Halo-independent bounds on Inelastic Dark Matter

We discuss halo-independent constraints on the Inelastic Dark Matter (IDM) scenario, in which a Weakly Interaction Massive Particle (WIMP) state $\chi$ with mass $m_\chi$ interacts with nuclear targets by upscattering to a heavier state $\chi^{\prime}$ with mass $m_\chi+\delta$. In order to do so we adopt the single-stream method, that exploits the complementarity of Direct Detection (DD) and Capture in the Sun to extend the experimental sensitivity to the full range of incoming WIMP speeds. We show that a non-vanishing mass splitting $\delta$ modifies such range, and that for particular combinations of $m_\chi$ and $\delta$ the complementarity between the two detection techniques required by the method is lost. Specifically, assuming for the escape velocity in our Galaxy $u_{esc}$ the reference value $u_{esc}^{ref}$ = 560 km/s a halo-independent bound is possible when $\delta\lesssim$ 510 keV for a Spin-Independent interaction and when $\delta\lesssim$ 245 keV for a Spin-Dependent interaction (with the Spin-Independent value slightly reduced to $\delta\lesssim$ 490 keV when $u_{esc}>u_{esc}^{ref}$). In the low-mass regime the bound from capture in the Sun is always more constraining than that for DD and is sufficient alone to provide a halo-independent constraint, while for large WIMP masses the halo-independent bound is given by a combination of capture in the Sun and DD. We also find that, for $u_{esc}$ = $u_{esc}^{ref}$, unless the mass of the target used in DD is larger than about four times that of the target driving capture in the Sun, DD does not play any role in the determination of the maximal value of $\delta$ for which a halo-independent bound is possible. We also discuss the issue of thermalization of IDM within the Sun and show that its impact on our results is mild.