Lattice QCD Calculation of the Pion Mass Splitting

TL;DR

This paper presents a lattice QCD calculation of the charged and neutral pion mass difference using the infinite volume reconstruction method, achieving results consistent with experimental data.

Contribution

The study introduces a lattice QCD approach combining hadronic tensor calculations with an analytic photon propagator to accurately determine pion mass splitting.

Findings

Calculated pion mass splitting: 4.534 MeV

Good agreement with experimental measurements

Finite volume effects are exponentially suppressed

Abstract

We use the infinite volume reconstruction method to calculate the charged/neutral pion mass difference. The hadronic tensor is calculated on lattice QCD and then combined with an analytic photon propagator, and the mass splitting is calculated with exponentially-suppressed finite volume errors. The calculation is performed using six gauge ensembles generated with $2+1$-flavor domain wall fermions, and five ensembles are at the physical pion mass. Both Feynman and Coulomb gauge are adopted in the calculation and result in a good agreement when the lattice spacing approaches zero. After performing the continuum extrapolation and examining the residual finite-volume effects, we obtain the pion mass splitting $\Delta m_\pi = 4.534(42)(43)~\mathrm{MeV}$, which agrees well with experimental measurements.