Phenomenological Consequences of sub-leading Terms in See-Saw Formulas

TL;DR

This paper analyzes next-to-leading order corrections in see-saw neutrino mass models, generalizing the formalism to various see-saw types and identifying phenomenologically relevant effects, including unitarity violations and scenarios with negligible corrections.

Contribution

It extends the calculation of NLO corrections to diverse see-saw variants and explores their phenomenological implications, including effects on neutrino masses and unitarity.

Findings

NLO effects are negligible in standard type I see-saw with very heavy fermions.

Percent-level effects can occur with moderate hierarchies in the mass matrix.

Unitarity violation can be systematically calculated within the formalism.

Abstract

Several aspects of next-to-leading (NLO) order corrections to see-saw formulas are discussed and phenomenologically relevant situations are identified. We generalize the formalism to calculate the NLO terms developed for the type I see-saw to variants like the inverse, double or linear see-saw, i.e., to cases in which more than two mass scales are present. In the standard type I case with very heavy fermion singlets the sub-leading terms are negligible. However, effects in the percent regime are possible when sub-matrices of the complete neutral fermion mass matrix obey a moderate hierarchy, e.g. weak scale and TeV scale. Examples are cancellations of large terms leading to small neutrino masses, or inverse see-saw scenarios. We furthermore identify situations in which no NLO corrections to certain observables arise, namely for mu-tau symmetry and cases with a vanishing neutrino mass. Finally, we emphasize that the unavoidable unitarity violation in see-saw scenarios with extra fermions can be calculated with the formalism in a straightforward manner.