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