Inelastic dark matter with spin-dependent couplings to protons and large modulation fractions in DAMA

Abstract

We discuss a scenario where the DAMA modulation effect is explained by a Weakly Interacting Massive Particle (WIMP) which upscatters inelastically to a heavier state and predominantly couples to the spin of protons. In this scenario constraints from xenon and germanium targets are evaded dynamically, due to the suppression of the WIMP coupling to neutrons, while those from fluorine targets are evaded kinematically, 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. In this scenario WIMP scatterings off sodium are usually sensitive to the large-speed tail of the WIMP velocity distribution and modulated fractions of the signal close to unity arise in a natural way. On the other hand, a halo-independent analysis with more conservative assumptions about the WIMP velocity distribution allows to extend the viable parameter space to configurations where large modulated fractions are not strictly necessary. We discuss large modulated fractions in the Maxwellian case showing that they imply a departure from the usual cosine time dependence of the expected signal in DAMA. However we explicitly show that the DAMA data is not sensitive to this distortion, both in time and frequency space, even in the extreme case of a 100 % modulated fraction. Moreover the same scenario provides an explanation of the maximum in the energy spectrum of the modulation amplitude detected by DAMA in terms of WIMPs whose minimal incoming speed matches the kinematic threshold for inelastic upscatters. For the elastic case the detection of such maximum suggests an inversion of the modulation phase below the present DAMA energy threshold, while this is not expected for inelastic scattering. This may allow to discriminate between the two scenarios in a future low-threshold analysis of the DAMA data.

28 pages, 11 figures, updated to published version

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