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

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1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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^2theta {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-.

Author: ** Quentin Duret - Bruno Machet - **

Source: https://hal.archives-ouvertes.fr/