Low-mass constraints on WIMP effective models of inelastic scattering using the Migdal effect

We use the Migdal effect to extend to low masses the bounds on each of the effective couplings of the non-relativistic effective field theory of a WIMP of mass $m_\chi$ and spin 1/2 that interacts inelastically with nuclei by either upscattering to a heavier state with mass splitting $\delta>0$ or by downscattering to a lighter state with $\delta<0$. In order to do so we perform a systematic analysis of the Migdal bounds in the $m_\chi-\delta$ parameter space comparing them to those from nuclear recoil searches. The Migdal effect allows to significantly extend to low WIMP masses the nuclear recoil bounds for $\delta<0$. In this case the bounds are driven by XENON1T, except when $\delta$ is vanishing or very small, when, depending on the WIMP-nucleus interaction, in the lower end of the $m_\chi$ range either DS50 or SuperCDMS are more constraining. On the other hand, when $\delta>0$ and the WIMP particle upscatters to a heavier state nuclear recoil bounds are stronger than those from the Migdal effect.