Halo-independent determination of the unmodulated WIMP signal in DAMA: the isotropic case

We present a halo-independent determination of the unmodulated signal corresponding to the DAMA modulation if interpreted as due to dark matter weakly interacting massive particles (WIMPs). First we show how a modulated signal gives information on the WIMP velocity distribution function in the Galactic rest frame, from which the unmodulated signal descends. Then we perform a mathematically-sound profile likelihood analysis in which we profile the likelihood over a continuum of nuisance parameters (namely, the WIMP velocity distribution). As a first application of the method, which is very general and valid for any class of velocity distributions, we restrict the analysis to velocity distributions that are isotropic in the Galactic frame. In this way we obtain halo-independent maximum-likelihood estimates and confidence intervals for the DAMA unmodulated signal. We find that the estimated unmodulated signal is in line with expectations for a WIMP-induced modulation and is compatible with the DAMA background+signal rate. Specifically, for the isotropic case we find that the modulated amplitude ranges between a few percent and about 25% of the unmodulated amplitude, depending on the WIMP mass.