ABSTRACT
Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at Zenodo.
ABSTRACT
Numerous theories extending beyond the standard model of particle physics predict the existence of bosons that could constitute dark matter. In the standard halo model of galactic dark matter, the velocity distribution of the bosonic dark matter field defines a characteristic coherence time τc. Until recently, laboratory experiments searching for bosonic dark matter fields have been in the regime where the measurement time T significantly exceeds τc, so null results have been interpreted by assuming a bosonic field amplitude Φ0 fixed by the average local dark matter density. Here we show that experiments operating in the T ⪠τc regime do not sample the full distribution of bosonic dark matter field amplitudes and therefore it is incorrect to assume a fixed value of Φ0 when inferring constraints. Instead, in order to interpret laboratory measurements (even in the event of a discovery), it is necessary to account for the stochastic nature of such a virialized ultralight field. The constraints inferred from several previous null experiments searching for ultralight bosonic dark matter were overestimated by factors ranging from 3 to 10 depending on experimental details, model assumptions, and choice of inference framework.
ABSTRACT
One of the simplest viable models for dark matter is an additional neutral scalar, stabilised by a Z 2 symmetry. Using the GAMBIT package and combining results from four independent samplers, we present Bayesian and frequentist global fits of this model. We vary the singlet mass and coupling along with 13 nuisance parameters, including nuclear uncertainties relevant for direct detection, the local dark matter density, and selected quark masses and couplings. We include the dark matter relic density measured by Planck, direct searches with LUX, PandaX, SuperCDMS and XENON100, limits on invisible Higgs decays from the Large Hadron Collider, searches for high-energy neutrinos from dark matter annihilation in the Sun with IceCube, and searches for gamma rays from annihilation in dwarf galaxies with the Fermi-LAT. Viable solutions remain at couplings of order unity, for singlet masses between the Higgs mass and about 300 GeV, and at masses above â¼ 1 TeV. Only in the latter case can the scalar singlet constitute all of dark matter. Frequentist analysis shows that the low-mass resonance region, where the singlet is about half the mass of the Higgs, can also account for all of dark matter, and remains viable. However, Bayesian considerations show this region to be rather fine-tuned.
