The new $(g-2)_\mu$ and Right-Handed Sneutrino Dark Matter

In this paper we investigate the $(g-2)_\mu$ discrepancy in the context of the R-parity conserving next-to-minimal supersymmetric Standard Model plus right-handed neutrinos superfields. The model has the ability to reproduce neutrino physics data and includes the interesting possibility to have the right-handed sneutrino as the lightest supersymmetric particle and a viable dark matter candidate. Since right-handed sneutrinos are singlets, no new contributions for $\delta a_{\mu}$ with respect to the MSSM and NMSSM are present. However, the possibility to have the right-handed sneutrino as the lightest supersymmetric particle opens new ways to escape Large Hadron Collider and direct detection constraints. In particular, we find that dark matter masses within $10 \lesssim m_{\tilde{\nu}_{R}} \lesssim 600$ GeV are fully compatible with current experimental constraints. Remarkably, not only spectra with light sleptons are needed, but we obtain solutions with $m_{\tilde{\mu}} \gtrsim 600$ GeV in the entire dark matter mass range that could be probed by new $(g-2)_\mu$ data in the near future. In addition, dark matter direct detection experiments will be able to explore a sizable portion of the allowed parameter space with $m_{\tilde{\nu}_{R}} \lesssim 300$ GeV, while indirect detection experiments will be able to probe a much smaller fraction within $200 \lesssim m_{\tilde{\nu}_{R}} \lesssim 350$ GeV.