Probing DAMA/LIBRA data in the full parameter space of WIMP effective models of inelastic scattering

We discuss the compatibility of the combined annual modulation effect measured by DAMA/LIBRA- phase1 and DAMA/LIBRA-phase2 with an explanation in terms of inelastic scattering events induced by the most general Galilean-invariant effective contact interaction of a weakly interacting massive particle (WIMP) dark matter particle of spin 0, 1/2 or 1. We take into account all the possible interferences among operators by studying the intersections among the ellipsoidal surfaces of constant signal of DAMA and other experiments in the space of the coupling constants of the effective theory. In our analysis we assume a standard Maxwellian velocity distribution in the Galaxy. We find that, compared to the elastic case, inelastic scattering partially relieves but does not eliminate the existing tension between the DAMA effect and the constraints from the null results of other experiments. Such tension is very large in all the parameter space with the exception of a small region for WIMP mass m(chi) similar or equal to 10 GeV and mass splitting delta greater than or similar to 20 keV, where it is partially, but not completely relieved. In such region the bounds from fluorine targets are evaded in a kinematic way because the minimal WIMP incoming speed required to trigger upscatters off fluorine exceeds the maximal WIMP velocity in the Galaxy, or is very close to it. As a consequence, we also find that the residual tension between DAMA and other results is considerably more sensitive on the astrophysical parameters compared to the elastic case. We find that the configurations with the smallest tension can produce enough yearly modulation in some of the DAMA bins in compliance with the constraints from other experiments, but the ensuing shape of the modulation spectrum is too steep compared to the measured one. For such configurations the recent COSINE-100 bound is evaded in a natural way due to their large expected modulation fractions.