Perturbative Unitarity Violation in Radiative Capture Transitions to Dark Matter Bound States

Fuente: arXiv
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Main Authors: Beneke, Martin, Binder, Tobias, de Ros, Lorenzo, Garny, Mathias, Lederer, Stefan
Format: Preprint
Published: 2024
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author Beneke, Martin
Binder, Tobias
de Ros, Lorenzo
Garny, Mathias
Lederer, Stefan
author_facet Beneke, Martin
Binder, Tobias
de Ros, Lorenzo
Garny, Mathias
Lederer, Stefan
contents We investigate the formation of bound states of non-relativistic dark matter particles subject to long-range interactions through radiative capture. The initial scattering and final bound states are described by Coulomb potentials with different strengths, as relevant for non-abelian gauge interactions or theories featuring charged scalars. For bound states with generic quantum numbers $n$ and $\ell$, we provide closed-form expressions for the bound-state formation (BSF) cross sections of monopole, dipole and quadrupole transitions, and of arbitrary multipole order when $\ell=n-1$. This allows us to investigate in detail a strong enhancement of BSF that occurs for initial states in a repulsive potential. For $\ell=n-1\gg 1$, we show that the BSF cross section for each single bound state violates the perturbative unitarity bound in the vicinity of a certain critical initial velocity, and provide an interpretation in terms of a smooth matching of classical trajectories. When summing the BSF cross section over all possible bound states in the final state, this leads to a unitarity violation below a certain velocity, but within the validity range of the weakly coupled non-relativistic description. We identify an effectively strong interaction as the origin of this unitarity violation, which is caused by an "anomalously" large overlap of scattering and bound-state wave functions in Coulomb potentials of different strength.
format Preprint
id arxiv_https___arxiv_org_abs_2411_08737
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Perturbative Unitarity Violation in Radiative Capture Transitions to Dark Matter Bound States
Beneke, Martin
Binder, Tobias
de Ros, Lorenzo
Garny, Mathias
Lederer, Stefan
High Energy Physics - Phenomenology
Cosmology and Nongalactic Astrophysics
We investigate the formation of bound states of non-relativistic dark matter particles subject to long-range interactions through radiative capture. The initial scattering and final bound states are described by Coulomb potentials with different strengths, as relevant for non-abelian gauge interactions or theories featuring charged scalars. For bound states with generic quantum numbers $n$ and $\ell$, we provide closed-form expressions for the bound-state formation (BSF) cross sections of monopole, dipole and quadrupole transitions, and of arbitrary multipole order when $\ell=n-1$. This allows us to investigate in detail a strong enhancement of BSF that occurs for initial states in a repulsive potential. For $\ell=n-1\gg 1$, we show that the BSF cross section for each single bound state violates the perturbative unitarity bound in the vicinity of a certain critical initial velocity, and provide an interpretation in terms of a smooth matching of classical trajectories. When summing the BSF cross section over all possible bound states in the final state, this leads to a unitarity violation below a certain velocity, but within the validity range of the weakly coupled non-relativistic description. We identify an effectively strong interaction as the origin of this unitarity violation, which is caused by an "anomalously" large overlap of scattering and bound-state wave functions in Coulomb potentials of different strength.
title Perturbative Unitarity Violation in Radiative Capture Transitions to Dark Matter Bound States
topic High Energy Physics - Phenomenology
Cosmology and Nongalactic Astrophysics
url https://arxiv.org/abs/2411.08737