**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 φ_{23} 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
θ_{23} = 2.367445^{°},
θ_{13} = 0.190987^{°},
θ_{12} = 12.920966^{°},
φ_{23} = 45^{°},
φ_{13} = 0.013665^{°}, and
φ_{12} = 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:
|V_{us}| = √0.05 = 2.236 × 10^{−1},
|V_{ub}| = 3.333 × 10^{−3}, and
|V_{cb}| = 4.131 × 10^{−2}.
For leptonic mixing the model predicts
sin^{2}φ_{12} = 0.3,
sin^{2}φ_{23} = 0.5, and
sin^{2}φ_{13} = 5.688 × 10^{−8}.
At the time of its 2007 introduction the model's values for |V_{us}| and
|V_{ub}| 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 |V_{us}| having been
reduced by 53%, and that for |V_{ub}| by 78%.

**Comments:** 18 Pages.

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[v1] 14 Feb 2011

[v2] 10 Apr 2011

[v3] 2011-12-21 14:11:28

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