%0 Journal Article
%T Unified halo-independent formalism from convex hulls for direct dark matter searches
%A Gelmini, G. B.
%A Huh, J. H.
%A Witte, S. J.
%J Journal of Cosmology and Astroparticle Physics
%D 2017
%V 12
%N 12
%I Iop Publishing Ltd
%@ 1475-7516
%G English
%F Gelmini_etal2017
%O WOS:000418922000002
%O exported from refbase (https://references.ific.uv.es/refbase/show.php?record=3440), last updated on Wed, 10 Jan 2018 08:55:54 +0000
%X Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1-speed distribution F(v) in Earth's frame or 2-Galactic velocity distribution f(gal) ((u) over right arrow), consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is (N-1), where N is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is N. Using time-averaged rates, the aforementioned form of F(v) results in a piecewise constant unmodulated halo function (eta) over tilde (BF)-B-0 (v(min)) (which is an integral of the speed distribution) with at most (N-1) downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, however, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise con fi dence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of f(gal) ((u) over right arrow), which is a sum of Galactic streams, yields a periodic time-dependent halo function (eta) over right arrow BF (v(min); t) which at any fixed time is a piecewise constant function of v(min) with at most N downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Finally, we show that requiring an isotropic Galactic velocity distribution leads to a Galactic speed distribution F(u)that is once again a sum of delta functions, and produces a time-dependent (eta) over tilde BF (v(min); t) function (and a time-averaged (eta) over tilde (0) BF (v(min))) that is piecewise linear, di ff ering significantly from best-fit halo functions obtained without the assumption of isotropy.
%K dark matter experiments
%K dark matter theory
%R 10.1088/1475-7516/2017/12/039
%U http://arxiv.org/abs/1707.07019
%U https://doi.org/10.1088/1475-7516/2017/12/039
%P 039-33pp