https://doi.org/10.1140/epja/s10050-020-00319-1
Regular Article – Theoretical Physics
P-wave two-particle bound and scattering states in a finite volume including QED
1
Helmholtz Institut für Strahlen- und Kernphysik, Universität Bonn, Nußallee 14-16, 53115, Bonn, Germany
2
Bethe Center for Theoretical Physics, Universität Bonn, Nußallee 12, 53115, Bonn, Germany
3
Insitute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, 52425, Jülich, Germany
4
Ivane Javakhishvili Tbilisi State University, 0186, Tbilisi, Georgia
Received:
21
August
2020
Accepted:
30
November
2020
Published online:
14
January
2021
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 box with periodic boundary conditions and we calculate the finite volume corrections to the energy of the lowest bound and unbound 
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 
are neglected, since the gapped nature of the momentum operator in the finite-volume environnement allows for a perturbative treatment of the QED interactions.
© The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
