Very light right-handed (RH) sneutrinos in the Next-to-Minimal Supersymmetric Standard Model can be viable candidates for cold dark matter. We investigate the prospects for their direct detection, addressing their compatibility with the recent signal observed by the CoGeNT detector, and study the implications for Higgs phenomenology. We find that in order to reproduce the correct relic abundance very light RH sneutrinos can annihilate into either a fermion-antifermion pair, very light pseudoscalar Higgses or RH neutrinos. If the main annihilation channel is into fermions, we point out that RH sneutrinos could naturally account for the CoGeNT signal. Furthermore, the lightest Higgs has a very large invisible decay width, and in some cases the second-lightest Higgs too. On the other hand, if the RH sneutrino annihilates mostly into pseudoscalars or RH neutrinos the predictions for direct detection are below the current experimental sensitivities and satisfy the constraints set by CDMS and XENON. We also calculate the gamma ray flux from RH sneutrino annihilation in the Galactic centre, including as an interesting new possibility RH neutrinos in the final state. These are produced through a resonance with the Higgs and the resulting flux can exhibit a significant Breit-Wigner enhancement.
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