Nonzero Theta13 and Neutrino Mixing Deviation from Bimaximal Geometric Symmetry

   Science is a human enterprise facing primary Nature. As a result, beside successfully created (by physicists) theories, mistakes happen and also serendipitous achievements that carry deep physical meaning. By that reasoning, meaningful discoveries can be made by ordinary people, physicists-thinkers, though with much less probability than by geniuses.                                                                   Neutrino physics is especially interesting at present time. Consider the following Equation for neutrino mixing angles

 cos^2(2Theta12) + cos^2(2Theta23) + cos^2(2Theta13) = 1 + sin^2(2Theta13).        (1) 

   This Equation for the three neutrino mixing angles is interesting. The goal of the present very short Note is to point out its rich neutrino flavor mixing phenomenology with important inferences.  

  1). At the approximation of zero second term at right in (1), neutrino mixing is bimaximal and that Equation means exact geometric symmetry of neutrino mixing double-angles: -- there exists in Euclidean geometry 3-space a vector with direction angles phi1 = (2Theta12), phi2 = (2Theta23) and phi3 = (2Theta13). In addition, this geometric approximation for neutrino mixing angles is bimaximal, and the deviation of realistic neutrino mixing angles from bimaximal one is small, see (4).

 2). Only two neutrino mixing angles are independent free empirical parameters since the Equation (1) determines neutrino reactor Theta13 angle by the two other solar and atmospheric ones (empirical data parameters) by a very simple formula  

                            cos(4Theta13) = 1 - cos^2(2Theta12) - cos^2(2Theta23)               (2)                        with prediction

                                                          Theta13 = ~ 8^o.                                               (3)

From (3) it follows

                                          sin^2(2Theta13) << cos^2(2Theta13).                                (4)

   The quantitative prediction for the Theta13 magnitude (3) is in good agreement with data and should be further supported by coming new neutrino data. 

  3). Thus Eq (1) may be unique, it has deep meaning in neutrino physics. It is phenomenological attractive and supported by data. Geometric symmetry of the leading bimaximal approximation is violated naturally at realistic neutrino mixing.                    


  10/12/16   Existence

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