P-wave two-particle bound and scattering states in a finite volume including QED

The mass shifts for two-fermion bound and scattering P-wave states subject to the long-range interactions due QED in non-relativistic regime are derived. Introducing a short range force coupling spinless fermions one unit of angular momentum framework pionless EFT, we first calculate both perturbatively non-perturbatively Coulomb corrections fermion-fermion continuum infinite volume context. Motivated by research on particle-antiparticle states, extend results identical opposite charge. Second, transpose system onto cubic lattice with periodic boundary conditions finite energy lowest unbound $T_1^{\pm}$ eigenstates. In particular, power law proportional fine structure constant resembling recent S-wave found. Higher order contributions $\alpha$ neglected, since gapped nature operator environnement allows perturbative treatment interactions.