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Sommerfeld factor for arbitrary partial wave processes · Around

2009

Sommerfeld factor for arbitrary partial wave processes

Cassel, S.

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The Sommerfeld factor for arbitrary partial wave processes is derived in the non-relativistic limit.

The s-wave and p-wave numerical results are presented for the case of Yukawa interactions.
An approximate analytic expression is also found for the Sommerfeld factor of Yukawa interactions with arbitrary partial waves, which is exact in the Coulomb limit.
It is demonstrated that this result is accurate to within 10% for some common scenarios.

Built on

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R. L. Greene and C. Aldrich, “Variational wave functions for a screened Coulomb potential,” Phys. Rev. A 14
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G. A. Natanzon, “General properties of potentials for which the Schrodinger equation can be solved by means of hypergeometric functions,” Theor. Math. Phys. 38
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Similar

V. B. Berestetskii, E. M. Lifshitz and L. P. Pitaevskii, “Quantum Electrodynamics,” Oxford, UK: Pergamon (1982) 652 P. (Course Of Theoretical Physics, 4)
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S. Cassel, D. M. Ghilencea and G. G. Ross, “Electroweak and Dark Matter Constraints on a Z’ in Models with a Hidden Valley,” arXiv:0903.1118 [hep-ph]
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R. Iengo, “Sommerfeld enhancement: general results from field theory diagrams,” arXiv:0902.0688 [hep-ph]
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R. Iengo, “Sommerfeld enhancement for a Yukawa potential,” arXiv:0903.0317 [hep-ph]
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Cited in the paper.

Then

M. Cirelli, A. Strumia and M. Tamburini, “Cosmology and Astrophysics of Minimal Dark Matter,” Nucl. Phys. B 787
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2007
Later among the works it cites.
F. Brau and F. Buisseret, “Existence of mesons after deconfinement,” Phys. Rev. C 76
2007
Later among the works it cites.
J. March-Russell, S. M. West, D. Cumberbatch and D. Hooper, “Heavy Dark Matter Through the Higgs Portal,” JHEP 0807
Original
2008
Later among the works it cites.
N. Arkani-Hamed, D. P. Finkbeiner, T. Slatyer and N. Weiner, “A Theory of Dark Matter,” Phys. Rev. D 79
Original
2009
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