Unitarity Bounds and the Cuspy Halo Problem

TL;DR

The paper addresses the cusp-core problem by testing whether quantum unitarity can constrain self-interacting and strongly annihilating dark matter scenarios. It uses the optical theorem and a partial-wave analysis to derive general, microphysics-agnostic bounds on scattering: $\sigma_{\rm tot} \le 16\pi/(m_X v_{\rm rel})^2$ and $\sigma_{\rm inel.} v_{\rm rel} \le 4\pi/(m_X^2 v_{\rm rel})$, which translate into mass limits $m_X \lesssim 12$ GeV for SIDM and $m_X \lesssim 25$ GeV for SADM at cluster velocities. Moreover, the analysis shows that efficient annihilation implies a nonzero elastic cross-section via $\sigma_{\rm el.} \gtrsim (\pi/k_1^2)[1-\sqrt{1-k_1^2\sigma_{\rm ann.}/\pi}]^2$, and that velocity-dependent cross-sections such as $\sigma \propto 1/v_{\rm rel}$ likely require inelastic or super-elastic processes, with important implications for halo structure and phenomenology. The results constrain viable microphysics for SIDM/SADM, highlight the need to account for inelastic channels in predictions, and guide future model-building and experimental searches.

Abstract

Conventional Cold Dark Matter cosmological models predict small scale structures, such as cuspy halos, which are in apparent conflict with observations. Several alternative scenarios based on modifying fundamental properties of the dark matter have been proposed. We show that general principles of quantum mechanics, in particular unitarity, imply interesting constraints on two proposals: collisional dark matter proposed by Spergel & Steinhardt, and strongly annihilating dark matter proposed by Kaplinghat, Knox & Turner. Efficient scattering required in both implies m < 12 GeV and m < 25 GeV respectively. The same arguments show that the strong annihilation in the second scenario implies the presence of significant elastic scattering, particularly for large enough masses. Recently, a variant of the collisional scenario has been advocated to satisfy simultaneously constraints from dwarf galaxies to clusters, with a cross section that scales inversely with velocity. We show that this scenario likely involves super-elastic processes, and the associated kinetic energy change must be taken into account when making predictions. Exceptions and implications for experimental searches are discussed.