## A Mathematical Model of the Quark and Lepton Mixing Angles

**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}
be
maximal, a framework is defined possessing just two free parameters. A mixing model is then specified using values for these two parameters that derive from the solution to a simple equation, where this solution also accurately reproduces the fine structure constant. The resultant model, which is entirely free from parameters adjusted to fit the mixing data, possesses the following angles *θ*_{23} = 2*.*367442^{◦},
*θ*_{13} =
0*.*190986^{◦},
*θ*_{12} =
12*.*920966^{◦},
*ϕ*_{23} = maximal, *ϕ*_{13} = 0*.*013665^{◦}, and *ϕ*_{12} = 33*.*210911^{◦}, which fit the experimental quark and lepton mixing angles. At the time of its introduction in 2007, this model had a 7*.*0σ disagreement with the value for *|**V*_{ub}*|*, whereas a revised value for *|**V*_{ub}*|
*from the same source now yields a disagreement of just 1*.*6σ.

**Comments:** 15 pages

**Download:** **PDF**

### Submission history

[v1] 30 Jul 2010

**Unique-IP document downloads:** 135 times

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