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.
