Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2009-10-29
JCAP 1002:028,2010
Physics
High Energy Physics
High Energy Physics - Phenomenology
33 pages, 5 figures, final published version. v2 corrects an error in Eq. 4.7, adds an explanatory figure, and clarifies and e
Scientific paper
10.1088/1475-7516/2010/02/028
We present an analysis of the Sommerfeld enhancement to dark matter annihilation in the presence of an excited state, where the interaction inducing the enhancement is purely off-diagonal, such as in models of exciting or inelastic dark matter. We derive a simple and accurate semi-analytic approximation for the s-wave enhancement, which is valid provided the mass splitting between the ground and excited states is not too large, and discuss the cutoff of the enhancement for large mass splittings. We reproduce previously derived results in the appropriate limits, and demonstrate excellent agreement with numerical calculations of the enhancement. We show that the presence of an excited state leads to generically larger values of the Sommerfeld enhancement, larger resonances, and shifting of the resonances to lower mediator masses. Furthermore, in the presence of a mass splitting the enhancement is no longer a monotonic function of velocity: the enhancement where the kinetic energy is close to that required to excite the higher state can be up to twice as large as the enhancement at zero velocity.
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