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

TL;DR

This work investigates neutrinoless double beta decay within a realistic $SU(5)$ grand unified framework, focusing on heavy scalar mediation and the tension with proton decay bounds. A ${\cal Z}_3$ symmetry is introduced to suppress dangerous diquark couplings, achieving viable fermion masses but leaving scalar-induced $0\nu\beta\beta$ subdominant due to the large $\Delta$-triplet mass required for neutrino masses. The authors then show that adding a decoupled extra $\mathbf{15}_H$ (with a triplet $\Delta_2$) can enhance the scalar contribution to $0\nu\beta\beta$, allowing interference effects with the standard light-neutrino contribution and enabling sensitivity to scalar masses across a wide range, from TeV scales to ~$10^{10}$ GeV. They provide quantitative fits to fermion masses, demonstrate that the canonical $m_{ee}^{\text{std}}$ remains the dominant term in many cases, and identify regions where the non-standard piece is important or even cancels, making ton-scale experiments like nEXO and LEGEND-1000 crucial probes of the extended scalar sector. Overall, the paper illustrates how carefully chosen scalar content in a GUT can yield testable predictions for $0\nu\beta\beta$ and connects high-scale physics to near-future experimental reach.

Abstract

We discuss the role of heavy scalar fields in mediating neutrinoless double beta decay $(0νββ)$ 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 $0νββ$ 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 $0νββ$ remain suppressed in this $SU(5) \times {\cal Z}_3$ model due to the neutrino mass constraint. We find that the $0νββ$ 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 $0νββ$ searches, which can be used as a sensitive probe of the new scalars across a broad range, from LHC-accessible scales up to $\sim 10^{10}\,\text{GeV}$.

Figures (10)

• Figure 1: The canonical effective operator that contributes to $0\nu\beta\beta$ . Left: SM interactions. Right: LEFT operator after integrating out the $W_L$ boson.
• Figure 2: Effective operators that contribute to $0\nu\beta\beta$ in the considered $SU(5)\times {\cal Z}_3$ model. Left: Diagrams contributing to $0\nu\beta\beta$ generated by the $SU(5)$ scalars. The number outside the bracket denote the $SU(5)$ representation while the labels in the bracket denote the field under SM charges. Right: The LEFT operator corresponding to the left diagrams after integrating out the heavy scalar fields.
• Figure 3: Left:$0\nu\beta\beta$ process where both vertices contain SM interaction terms $\left( j^\mu_{V-A}\,J_{V-A\;\mu}\right)$. Right:$0\nu\beta\beta$ process where one of the SM interaction vertices in the left diagram is replaced by the non standard operators ($j_{i}\,J^{i}$) generated from $SU(5)$ scalars.
• Figure 4: Variation of $\Delta\chi^2$ with $\left(Y_{15}\right)_{11}$ (left panels) and $\left(Y_{45}\right)_{11}$ (right panels) in the range of $(-3.5, 3.5)$. The top panel is for Case-I with real $Y_{15}$, while the bottom panel is for Case-II with complex $Y_{15}$. The cyan (purple)-colored points represent the normal (inverted) mass ordering.
• Figure 5: Variation of $m_{ee}^{\rm eff}$ as a function of lightest neutrino mass obtained from the fermion mass fitting in our $SU(5)$ model with fixed leptoquark masses $M_{S_3}=2$ TeV, $M_{R_2}=2.5$ TeV, $M_{\tilde{R}_2}=10^3$ TeV. The left (right) panel is for Case-I (II). The gray and pink regions show the allowed ranges for NO and IO in the standard $0\nu\beta\beta$ mechanism. The teal and orange bands show the current KamLAND-Zen limit and future LEGEND-1000 sensitivity, respectively. The vertical lines show the direct (KATRIN) and indirect (Planck, DESI) limits on the absolute neutrino mass.