Unitarity violation and restoration in radiative bound-state formation

Abstract

State-of-the-art calculations motivated by dark matter exhibit severe violation of partial-wave unitarity in the non-relativistic regime in radiative bound-state-formation processes. It has been recently shown, in a model-independent fashion, that unitarity is restored by the proper resummation of the inelastic contributions to the self-energy of the incoming state. In this work, we first derive Kramers-like formulae for individual partial waves, demonstrating that existing calculations of bound-state formation severely violate unitarity. We then discuss how unitarity is restored through the resummation of the absorptive contributions to the incoming-state self-energy, generated by bound-state formation processes, taking into account their analytic structure in the complex momentum plane. Our results can be generalized to a variety of theories and employed in phenomenological studies, such as dark-matter freeze-out, indirect detection and self-interactions.

60 pages, 13 figures; revised version matches publication in JHEP

References in corpus (27)

• Sommerfeld factor for arbitrary partial wave processes
• Bound-state formation for thermal relic dark matter and unitarity
• Unitarity Bounds and the Cuspy Halo Problem
• Dark Matter's secret liaisons: phenomenology of a dark U(1) sector with bound states
• Dark-matter bound states from Feynman diagrams
• Self-healing of unitarity in effective field theories and the onset of new physics
• Self-consistent Calculation of the Sommerfeld Enhancement
• Radiative bound-state-formation cross-sections for dark matter interacting via a Yukawa potential
• Homeopathic Dark Matter, or how diluted heavy substances produce high energy cosmic rays
• Capture and Decay of Electroweak WIMPonium
• Asymmetric dark matter: residual annihilations and self-interactions
• Radiative bound-state formation in unbroken perturbative non-Abelian theories and implications for dark matter
• Indirect Detection of Self-Interacting Asymmetric Dark Matter
• Signals from dark atom formation in halos
• Higgs Enhancement for the Dark Matter Relic Density
• Higgs-mediated bound states in dark-matter models
• On Minimal Dark Matter coupled to the Higgs
• Dark Matter Bound State Formation in Fermionic $Z_2$ DM model with Light Dark Photon and Dark Higgs Boson
• Dark matter bound state formation via emission of a charged scalar
• Excited bound states and their role in dark matter production
• Indirect searches for dark matter bound state formation and level transitions
• Perturbative Unitarity of Strongly Interacting Massive Particle Models
• Bound states of WIMP dark matter in Higgs-portal models. Part I. Cross-sections and transition rates
• Bound states of WIMP dark matter in Higgs-portal models. Part II. Thermal decoupling
• Unitarity in the non-relativistic regime and implications for dark matter
• The role of unitarisation on dark-matter freeze-out via metastable bound states
• Unitarizing non-relativistic scattering