An origin for small neutrino masses in the NMSSM
  We consider the Next to Minimal Supersymmetric Standard Model (NMSSM) which provides a natural solution to the so-called mu problem by introducing a new gauge-singlet superfield S. We realize that a new mechanism of neutrino mass suppression, based on the R-parity violating bilinear terms mu_i L_i H_u mixing neutrinos and higgsinos, arises within the NMSSM, offering thus an original solution to the neutrino mass problem (connected to the solution for the mu problem). We generate realistic (Majorana) neutrino mass values without requiring any strong hierarchy amongst the fundamental parameters, in contrast with the alternative models. In particular, the ratio |mu_i/mu| can reach about 10^-1, unlike in the MSSM where it has to be much smaller than unity. We check that the obtained parameters also satisfy the collider constraints and internal consistencies of the NMSSM. The price to pay for this new cancellation-type mechanism of neutrino mass reduction is a certain fine tuning, which get significantly improved in some regions of parameter space. Besides, we discuss the feasibility of our scenario when the R-parity violating bilinear terms have a common origin with the mu term, namely when those are generated via a VEV of the S scalar component from the couplings lambda_i S L_i H_u. Finally, we make comments on some specific phenomenology of the NMSSM in the presence of R-parity violating bilinear terms. 
Asmaa Abada and Gregory Moreau