Unitarizing non-relativistic scattering
Abstract
Unitarity imposes coupled constraints on elastic and inelastic amplitudes. Satisfying them requires resummation of the self-energy contributions from both elastic and inelastic channels. Inelastic channels generate anti-Hermitian contributions that can be consistently deduced from the unitarity relation underlying the optical theorem, leading to non-local separable potentials and a compact unitarization scheme in the non-relativistic regime. We present two alternative derivations of the anti-Hermitian kernel, from the continuity equation and by integrating out inelastic channels. We further extend this framework to treat non-analytic and non-convergent behavior of inelastic amplitudes in the complex momentum plane and to incorporate bound states. For non-convergent amplitudes, we demonstrate a simple renormalization procedure in which anti-Hermitian separable potentials necessarily induce Hermitian separable counterterms, yielding finite cross sections consistent with unitarity. These results provide a general tool for non-relativistic scattering problems, with clear applications to dark-matter phenomenology.
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BibTeX
@article{flores2026unitarizing,
title = {{Unitarizing non-relativistic scattering}},
author = {Marcos M Flores and Kalliopi Petraki},
journal = {Journal of High Energy Physics},
year = {2026},
month = jun,
doi = {10.1007/jhep06(2026)148},
eprint = {2512.02097},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05419497v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Unitarizing non-relativistic scattering
AU - Marcos M Flores
AU - Kalliopi Petraki
PY - 2026
DA - 2026/06/12
JO - Journal of High Energy Physics
DO - 10.1007/jhep06(2026)148
UR - https://hal.science/hal-05419497v1
AB - Unitarity imposes coupled constraints on elastic and inelastic amplitudes. Satisfying them requires resummation of the self-energy contributions from both elastic and inelastic channels. Inelastic channels generate anti-Hermitian contributions that can be consistently deduced from the unitarity relation underlying the optical theorem, leading to non-local separable potentials and a compact unitarization scheme in the non-relativistic regime. We present two alternative derivations of the anti-Hermitian kernel, from the continuity equation and by integrating out inelastic channels. We further extend this framework to treat non-analytic and non-convergent behavior of inelastic amplitudes in the complex momentum plane and to incorporate bound states. For non-convergent amplitudes, we demonstrate a simple renormalization procedure in which anti-Hermitian separable potentials necessarily induce Hermitian separable counterterms, yielding finite cross sections consistent with unitarity. These results provide a general tool for non-relativistic scattering problems, with clear applications to dark-matter phenomenology.
SN - 1126-6708
SN - 1029-8479
ER -