Semi-Empirical Neutrino and Quark Mixing Angle Broken 4-Color Geometric Symmetry

TL;DR

This paper proposes a novel geometric and semi-empirical framework for understanding neutrino and quark mixing angles, predicting their values through a Pythagorean relation that aligns with experimental data, especially for N=3 colors.

Contribution

It introduces a new phenomenological quadratic Pythagorean equation linking quark and neutrino mixing angles, predicting their values with no free parameters and explaining experimental observations.

Findings

Predicts non-zero theta-13 neutrino angle consistent with recent data

Establishes N=3 as the number of quark colors for agreement with experiments

Provides a benchmark mixing pattern matching observed quark and neutrino angles

Abstract

Two semi-empirical ideas are guiding the present research: 1) one neutrino and N color quark triple mixing angles have second physical meaning of vector direction angles in euclidean 3-space, and 2) the difference between neutrino and quark mixing in the SM weak interactions is mostly conditioned by known fundamental difference of these particles by numbers of color degree of freedom. As main physical inference, the elementary particle mixing angles obey a novel phenomenological quark-neutrino (N+1)-color and 3 mixing angle symmetric positive definite quadratic Pythagorean equation in terms of double mixing angles. This equation predicts immediately that two large solar and atmospheric angles must be accompanied by one small not zero theta-13 neutrino angle in convincing agreement with recent new theta-13 experimental data. Benchmark flavor mixing pattern - united bimaximal neutrino and zero quark ones - follows from solutions of the primary equation without free parameters. Agreement with known experimental data follows only when the number of quark colors is equal to the number of particle flavors, N = 3. Together with closely related to the fine structure constant one empirical small parameter, that benchmark pattern determines realistic quark and neutrino mixing angles in good agreement with data and especially accurate for quark Cabibbo and neutrino solar angles. Coming accurate neutrino mixing angle data are important for testing the Pythagorean equation.