P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED

TL;DR

This paper derives and analyzes the effects of QED long-range interactions on P-wave two-fermion bound and scattering states in finite volume, extending non-relativistic EFT methods to lattice systems.

Contribution

It introduces a framework for calculating Coulomb corrections to P-wave states in finite volume using pionless EFT, including both continuum and lattice analyses.

Findings

Finite volume corrections to P-wave states are derived.

Power law finite volume effects proportional to the fine structure constant are identified.

The approach allows perturbative treatment of QED effects in lattice simulations.

Abstract

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.