A Bayesian analysis of sneutrino DM in the NMSSM with Type-I seesaw mechanism

In the Next-to-Minimal Supersymmetric Standard Model (NMSSM) with extra heavy neutrino superfields, neutrino can acquire its mass via a seesaw mechanism and sneutrino may act as a viable dark matter (DM) candidate. Given the strong tension between the naturalness for $Z$ boson mass and the DM direct detection experiments for customary neutralino DM candidate, we augment the NMSSM with Type-I seesaw mechanism, which is the simplest extension of the theory to predict neutrino mass, and study the scenarios of sneutrino DM. We construct likelihood function with B-physics measurements, LHC Higgs data, DM relic density and its direct and indirect search limits, and perform a comprehensive scan over the parameter space of the theory by Nested Sampling method. We adopt both Bayesian and frequentist statistical quantities to illustrate the favored parameter space of the scenarios, the DM annihilation mechanism as well as the features of DM-nucleon scattering. We find that the scenarios are viable over broad parameter regions,and the DM usually co-annihilated with the Higgsinos to get the measured relic density. Interestingly, our results indicate that a rather low Higgsino mass, $\mu \lesssim 250 {\rm GeV}$, is preferred in the scan, and the DM-nucleon scattering rate is naturally suppressed to coincide with the recent XENON-1T results. Other issues, such as the LHC search for the Higgsinos, are also addressed.