Sommerfeld Enhancement from Unstable Final State Particles in Dark Matter Annihilation

概要

We discuss the Sommerfeld enhancement of the annihilation cross section of dark matter into heavier unstable particles. In this process, the annihilation products become non-relativistic near the kinematical threshold. If they experience long-range interactions with each other, their wave function is distorted from a plane wave, and the annihilation cross section can be significantly enhanced. When evaluating the Sommerfeld enhancement from the long-range interactions between the annihilation products, the lifetime of the products needs to be taken into account. We formulate the Sommerfeld enhancement from the annihilation products by solving the Schroedinger equation with the decay width. We find that bound states of the annihilation products with a narrow decay width enhance the annihilation cross section because of a resonant effect. At the same time, this formulation automatically includes annihilation processes with off-shell final state particles, which is relevant for the wide decay width. We show that the resonant effect has an impact on the prediction of the dark matter relic abundance.

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