Determination of the mixing between active neutrinos and sterile neutrino through the quark-lepton complementarity and self-complementarity

TL;DR

This paper explores the relationship between quark and lepton mixing matrices, proposing that sterile neutrinos cause observable deviations from expected symmetries, and derives specific mixing parameters consistent with experimental data.

Contribution

It introduces a model linking quark-lepton complementarity to sterile neutrino mixing, providing new relations and parameter estimates at the electroweak scale.

Findings

Estimated sterile neutrino mixing matrix elements: |U_{e4}|^2=0.040, |U_{μ4}|^2=0.009

Discovered a new self-complementarity relation summing to approximately 90°

Results align with recent experimental measurements and do not conflict with LEP data.

Abstract

It is suggested that there is an underlying symmetry which relates the quark and lepton sectors. Namely, among the mixing matrix elements of CKM for quarks and PMNS for leptons there exist complementarity relations at a high energy scale (such as the see-saw or even the GUT scales). Assuming that the relations would remain during the matrix elements running down to the EW scale. Observable breaking of the rational relation is attributed to existence of sterile neutrinos which mix with the active neutrino to result in the observable PMNS matrix. We show that involvement of a sterile in the (3+1) model, induces that $|U_{e4}|^2= 0.040$, $|U_{\mu4}|^2= 0.009$ and $\sin^2 2\alpha=0.067$. We also find a new self-complementarity $\vartheta_{12}+\vartheta_{23}+\vartheta_{13}+\alpha\approx90^\circ$. The numbers are generally consistent with those obtained by fitting recent measurements, especially in this scenario, the existence of a sterile neutrino does not upset the LEP data i.e. the number of neutrino types is very close to 3.