Lattice QCD Calculation of the Pion Mass Splitting

Understand

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.