Asymptotic Analysis on Binned Likelihood and Neutrino Floor

Observations of suspected coherent elastic neutrino-nucleus scatterings by dark matter direct detection experiments highlight the need for an investigation into the so-called "neutrino floor". We focus on the discovery limit, a statistical concept to identify the neutrino floor, and analyze the asymptotic behaviour of the profile binned likelihood ratio test statistic where the likelihood is constructed by variate from events in each bin and pull terms from neutrino fluxes. To achieve the asymptotic result, we propose two novel methods: i) Asymptotic-Analytic method, which furnishes the analytic result for large statistics, is applicable for more extra nuisance parameters, and enables the identification of the most relevant parameters in the statistical analysis; ii) Quasi-Asimov dataset, which is analogous to Asimov dataset but with improved speed. Applying our methods to the neutrino floor, we significantly accelerate the computation procedure compared to the previous literature, and successfully address cases where Asimov dataset fails. Our derivation on the asymptotic behavior of the test statistic not only facilitates research into the impact of neutrinos on the search for dark matter, but may also prove relevant in similar application scenarios.