Origin of a two-loop neutrino mass from SU(5) grand unification

In this work we propose a renormalizable model based on the $SU(5)$ gauge group where neutrino mass originates at the two-loop level without extending the fermionic content of the Standard Model (SM). Unlike the conventional $SU(5)$ models, in this proposed scenario, neutrino mass is intertwined with the charged fermion masses. In addition to correctly reproducing the SM charged fermion masses and mixings, neutrino mass is generated at the quantum level, hence naturally explains the smallness of neutrino masses. In this setup, we provide examples of gauge coupling unification that simultaneously satisfy the proton decay constraints. This model has the potential to be tested experimentally by measuring the proton decay in the future experiments. Scalar leptoquarks that are naturally contained within this framework can accommodate the recent B-physics anomalies.

Figure 1

Left: Zee mechanism to generate neutrino mass at one-loop level. Right: Zee-Babu mechanism to generate neutrino mass at two-loop level.

Figure 2

Two-loop Feynman diagrams responsible for neutrino mass generation in our proposed renormalizable $\mathit{S}\mathit{U}(\mathbf{5})$ GUT. The propagators in red are the multiplets that belong to the $\mathbf{4}{\mathbf{0}}_{\mathit{H}}$ and $\mathbf{5}{\mathbf{0}}_{\mathit{H}}$ representations. For each of these diagrams, there is a second set of diagrams that can be achieved by replacing the multiplet by the associated multiplet shown in the parenthesis.

Figure 3

The behavior of the loop function given in Eq. (3.23) as a function of $r_{ca}^2={(\frac{m_c^{++}}{m_a^{+}})}^2$.

Figure 4

Here we present the plot of the gauge coupling unification in the MRSU5 model as discussed in the text.

Figure 5

Here we present the plots of the gauge coupling unification scenarios within our framework that are summarized in Table 3.