Abstract
If dark matter has strong self-interactions, future astrophysical and cosmological observations, together with a clearer understanding of baryonic feedback effects, might be used to extract the velocity dependence of the dark matter scattering rate. To interpret such data, we should understand what predictions for this quantity are made by various models of the underlying particle nature of dark matter. In this paper, we systematically compute this function for fermionic dark matter with light bosonic mediators of vector, scalar, axial vector, and pseudoscalar type. We do this by matching to the nonrelativistic effective theory of self-interacting dark matter and then computing the spin-averaged viscosity cross section nonperturbatively by solving the Schrödinger equation, thus accounting for any possible Sommerfeld enhancement of the low-velocity cross section. In the pseudoscalar case, this requires a coupled-channel analysis of different angular momentum modes. We find, contrary to some earlier analyses, that nonrelativistic effects only provide a significant enhancement for the cases of light scalar and vector mediators. Scattering from light pseudoscalar and axial vector mediators is well described by tree-level quantum field theory.
Highlights
Dark matter self-interactions have been posited as a possible explanation for a number of discrepancies on small scales between observation and the results of classic N -body dark matter simulations of standard ΛCDM cosmology, such as the core/cusp problem [4, 5], the missing satellites problem [6, 7], the too-big-to-fail problem [8], and the diversity problem [9, 10]
Because the typical velocity of a dark matter particle is much lower in a dwarf galaxy than in a galaxy cluster, such observations could map out the velocity dependence of dark matter scattering, which encodes information about the underlying particle physics [17,18,19]
With such measurements in hand, we would naturally want to answer the inverse problem: what underlying model of dark matter self-interactions produces the observed velocity dependence of the cross section? This question is nontrivial because dark matter is nonrelativistic, and in the nonrelativistic limit low-velocity scattering can be nonperturbatively enhanced by the Sommerfeld effect [21]
Summary
Our goal in this paper is to calculate the velocity dependence of dark matter self-interactions for the case of spin-1/2 dark matter interacting via a light boson, which may be a scalar, pseudoscalar, vector, or axial vector. We find that the correct matching of a weakly-coupled effective field theory with a light pseudoscalar or axial vector mediator leads to a nonrelativistic effective theory in which there is no enhancement of the cross section at low velocities. For these theories, unlike the case of light scalar or vector mediators, tree-level QFT is reliable. Unlike the case of light scalar or vector mediators, tree-level QFT is reliable This simple result is in contrast with some earlier claims in the literature, for instance, in studies of annihilating dark matter with a pseudoscalar mediator [36, 37].
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