PoS - Proceedings of Science
Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Poster
Two-Fermion Bound and Scattering States in a Finite Volume including QED in P-wave and Beyond
G. Stellin
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Pre-published on: May 16, 2022
Published on:
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.
DOI: https://doi.org/10.22323/1.396.0046
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