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

TL;DR

This paper explores a supersymmetric model where a right-handed neutrino acts as a pseudo-Goldstone fermion from a spontaneously broken $U(1)_{L_L_ au}$ symmetry, leading to testable neutrino mass and mixing predictions.

Contribution

It introduces a novel scenario where the right-handed neutrino is a pseudo-Goldstone fermion, providing a constrained framework for neutrino masses with potential collider signatures.

Findings

Viable neutrino masses and mixings without flavor violation in the soft sector.

Consistent Majoron couplings with astrophysical and cosmological constraints.

Potential collider signals via displaced decay vertices of the pseudo-Goldstone fermion.

Abstract

Possibility of a Right-Handed (RH) neutrino being a Goldstone fermion of a spontaneously broken global $U(1)$ symmetry in a supersymmetric theory is considered. This fermion obtains mass from the supergravity effects leading to a RH neutrino at the electroweak scale with a mass similar to the gravitino mass. A prototype model realizing this scenario contains just three gauge singlet superfields needed for the type I seesaw mechanism. Masses of the other two neutrinos are determined by the $U(1)$ breaking scale which too can be around the electroweak scale. Light neutrinos obtain their masses in this scenario through (a) mixing with the RH neutrinos (type I seesaw), (b) mixing with neutralinos ($R$-parity breaking), (c) indirectly through mixing of the RH neutrinos with neutralinos, and (d) radiative corrections. All these contributions are described by the same set of a small number of underlying parameters and provide a very constrained and predictive framework for the neutrino masses which is investigated in detail for various choices of $U(1)$ symmetries. It is found that flavour independent $U(1)$ symmetries cannot describe neutrino masses if the soft supersymmetry breaking terms are flavour universal and one needs to consider flavour dependent symmetries. Considering a particular example of $L_\mu - L_\tau$ symmetry, it is shown that viable neutrino masses and mixing can be obtained without introducing any flavour violation in the soft sector. The leptonic couplings of Majoron are worked out in the model and shown to be consistent with various laboratory, astrophysical and cosmological constraints. The neutrino data allows sizeable couplings between the RH neutrinos and Higgsinos which can be used to probe the pseudo-Goldstone fermion at colliders through its displaced decay vertex.