Assessing Compatibility of Direct Detection Data: Halo-Independent Global Likelihood Analyses

Understand

We present two different halo-independent methods to assess the compatibility of several direct dark matter detection data sets for a given dark matter model using a global likelihood consisting of at least one extended likelihood and an arbitrary number of Gaussian or Poisson likelihoods.

• In the first method we find the global best fit halo function (we prove that it is a unique piecewise constant function with a number of down steps smaller than or equal to a maximum number that we compute) and construct a two-sided pointwise confidence band at any desired confidence level, which can then be compared with those derived from the extended likelihood alone to assess the joint compatibility of the data.
• In the second method we define a "constrained parameter goodness-of-fit" test statistic, whose $p$-value we then use to define a "plausibility region" (e.g.
• where $p \geq 10\%$).