Flipped SU(5) GUT phenomenology: proton decay and $$\mathbf {g_\mu - 2}$$

We consider proton decay and $$g_\mu - 2$$ 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 $$M_{in}$$ M in above the standard GUT scale where the QCD and electroweak SU(2) couplings unify. In this case the proton lifetime is typically $$ > rsim 10^{36}$$ ≳ 10 36 years, too long to be detected in the foreseeable future, and the supersymmetric contribution to $$g_\mu - 2$$ 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 $$p \rightarrow e^+ \pi ^0$$ p → e + π 0 decay may be detectable in the Hyper-Kamiokande experiment now under construction, though the contribution to $$g_\mu -2$$ g μ - 2 is still small. A substantial contribution to $$g_\mu - 2$$ 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 $$g_\mu - 2$$ g μ - 2 discrepancy and acceptable values of $$m_h$$ m h and the relic LSP density.