Unified Halo-Independent Analysis for Direct Dark Matter Searches

Sam Witte

IFIC

 

Conventional halo-independent analyses of direct dark matter detection data are subject to a number of caveats, typically limiting either the applicability or ease of interpretation. Using theorems from convex geometry, I will present a generalized halo-independent formalism that allows for the identification of the best-fit halo function and the construction of two-sided point-wise confidence bands, effectively removing the constraining caveats contained within prior analyses. Interestingly, this formalism naturally proves that any likelihood can always be maximized with either a dark matter speed distribution or a galactic velocity distribution consisting of a sum of a small identifiable number of delta functions. Lastly, I will show that enforcing the additional constraint that the dark matter velocity distribution be isotropic in the galactic frame leads to best-fit halo functions that are piecewise linear, differing significantly from the best-fit halo function obtained without the assumption of isotropy.