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 μ problem by introducing a new gauge-singlet superfield S. We realize that a mechanism of neutrino mass suppression arises, based on the R-parity violating bilinear terms μ_iL_iH_u mixing neutrinos and higgsinos, offering thus an original approach to the neutrino mass problem (connected to the solution for the μ 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 |μ_i/μ| can reach ∼ 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 μ term, namely when those are generated via a VEV of the S scalar component from the couplings λ_iSL_iH_u. Finally, we make comments on some specific phenomenology of the NMSSM in the presence of R-parity violating bilinear terms.