Abstract
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.
Highlights
Though not a genuine grand unified theory (GUT), the flipped SUð5Þ gauge theory [1,2,3] still attracts significant attention [4,5,6,7] due to several rather unique features it exhibits
It is clear from Eq (19) that, since I3ðsÞ is bounded, Icannot be made arbitrarily large to compensate for the suppression factors noted in Sec
To develop some sense of the allowed size of I, it is useful to substitute for si from Eq (B7) and inspect Ias a function of ν, λ2, λ5, and g5, neglecting all terms that are of the order of v2
Summary
Though not a genuine grand unified theory (GUT), the flipped SUð5Þ gauge theory [1,2,3] still attracts significant attention [4,5,6,7] due to several rather unique features it exhibits. Besides enlarging the scalar sector enormously (and, disposing of the uniquely small size of the “minimal” Higgs sector noted above as one of the most attractive structural features of the framework), the extra scalar and the associated Yukawa at play reduces the value of the low-energy neutrino masses and the lepton mixing data as constraints for the proton lifetime estimates as it essentially leaves the neutrino sector on its own Enough, this dichotomy may be overcome by noticing [12,13] that the RH neutrino masses in flipped SUð5Þ models may be generated even without the unpleasant extra 50S at the two-loop level by means of a variant of the mechanism first identified by Witten in the SOð10Þ context [14]. Most of the technical details of the lengthy calculations are deferred to a set of Appendices
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