Mixing angles of quarks and leptons in quantum field theory

• Published in: The European physical journal. C, Particles and fields Vol. 61; no. 2; pp. 247 - 278
• Main Authors: Duret, Q., Machet, B., Vysotsky, M. I.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.05.2009; Springer Nature B.V; Springer Verlag (Germany)
• Subjects: Algebra; Astronomy; Astrophysics and Cosmology; Breaking; Broken symmetry; CP violation; Eigenvectors; Elementary Particles; Fermions; Field theory; Flavor (particle physics); Gauge invariance; Hadrons; Heavy Ions; High Energy Physics - Phenomenology; Leptons; Matrices; Matrices (mathematics); Measurement Science and Instrumentation; Neutral currents; Neutrinos; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum entanglement; Quantum Field Theories; Quantum Field Theory; Quantum theory; Quarks; Regular Article - Theoretical Physics; Standard model (particle physics); String Theory; Symmetry; 11.40.-q; 12.15.Ff; 12.15.Hh; 12.15.Mm; 14.60.Pq; 11.30.Hv; mixing angles; flavor symmetries; gauge symmetries and currents
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-009-1013-3

Arguments coming from Quantum Field Theory are supplemented with a 1-loop perturbative calculation to settle the non-unitarity of mixing matrices linking renormalized mass eigenstates to bare flavor states for non-degenerate coupled fermions. We simultaneously diagonalize the kinetic and mass terms and counterterms in the renormalized Lagrangian. SU (2) L gauge invariance constrains the mixing matrix in charged currents of renormalized mass states, for example the Cabibbo matrix, to stay unitary. Leaving aside CP violation, we observe that the mixing angles exhibit, within experimental uncertainty, a very simple breaking pattern of SU (2) f horizontal symmetry linked to the algebra of weak neutral currents, the origin of which presumably lies beyond the Standard Model. It concerns on the one hand the three quark mixing angles; on the other hand a neutrino-like pattern in which θ 23 is maximal and tan (2 θ 12 )=2. The Cabibbo angle fulfills the condition tan (2 θ c )=1/2 and θ 12 for neutrinos satisfies accordingly the “quark–lepton complementarity condition” θ c + θ 12 = π /4. θ 13 =±5.7⋅10 −3 are the only values obtained for the third neutrino mixing angle that lie within present experimental bounds. Flavor symmetries, their breaking by a non-degenerate mass spectrum, and their entanglement with the gauge symmetry, are scrutinized; the special role of flavor rotations as a very mildly broken symmetry of the Standard Model is outlined.