Scalar-induced Neutrinoless Double Beta Decay in $SU(5)$

Abstract

We discuss the role of heavy scalar fields in mediating neutrinoless double beta decay $(0\nu\beta\beta)$ within the $SU(5)$ Grand Unified Theory framework, extended suitably to include neutrino mass. In such a minimal realistic $SU(5)$ setup for fermion masses, the scalar contributions to $0\nu\beta\beta$ are extremely suppressed as a consequence of the proton decay bound. We circumvent this problem by imposing a discrete ${\cal Z}_3$ symmetry. However, the scalar contributions to $0\nu\beta\beta$ remain suppressed in this $SU(5) \times {\cal Z}_3$ model due to the neutrino mass constraint. We find that the $0\nu\beta\beta$ contribution can be enhanced by extending the scalar sector with an additional $\mathbf{15}$-dimensional scalar representation with suitable ${\cal Z}_3$ charge. Such an extension not only yields realistic fermion mass spectra but also leads to experimentally testable predictions in upcoming ton-scale $0\nu\beta\beta$ searches, which can be used as a sensitive probe of the new scalars across a broad range, from LHC-accessible scales up to $\sim 10^{10}\,\text{GeV}$.