Abstract
Dark matter self-scattering is one of key ingredients for small-scale structure of the Universe, while dark matter annihilation is important for the indirect measurements. There is a strong correlation between the velocity-dependent self-scattering cross section and the Sommerfeld enhancement factor for the dark matter annihilation cross section. In this study, we formulate a direct relation between them by the use of Watson’s (initial state/final state) theorem and Omnès solution, and our formulation reproduces the Sommerfeld enhancement factor, which directly computed by solving the Schrödinger equation, from the scattering phase shift.
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Acknowledgments
A. K. acknowledges partial support from Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan, 18K13535 and 19H04609; from World Premier International Research Center Initiative (WPI), MEXT, Japan; from Norwegian Financial Mechanism for years 2014-2021, grant nr 2019/34/H/ST2/00707; and from National Science Centre, Poland, grant 2017/26/E/ST2/00135 and DEC-2018/31/B/ST2/02283. The work of T. K. is supported in part by the National Science Foundation of China under Grant Nos. 11675002, 11635001, 11725520, 12235001, and 12250410248.
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Kamada, A., Kuwahara, T. & Patel, A. Quantum theory of dark matter scattering. J. High Energ. Phys. 2023, 105 (2023). https://doi.org/10.1007/JHEP11(2023)105
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DOI: https://doi.org/10.1007/JHEP11(2023)105