Renormalizable SU(5) unification

We propose a simple renormalizable grand unified theory based on the SU(5) gauge symmetry where the neutrino masses are generated at the quantum level through the Zee mechanism. In this model the same Higgs needed to correct the mass relation between charged leptons and down-type quarks plays a crucial role in generating neutrino masses. We show that in this model one can satisfy the constraints coming from the unification of gauge couplings and the mechanism for neutrino masses is discussed in detail. The predictions for proton decay are discussed in order to understand the testability at current and future experiments such as Hyper-Kamiokande. This simple theory predicts a light colored octet which could give rise to exotic signatures at the LHC.

Figure 1

$B-L$ violating proton decay contribution.

Figure 2

Unification constraints shown by the blue line when $M_{H_2}=1\mathrm{TeV}$. The dashed green line shows the naive LHC bound on the colored octet mass, $M_{{\mathrm{\Phi }}_1}>3.1\mathrm{TeV}$ [25]. The red dashed line shows the limit on the GUT scale from the current experimental value on proton decay lifetime, ${\tau }_p(p\to {\pi }^0{e}^{+})>1.29\times 10^{34}$ years [26]. The orange dashed line shows the projected limit on the proton decay lifetime from the Hyper-Kamiokande Collaboration, ${\tau }_p(p\to {\pi }^0{e}^{+})>1.3\times 10^{35}$ years [27]. The mass of the ${\mathrm{\Phi }}_3$ is in the range $10^{8.6}–10^{8.9}\mathrm{GeV}$ from left to right.

Figure 3

Predictions for the proton decay lifetimes. The blue line shows the predictions for the decay $p\to {\pi }^0{e}^{+}$, while the purple line shows the predictions for the decay $p\to K^{+}\overline{\nu }$. The horizontal red dashed line shows the current experimental value on proton decay lifetime, ${\tau }_p(p\to {\pi }^0{e}^{+})>1.29\times 10^{34}$ years [26] from the Super-Kamiokande Collaboration. The orange dashed line shows the projected limit on the proton decay lifetime from the Hyper-Kamiokande Collaboration, ${\tau }_p(p\to {\pi }^0{e}^{+})>1.3\times 10^{35}$ years [27]. The green vertical line represents the LHC bound, $M_{{\mathrm{\Phi }}_1}\ge 3.1\mathrm{TeV}$ [25], on the colored octet mass.