Can one have significant deviations from leptonic 3 $$\times $$ × 3 unitarity in the framework of type I seesaw mechanism?

Abstract

We address the question of deviations from 3 × 3 unitarity of the leptonic mixing matrix showing that, in the framework of type I seesaw mechanism, one may have significant deviations from unitarity that can be detected at the next round of experiments while some of the heavy neutrino masses are sufficiently low to become within experimental reach. For that purpose we introduce a specially useful parametrisation that enables to control all deviations of unitarity through a single 3 × 3 matrix, which we denote by X and which connects the mixing of the light and heavy neutrinos in the context of type I seesaw. We show that there is no need for the Yukawa couplings to be extremely suppressed. We present specific examples where deviations from 3 × 3 unitarity are sufficiently small to conform to all the present stringent experimental bounds.

Inverse seesaw model with global U(1)H symmetry

“…The constraint from nonunitarity can simply be obtained by considering the Hermitian matrix F ≡ M −1 m D . Combining several experimental results [24], the upper bounds are given by [25] jFF † j ≤ Since F is assumed to be diagonal, the stringent constraint originates from the 2-2 component of jFF † j. It suggests that jFj ∼ m D =M ≲ 10 −2 is always safe in our model thanks to the small VEV v 0 2 .…”

Unified SU(4) theory for the RD(*) and RKBalaji1, Schmidt2 2020Phys. Rev. D

“…We also impose the 3σ unitarity deviation bound derived from |2η αβ | as shown in Ref. [82] on |U U † |. The allowed regions are then constrained by the combination of Yukawa coupling ranges in conjunction with the Z → µµ constraint in Eq.…”

Type-I seesaw with eV-scale neutrinos

“…, one can obtain [30] a series of exact relations relating the matrices K, R, S, and Z, examples of which are KK † + RR † = 1 and KS † + RZ † = 0. We shall show that in order to study deviations of unitarity, it is useful to parametrise V in a different way.…”

“…In ref. [30] we introduced an especially useful parametrisation of the 6 × 6 leptonic mixing matrix that enables to control all deviations from unitarity through a single 3 × 3 matrix which connects the mixing of the active and sterile neutrinos in the context of type I seesaw. It was written:…”

“…The parameterisation we are using has recently been developed in ref. [30], where it was applied to a different spectra of heavy neutrinos, with all heavy neutrino masses at the TeV scale -a quasi-decoupled regime, as opposed to the decoupled/seesaw regime. We want to show that it is both possible and useful to apply this parameterisation to other spectra of heavy neutrinos, namely to a non-decoupled regime including light sterile neutrinos.…”