A new mechanism of neutrino mass generation in the NMSSM with broken lepton number

In the Minimal Supersymmetric Standard Model with bilinear R-parity violation, only one neutrino eigenstate acquires a mass at tree level, consequently experimental data on neutrinos cannot be accommodated at tree level. We show that in the next-to-minimal extension, where a gauge singlet superfield is added to primarily address the so-called μ-problem, it is possible to generate two massive neutrino states at tree level. Hence, the global three-flavour neutrino data can be reproduced at tree level, without appealing to loop dynamics which is vulnerable to model-dependent uncertainties. We give analytical expressions for the neutrino mass eigenvalues and present examples of realistic parameter choices.