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<p>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 <i>n</i> and <i>ℓ</i>, 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 <i>ℓ</i> = <i>n</i> – 1. This allows us to investigate in detail a strong enhancement of BSF that occurs for initial states in a repulsive potential. For <i>ℓ</i> = <i>n</i> – 1 ≫ 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.</p>

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Perturbative unitarity violation in radiative capture transitions to dark matter bound states

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月27日

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  • Martin Beneke,
  • Tobias Binder,
  • Lorenzo De Ros,
  • Mathias Garny,
  • Stefan Lederer

摘要

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 ℓ, 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 ℓ = n – 1. This allows us to investigate in detail a strong enhancement of BSF that occurs for initial states in a repulsive potential. For ℓ = n – 1 ≫ 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.