  The scattering of dark matter particles off nuclei in direct detection
experiments can be described in terms of a multidimensional effective field
theory (EFT). A new systematic analysis technique is developed using the EFT
approach and Bayesian inference methods to exploit, when possible, the
energy-dependent information of the detected events, experimental efficiencies,
and backgrounds. Highly dimensional likelihoods are calculated over the mass of
the weakly interacting massive particle (WIMP) and multiple EFT coupling
coefficients, which can then be used to set limits on these parameters and
choose models (EFT operators) that best fit the direct detection data.
Expanding the parameter space beyond the standard spin-independent isoscalar
cross section and WIMP mass reduces tensions between previously published
experiments. Combining these experiments to form a single joint likelihood
leads to stronger limits than when each experiment is considered on its own.
Simulations using two nonstandard operators (3 and 8) are used to test the
proposed analysis technique in up to five dimensions and demonstrate the
importance of using multiple likelihood projections when determining
constraints on WIMP mass and EFT coupling coefficients. In particular, this
shows that an explicit momentum dependence in dark matter scattering can be
identified.
