Planck-Scale Effects on Nucleon Decay in Minimal Supersymmetric SU(5)

Abstract

We examine the impact on the phenomenology of the minimal supersymmetric SU(5) Grand Unified Theory (GUT) of dimension-5 operators with coefficients suppressed by the Planck mass scale, with particular emphasis on predictions for nucleon decay. We incorporate dimension-5 operators in both the Higgs sector and the Yukawa interactions in the theory, and take account of the constraints from gauge coupling measurements, the mass of the Higgs boson, fermion masses and the cold dark matter density. We consider two scenarios for soft supersymmetry breaking: the constrained minimal supersymmetric extension of the Standard Model (CMSSM) and the Non-Universal Higgs Model (NUHM). We present predictions for the nucleon decay modes $p \to π^0 e^+, π^0 μ^+, K^+ \bar ν, π^+ \bar ν$, $K^0 e^+, K^0 μ^+$ and $n\to π^0 \bar ν$, $π^- e^+, K^0 \bar ν$, which we compare with both the present experimental sensitivities and those projected for the JUNO and Hyper-Kamiokande experiments. We find that these experiments may have interesting possibilities for discovering several of these decay modes.

Figures (8)

• Figure 1: Left: GUT mass spectra and the dependences of nucleon lifetimes on $\lambda'$ in limit (i), where we set $\lambda=1$, $\kappa_1=0$. Right: GUT mass spectra and the dependences of nucleon lifetimes on $\kappa_1$ in limit (ii), where we set $\lambda=1$, $\lambda'=0$. The GUT phases $\varphi_i$ are assumed to vanish in both scenarios, and the supersymmetry parameters taken to be those of Point 1 given in Table \ref{['tab:point1']}. The color-coded solid lines in the lower panels are the calculated nucleon lifetimes, the shaded regions show the current constraints on the corresponding nucleon lifetimes, and the dashed lines show prospective Hyper-Kamiokande sensitivities.
• Figure 2: Left panels: dependences of proton lifetimes on $((r_{ql})_2, (r_{ql})_3)$ for point 1 with $(r_{ql})_1=(r_{qq})_i=(r_{ue})_i=1$. Right panels: dependences of proton lifetimes on $(r_{qq})_{2}, (r_{ql})_{i=1,2,3})$ for point 1 with $(r_{qq})_{i=1,3},(r_{ue})_{i=1,2,3}=1$. In both cases it is assumed that the GUT phases $\varphi_i=0$. The shaded areas show the current constraints from $p \to K^+ \bar{\nu}$ (top panels), $p \to \pi^+ \bar{\nu}$ (middle panels) and $n \to \pi^0 \bar{\nu}$ (bottom panels).
• Figure 3: Lower limits on $\lambda$ as functions of $(r_{ql})_i$ assuming $\lambda'=1$ (left panels) and upper limits on $\lambda'$ assuming $\lambda=1$ as functions of $(r_{ql})_i$ (right panels), for Benchmark point 1 (upper plots) and Benchmark point 2 (lower plots). We assume in all cases that the GUT phases $\varphi_i = 0$ and $(r_{qq})_i = (r_{ue})_i = 1$ . The solid lines correspond to the current experimental bounds and the dashed lines correspond to future proton decay sensitivities of Hyper-Kamiokande.
• Figure 4: Contours of the $p \to K^+ {\bar{\nu}}$ proton lifetime for Benchmark point 1 as functions of the $(c_{\Delta h,1})_i$ around the values yielding exact cancellation of $f_{QL,i}$. The left panels show the proton lifetimes when the GUT phases $\varphi_i=0$, whereas the right panels show the longest lifetimes found in scans over the phases $\varphi_i$. In the $((c_{\Delta h,1})_1, (c_{\Delta h,1})_2)$ plane, $(c_{\Delta h,1})_3$ is fixed to the value that yields an exact cancellation of $f_{QL,3}$, i.e., $(c_{\Delta h,1})_3=-\frac{\sqrt{2}}{5}\frac{1}{R}(f_e)_3$, and similarly for the other planes. In addition, we set $c_{\Delta h, 2}= c_{\Delta h,3} =c_{\Delta h,4} =0$.
• Figure 5: Contour plots of the proton lifetime for Benchmark point 1 as functions of $(c_{\Delta h,1})_3$. The values of $(c_{1,\Delta h})_{i=1,2}$ are chosen so that $f_{QL,i=1,2}$ are cancelled. The shaded areas depict the current limit from Super-Kamiokande, while the dashed lines represent the future sensitivities of Hyper-Kamiokande.