In the next-to-minimal supersymmetric Standard Model (NMSSM) with extra heavy neutrino superfields, a neutrino may 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 a likelihood function with LHC Higgs data, B-physics measurements, DM relic density and its direct and indirect search limits, and perform a comprehensive scan over the parameter space of the theory by the 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, especially the Higgsino mass $\mu$ can be below about 250 GeV for a significant part of the region, which predicts $Z$ boson mass in a natural way. We also find that the DM usually coannihilated with the Higgsinos to get the measured relic density, and consequently the DM-nucleon scattering rate is naturally suppressed to coincide with the recent XENON-1T results even for light Higgsinos. Other issues, such as the LHC search for the Higgsinos, are also addressed.

• Received 4 December 2018

DOI:https://doi.org/10.1103/PhysRevD.99.115033

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Published by the American Physical Society