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

TL;DR

This paper analyzes two-fermion bound and scattering states in a finite volume with Coulomb corrections, extending previous work to include QED effects and finite-volume energy corrections relevant for lattice simulations.

Contribution

It introduces a perturbative approach to include QED corrections in finite-volume two-fermion systems with angular momentum, extending prior pionless EFT results.

Findings

Finite-volume energy corrections include Coulomb effects.

QED contributions are treated perturbatively due to the gapped momentum operator.

Extension to D-wave interactions is proposed.

Abstract

Introducing a short range force coupling the spinless fermions to one unit of angular momentum in the framework of pionless EFT, we first report the two-body scattering amplitudes with Coulomb corrections, extended to two fermions of opposite charge in refs. [1,2]. Motivated by the growing interest in lattice approaches, we immerse the system into a cubic box with periodic boundary conditions and display the finite-volume corrections to the energy of the lowest bound and unbound $T_1^{-}$ eigenstates. The latter turn out to consist of power law terms proportional to the fine-structure constant. In the calculations, quadratic and higher order contributions in $\alpha$ are discarded, on the grounds that the gapped nature of the momentum operator in the finite-volume environment allows for a perturbative treatment of the QED interactions. An outlook on the extension of the analysis to D-wave short-range interactions is eventually given.