An Update on the Isospin-Breaking Effects in the Pion Decay Constant with Staggered Quarks

TL;DR

This paper updates the computation of isospin-breaking effects in the Pion Decay Constant using staggered quarks, providing preliminary results and discussing future plans.

Contribution

It presents new calculations of isospin-breaking effects in the pion decay constant with near-physical quark masses and lattice spacings.

Findings

Updated isosymmetric value and gradient-flow scale $w_{0}$

Preliminary results on valence-valence contribution to axial-pseudoscalar correlator

Discussion of next steps and future plans

Abstract

We present an update on the ongoing computation of the isospin-breaking effects in the Pion Decay Constant from the BMW Collaboration. The calculation is carried out with N$_f$=2+1+1 staggered quarks with a near-physical pion mass and QED$_{\text{L}}$. We give an update on the isosymmetric value and the current determination used to compute the gradient-flow scale $w_{0}$, then we present some preliminary results of the valence-valence contribution to the axial-pseudoscalar correlator for different volumes and lattice spacings. We also discuss the next steps and plans.