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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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