Enhanced Γ(p→K0μ+)/Γ(p→K+ ˉ ν μ) as a signature of minimal renormalizable SUSY SO (10) GUT

The ratio of the partial widths of some dimension-5 proton decay modes can be predicted without detailed knowledge of supersymmetric (SUSY) particle masses, and this allows us to experimentally test various SUSY grand unified theory (GUT) models without discovering SUSY particles. In this paper, we study the ratio of the partial widths of the p→K0μ+ and p→K+ν¯μ decays in the minimal renormalizable SUSY SO(10) GUT, under only a plausible assumption that the 1st- and 2nd-generation left-handed squarks are mass-degenerate. In the model, we expect that the Wilson coefficients of dimension-5 operators responsible for these modes are on the same order and that the ratio of p→K0μ+ and p→K+ν¯μ partial widths is O(0.1). Hence, we may be able to detect both p→K0μ+ and p→K+ν¯μ decays at Hyper-Kamiokande, thereby gaining a hint for the minimal renormalizable SUSY SO(10) GUT. Moreover, since this partial width ratio is quite suppressed in the minimal SU(5) GUT, it allows us to distinguish the minimal renormalizable SUSY SO(10) GUT from the minimal SU(5) GUT. In the main body of the paper, we perform a fitting of the quark and lepton masses and flavor mixings with the Yukawa couplings of the minimal renormalizable SO(10) GUT, and derive a concrete prediction for the partial width ratio based on the fitting results. We find that the partial width ratio generally varies in the range 0.05–0.6⁠, confirming the above expectation.