Detectable dimension-6 proton decay in SUSY SO(10) GUT at Hyper-Kamiokande

In the minimal SUSY SU(5) GUT with $O(1)$ TeV SUSY particles and $O(1)$ or below self-coupling for the GUT-breaking Higgs field, the width of the dimension-6 proton decay is suppressed below the reach of Hyper-Kamiokande. In this paper, we point out that a SUSY SO(10) GUT which adopts only ${\bf 45}{\rm H}+{\bf 16}{\rm H}+{\bf \overline{16}}{\rm H}$ GUT-breaking Higgs fields leads to an enhanced dimension-6 proton decay width detectable at Hyper-Kamiokande. The enhancement is because the SU(5)-breaking VEV of ${\bf 45}{\rm H}$arisesduetoPlanck-suppressedterms,$W\propto ({\bf 45}{\rm H}^2)^2/M+{\bf 45}{\rm H}^4/M$, and is therefore substantially larger than the other VEVs that conserve SU(5). As a result, the $(\mathbf{3},\mathbf{2},1\mathrm{/}6)$ GUT gauge boson mass is about $1\mathrm{/}5$ smaller than the $(\mathbf{3},\mathbf{2},-5\mathrm{/}6)$ GUT gauge boson mass and can induce a fast dimension-6 proton decay. Through a numerical analysis on threshold corrections of the GUT gauge bosons and the physical components of the GUT-breaking Higgs fields, we confirm that the dimension-6 proton decay can be within the reach of Hyper-Kamiokande.