Witten's loop in the minimal flipped $SU(5)$ unification revisited

In the simplest potentially realistic renormalizable variants of the flipped $SU(5)$ unified model the right-handed neutrino masses are conveniently generated by means of the Witten's two-loop mechanism. As a consequence, the compactness of the underlying scalar sector provides strong correlations between the low-energy flavor observables such as neutrino masses and mixing and the flavor structure of the fermionic currents governing the baryon and lepton number violating nucleon decays. In this study, the associated two-loop Feynman integrals are fully evaluated and, subsequently, are used to draw quantitative conclusions about the central observables of interest such as the proton decay branching ratios and the absolute neutrino mass scale.