Abstract: 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.

Abstract: As dark matter (DM) direct detection experiments continue to improve their sensitivity they will inevitably encounter an irreducible background arising from coherent neutrino scattering. This so-called “neutrino floor” may significantly reduce the sensitivity of an experiment to DM-nuclei interactions, particularly if the recoil spectrum of the neutrino background is approximately degenerate with the DM signal. This occurs for the conventionally considered spin-independent (SI) or spin-dependent (SD) interactions. In such case, an increase in the experiment's exposure by multiple orders of magnitude may not yield any significant increase in sensitivity. The typically considered SI and SD interactions, however, do not adequately reflect the whole landscape of the well-motivated DM models, which includes other interactions. Since particle DM has not been detected yet in laboratories, it is essential to understand and maximize the detection capabilities for a broad variety of possible models and signatures. In this work we explore the impact of the background arising from various neutrino sources on the discovery potential of a DM signal for a large class of viable DM-nucleus interactions and several potential futuristic experimental settings, with different target elements. For some momentum suppressed cross sections, large DM particle masses and heavier targets, we find that there is no suppression of the discovery limits due to neutrino backgrounds. Further, we explicitly demonstrate that inelastic scattering, which could appear in models with multicomponent dark sectors, would help to lift the signal degeneracy associated with the neutrino floor. This study could assist with mapping out the optimal DM detection strategy for the next generation of experiments.