The neighborhood of the Standard Model: mixing angles and quark-lepton complementarity for three generations of non-degenerate coupled fermions

TL;DR

This paper explores deviations from unitarity in fermion mixing matrices, revealing patterns consistent with the Standard Model and suggesting potential physics beyond it, including specific neutrino mixing angles and quark-lepton complementarity.

Contribution

It extends previous analysis to three generations, identifying precise mixing angle relations and patterns that align with the Standard Model and hint at new physics.

Findings

CKM mixing angles match experimental precision

Neutrino-like mixing pattern with maximal theta_{23}

Two solutions for theta_{13} satisfying bounds

Abstract

We investigate the potential (small) deviations from the unitarity of the mixing matrix that are expected to occur, because of mass splittings, in the Quantum Field Theory of non-degenerate coupled systems. We extend our previous analysis concerning mixing angles, which led to a precise determination of the Cabibbo angle, to the case of three generations of fermions. We show that the same condition for neutral currents of mass eigenstates, i.e. that universality of diagonal currents is violated with the same strength as the absence of non-diagonal ones, is satisfied: on one hand, by the three CKM mixing angles with a precision higher than the experimental uncertainty; on the other hand, by a neutrino-like mixing pattern in which theta_{23} is maximal, and tan (2 theta_{12})=2. This last pattern turns out to satisfy exactly the "quark-lepton complementarity condition" theta_c + theta_{12}= pi/4. Moreover, among all solutions, two values for the third neutrino mixing angle arise which satisfy the bound sin^2(theta_{13}) < 0.1: theta_{13} = +/- 5.7 10^{-3} and theta_{13} = +/- 0.2717. The so-called "Neighborhood of the Standard Model" is thus confirmed to exhibit special patterns which presumably originate in physics "Beyond the Standard Model".