Phenomenological relations for quark and neutrino mixing angles
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EMENTARY PARTICLES AND FIELDS Theory
Phenomenological Relations for Quark and Neutrino Mixing Angles Yu. V. Gaponov, V. V. Khruschov, and S. V. Semenov Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia Received December 22, 2006; in final form, March 29, 2007
Abstract—The most recent experimental data on quark and neutrino mixing angles are discussed. It is indicated that the results of the latest kaon-decay experiments are consistent with the unitarity condition for the first row of the Cabibbo–Kobayashi–Maskawa matrix if the currently available world-average value of the neutron lifetime is used to determine the element Vud of this matrix. The quark mixing angles are calculated within the Fritzsch–Scadron–Delbourgo–Rupp phenomenological approach on the basis of values of the masses of light and heavy constituent quarks. The neutrino mixing angles are calculated to a high precision with the aid of the hypothesis that the quark and neutrino mixing angles are complementary. The results are compatible with experimental data. PACS numbers: 14.60.Pq, 12.10.Dm, 14.40.Aq DOI: 10.1134/S1063778808010171
1. INTRODUCTION Among unsolved problems of the standard model of electroweak and strong interactions, that of clarifying the nature of the mixing of quark and neutrino states, along with calculating specific values of mixing angles consistent with experimental data, is one of the most important. A great many theoretical studies that propose various approaches (see, for example, the review articles in [1–4]) were devoted to this problem, but a decisive solution has yet to be obtained. There is every reason to believe that the required solution will be found upon extending the Standard Model by including new elements that are necessary for describing phenomena beyond the Standard Model, such as neutrino oscillations. An exhaustive solution to the problem of mixing of quark and neutrino states is expected to appear in Grand Unified Theories, whose ultimate version has yet to be developed. By studying various relationships between the quark and lepton mixing angles, one can get an idea of the lines along which the Standard Model may be developed. Phenomenological rules observed in the quark and lepton sectors of the Standard Model—in particular, the hypothesis of mutual complementarity of the corresponding mixing angles of quarks and neutrinos—indicate that the mixing of states may be due to a physical reason common to the above particles. The discovery of such facts could contribute to clarifying ways to extend the Standard Model and to construct subsequently Grand Unified Theories. From this point of view, it is of interest to verify experimentally phenomenological relations for mixing
angles to the highest possible degree of precision, on one hand, and to study feasible interpretations of these relations within the existing models and the dependences of mixing angles on other parameters of the theory (for example, on the masses of fundamental particles), on the other hand. Since the Standard M
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