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Flipped SU(5) GUT Phenomenology: Proton Decay and $g_μ-2$

We consider proton decay and $g_μ- 2$ in flipped SU(5) GUT models. We first study scenarios in which the soft supersymmetry-breaking parameters are constrained to be universal at some high scale $M_{in}$ above the standard GUT scale where the QCD and electroweak SU(2) couplings unify. In this case the proton lifetime is typically $\gtrsim 10^{36}$~yrs, too long to be detected in the foreseeable future, and the supersymmetric contribution to $g_μ- 2$ is too small to contribute significantly to resolving the discrepancy between the experimental measurement and data-driven calculations within the Standard Model. However, we identify a region of the constrained flipped SU(5) parameter space with large couplings between the 10- and 5-dimensional GUT Higgs representations where $p \to e^+ π^0$ decay may be detectable in the Hyper-Kamiokande experiment now under construction, though the contribution to $g_μ-2$ is still small. A substantial contribution to $g_μ- 2$ is possible, however, if the universality constraints on the soft supersymmetry-breaking masses are relaxed. We find a `quadrifecta' region where observable proton decay co-exists with a (partial) supersymmetric resolution of the $g_μ- 2$ discrepancy and acceptable values of $m_h$ and the relic LSP density.