Unitarizing non-relativistic scattering
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913011043663872 |
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| author | Flores, Marcos M. Petraki, Kalliopi |
| author_facet | Flores, Marcos M. Petraki, Kalliopi |
| contents | 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, unique and complete unitarization scheme in the non-relativistic regime. We present two alternative derivations of the anti-Hermitian kernel, from the continuity equation combined with LSZ reduction, and by integrating out inelastic channels. We further extend the unitarization 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 two renormalization procedures 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, with clear applications to dark-matter phenomenology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_02097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unitarizing non-relativistic scattering Flores, Marcos M. Petraki, Kalliopi High Energy Physics - Phenomenology High Energy Physics - Theory 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, unique and complete unitarization scheme in the non-relativistic regime. We present two alternative derivations of the anti-Hermitian kernel, from the continuity equation combined with LSZ reduction, and by integrating out inelastic channels. We further extend the unitarization 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 two renormalization procedures 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, with clear applications to dark-matter phenomenology. |
| title | Unitarizing non-relativistic scattering |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.02097 |