High Energy Particle Physics


Underlying Symmetry Among the Quark and Lepton Mixing Angles (Nine Year Update)

Authors: J. S. Markovitch

In 2007 a single mathematical model encompassing both quark and lepton mixing was described. This model exploited the fact that when a $3 \times 3$ rotation matrix whose elements are squared is subtracted from its transpose, a matrix is produced whose non-diagonal elements have a common absolute value, where this value is an intrinsic property of the rotation matrix. For the traditional CKM quark mixing matrix with its second and third rows interchanged (i.e., c - t interchange) this value equals one-third the corresponding value for the leptonic matrix (roughly, 0.05 versus 0.15). This model is distinguished by three such constraints on mixing. As nine years have elapsed since its introduction, it is timely to assess the accuracy of the model's six mixing angles. In 2012 a large experimental conflict with leptonic angle $\theta_{13}$ required toggling the sign of one of the model's integer exponents; this change did not significantly impair the model's economy, where it is just this economy that makes the model notable. There followed a nearly fourfold improvement in the accuracy of the measurement of leptonic $\theta_{13}$. Despite this much-improved measurement, and despite much-improved measurements for three other mixing angles since the model's introduction in 2007, no other conflicts have emerged. The model's mixing angles in degrees are 45, 33.210911, 8.034394 (originally 0.013665) for leptons; and 12.920966, 2.367442, 0.190986 for quarks.

Comments: 9 Pages.

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[v1] 2016-12-29 13:15:23

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