High Energy Particle Physics


A Mathematical Model of the Quark and Lepton Mixing Angles (2011 Update)

Authors: J. S. Markovitch

A single mathematical model encompassing both quark and lepton mixing is described. This model exploits the fact that when a 3 × 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). By imposing this and two additional related constraints on mixing, and letting leptonic φ23 equal 45°, a framework is defined possessing just two free parameters. A mixing model is then specified using values for these two parameters that derive from an equation that reproduces the fine structure constant. The resultant model, which possesses no constants adjusted to fit experiment, has mixing angles of θ23 = 2.367445°, θ13 = 0.190987°, θ12 = 12.920966°, φ23 = 45°, φ13 = 0.013665°, and φ12 = 33.210911°. A fourth, newly-introduced constraint of the type described above produces a Jarlskog invariant for the quark matirx of 2.758 ×10−5. Collectively these achieve a good fit with the experimental quark and lepton mixing data. The model predicts the following CKM matrix elements: |Vus| = √0.05 = 2.236 × 10−1, |Vub| = 3.333 × 10−3, and |Vcb| = 4.131 × 10−2. For leptonic mixing the model predicts sin2φ12 = 0.3, sin2φ23 = 0.5, and sin2φ13 = 5.688 × 10−8. At the time of its 2007 introduction the model's values for |Vus| and |Vub| had disagreements with experiment of an improbable 3.6σ and 7.0σ, respectively, but 2010 values from the same source now produce disagreements of just 2.4σ and 1.1σ, the absolute error for |Vus| having been reduced by 53%, and that for |Vub| by 78%.

Comments: 18 Pages.

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Submission history

[v1] 14 Feb 2011
[v2] 10 Apr 2011
[v3] 2011-12-21 14:11:28

Unique-IP document downloads: 303 times

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