ fm. By comparing our results to those from different actions and a $2+1$-flavor case, We find that the fermion action has the dominant impact, the gauge action has a secondary but measurable effect, and the contribution from charm quark loops is negligible within our current uncertainties.