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Possibility of a Right-Handed (RH) neutrino being a Goldstone fermion of aspontaneously broken global $U(1)$ symmetry in a supersymmetric theory isconsidered. This fermion obtains mass from the supergravity effects leading toa RH neutrino at the electroweak scale with a mass similar to the gravitinomass. A prototype model realizing this scenario contains just three gaugesinglet superfields needed for the type I seesaw mechanism. Masses of the othertwo neutrinos are determined by the $U(1)$ breaking scale which too can bearound the electroweak scale. Light neutrinos obtain their masses in thisscenario through (a) mixing with the RH neutrinos (type I seesaw), (b) mixingwith neutralinos ($R$-parity breaking), (c) indirectly through mixing of the RHneutrinos with neutralinos, and (d) radiative corrections. All thesecontributions are described by the same set of a small number of underlyingparameters and provide a very constrained and predictive framework for theneutrino masses which is investigated in detail for various choices of $U(1)$symmetries. It is found that flavour independent $U(1)$ symmetries cannotdescribe neutrino masses if the soft supersymmetry breaking terms are flavouruniversal and one needs to consider flavour dependent symmetries. Considering aparticular example of $L_\mu - L_\tau$ symmetry, it is shown that viableneutrino masses and mixing can be obtained without introducing any flavourviolation in the soft sector. The leptonic couplings of Majoron are worked outin the model and shown to be consistent with various laboratory, astrophysicaland cosmological constraints. The neutrino data allows sizeable couplingsbetween the RH neutrinos and Higgsinos which can be used to probe thepseudo-Goldstone fermion at colliders through its displaced decay vertex.

Weak scale right-handed neutrino as pseudo-Goldstone fermion of spontaneously broken $U(1)_{L_\mu-L_\tau}$