Low-Energy Probes of No-Scale SU(5) Super-GUTs

We explore the possible values of the $\mu \rightarrow e \gamma $ branching ratio, $\text {BR}(\mu \rightarrow e\gamma )$, and the electron dipole moment (eEDM), $d_e$, in no-scale SU(5) super-GUT models with the boundary conditions that soft supersymmetry-breaking matter scalar masses vanish at some high input scale, $M_\mathrm{in}$, above the GUT scale, $M_{\mathrm{GUT}}$. We take into account the constraints from the cosmological cold dark matter density, $\Omega _{CDM} h^2$, the Higgs mass, $M_h$, and the experimental lower limit on the lifetime for $p \rightarrow K^+ \bar{\nu }$, the dominant proton decay mode in these super-GUT models. Reconciling this limit with $\Omega _{CDM} h^2$ and $M_h$ requires the Higgs field responsible for the charge-2/3 quark masses to be twisted, and possibly also that responsible for the charge-1/3 and charged-lepton masses, with model-dependent soft supersymmetry-breaking masses. We consider six possible models for the super-GUT initial conditions, and two possible choices for quark flavor mixing, contrasting their predictions for proton decay with versions of the models in which mixing effects are neglected. We find that $\tau \left( p\rightarrow K^+ \bar{\nu }\right) $ may be accessible to the upcoming Hyper-Kamiokande experiment, whereas all the models predict $\text {BR}(\mu \rightarrow e\gamma )$ and $d_e$ below the current and prospective future experimental sensitivities or both flavor choices, when the dark matter density, Higgs mass and current proton decay constraints are taken into account. However, there are limited regions with one of the flavor choices in two of the models where $\mu \rightarrow e$ conversion on a heavy nucleus may be observable in the future. Our results indicate that there is no supersymmetric flavor problem in the class of no-scale models we consider.