Gauge coupling unification and proton decay via 45 Higgs boson in SU(5) GUT

Abstract

We study the gauge coupling unification (GCU) and proton decay in a non-supersymmetric SU(5) grand unified theory (GUT) incorporating a 45 representation Higgs field. Our analysis is based on the assumption that Georgi-Jarlskog-type mass matrices for fermions are responsible for explaining the mass ratio of the strange quark and the muon. We examine the conditions of GCU, taking into account the possibility that certain components of the 45 Higgs field have masses much smaller than the GUT scale. We have found that to satisfy the GCU conditions, at least two components of the 45 Higgs field should have such small masses. We search the parameter space to identify regions where the GCU conditions are satisfied, in the scenarios where two or three components of the 45 Higgs boson are hierarchically light. If the colored Higgs component of the 45 Higgs boson has a mass much smaller than the GUT scale, proton decay via colored Higgs boson exchange can occur with an observably large rate. We estimate the mass bounds for the colored Higgs component from the proton decay search at Super- Kamiokande and thereby further restrict the parameter space.

Figures (5)

• Figure 1: Runnings of the gauge coupling constants that achieve GCU with two light components of the 45 Higgs field. The left panel is for the mass spectrum (1) and the right panel is for (2).
• Figure 2: The blue solid lines illustrate the solutions to the GCU conditions. In the left panel, the solutions are plotted on the $\overline{M}-M(8,2)$ plane, in the central panel, they are plotted on the $\overline{M}-M(\overline{3},3)$ plane, and in the right panel, they are plotted on the $M(8,2)-M(\overline{3},3)$ plane. The red dashed lines correspond to the constraint from the LHC that the mass of $(8,2)$ be larger than 1 TeV.
• Figure 3: Runnings of the gauge coupling constants, which realize GCU with three light components of 45 Higgs, are depicted for the mass spectrum (1) in the left panel and (2) in the right panel.
• Figure 4: Feynman diagram inducing proton decay via the exchange of $(\overline{3},1)_{1/3}$ in the 45 Higgs boson.
• Figure 5: Allowed region on the ${\overline M}$-$M(\overline{3},1)$ plane where GCU is realized and the proton lifetime bounds are satisfied, in the scenario where three components of the 45 Higgs boson are light. The colored region is allowed. The dashed lines correspond to the bounds on $M(\overline{3},1)$ obtained from various proton decay channels in Table \ref{['proton decay']}, of which the $p\rightarrow \bar{\nu}K^+$ mode gives the most stringent bound of $M(\overline{3},1)>3.4\times 10^{13}$ GeV. The left side of the colored region is excluded by the constraint from proton decay via the $XY$ gauge boson exchange, while the right side is excluded by the fact that $M(8,2)$ is smaller than the current bound set by the LHC.