Perturbative Unitarity Violation in Radiative Capture Transitions to Dark Matter Bound States
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| Format: | Preprint |
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2024
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| _version_ | 1866929589724381184 |
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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 |
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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 |