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.
Description
P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED
%0 Generic
%1 stellin2020pwave
%A Stellin, Gianluca
%A Meißner, Ulf-G.
%D 2020
%K qed
%R 10.1140/epja/s10050-020-00319-1
%T P-Wave Two-Particle Bound and Scattering States in a Finite Volume
including QED
%U http://arxiv.org/abs/2008.06553
%X 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.
@misc{stellin2020pwave,
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.},
added-at = {2021-06-14T16:52:17.000+0200},
author = {Stellin, Gianluca and Meißner, Ulf-G.},
biburl = {https://www.bibsonomy.org/bibtex/2e32a9743e61f894064a5850dddd35e63/cmcneile},
description = {P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED},
doi = {10.1140/epja/s10050-020-00319-1},
interhash = {a231f51d16446b49e98234ba79356568},
intrahash = {e32a9743e61f894064a5850dddd35e63},
keywords = {qed},
note = {cite arxiv:2008.06553Comment: 73 pages, 7 figures, 0 tables. To be submitted to the European Physical Journal A},
timestamp = {2021-06-14T16:52:17.000+0200},
title = {P-Wave Two-Particle Bound and Scattering States in a Finite Volume
including QED},
url = {http://arxiv.org/abs/2008.06553},
year = 2020
}