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 Δmπ=4.534(42)(43)MeV, which agrees well with experimental measurements.
@article{arxiv.2108.05311,
title = {Lattice QCD Calculation of the Pion Mass Splitting},
author = {Xu Feng and Luchang Jin and Michael Joseph Riberdy},
journal= {arXiv preprint arXiv:2108.05311},
year = {2022}
}