Abstract
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 ${m}_{\ensuremath{\chi}}\ensuremath{\simeq}10\text{ }\text{ }\mathrm{GeV}$ and mass splitting $\ensuremath{\delta}\ensuremath{\gtrsim}20\text{ }\text{ }\mathrm{keV}$, 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.
Highlights
For more than 15 years the DAMA collaboration [1,2,3,4] has been measuring a yearly modulation effect in a large– mass low–background sodium iodide target compatible to the signal of the dark matter (DM) particles that are believed to make up 27% of the total mass density of the Universe [5] and more than 90% of the halo of our Galaxy
Such model dependence has been shown to persist [7] after the bound from the COSINE–100 collaboration [8], that has recently published an exclusion plot for a standard elastic, spin-independent isoscalar weakly interacting massive particle (WIMP) nucleus interaction and a WIMP Maxwellian velocity distribution that for the first time rules out the DAMA effect at low WIMP masses using 106 kg of NaI, the same target of DAMA
In the present paper we have discussed the compatibility of the combined annual modulation effect measured by DAMA/LIBRA–phase1 and DAMA/LIBRA–phase2 [1,2,3,4] with an explanation in terms of inelastic scattering events induced by the most general Galilean-invariant effective contact interaction of a spin 0, 1=2 or 1 WIMP dark matter particle taking 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, following the approach introduced in Ref. [27]
Summary
For more than 15 years the DAMA collaboration [1,2,3,4] has been measuring a yearly modulation effect in a large– mass low–background sodium iodide target compatible to the signal of the dark matter (DM) particles that are believed to make up 27% of the total mass density of the Universe [5] and more than 90% of the halo of our Galaxy. Due to the large dimensionality, its direct scanning appears to be challenging this has been achieved by using matricial techniques [27], exploiting the fact that in terms of the couplings vector c 1⁄4 ðcð10Þ; cð11Þ; ...; cðn0Þ; cðn1ÞÞT for all direct detection experiments the expected event rate can be written in the form: event rate ∝ cTXc; ð2Þ where X is a real symmetric 2n × 2n matrix, which encodes all the information about nuclear responses, the dark matter velocity distribution, experimental efficiencies, etc., but which is independent of the underlying particle physics model (for a given dark matter mass) Due to this factorization in the effective field theory parameter space the surfaces of constant signal in different detectors are ellipsoids, and, as discussed in Refs. For completeness we summarize the response functions of a WIMP of spin ≤1 in Appendix A and we provide the details of our treatment of experimental constraints in Appendix B
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