Deviations of the Lepton Mapping Matrix from the Harrison-Perkins-Scott Form

Details Deviations of the Lepton Mapping Matrix from the Harrison-Perkins-Scott Form Deviations of the Lepton Mapping Matrix from the Harrison-Perkins-Scott Form

2010-08-03

arxiv.org/abs/1008.0453v3

Chin.Phys.C34:1547-1555,2010; Erratum-ibid.C34:1905,2010

Physics

High Energy Physics

High Energy Physics - Phenomenology

31 pages, 2 figures

Scientific paper

10.1088/1674-1137/34/12/022

We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott (HPS) form. These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector. The perturbing matrix is assumed to be purely imaginary (thus maximally $T$-violating) and to have a strength in energy scale no greater (but perhaps smaller) than the muon mass. As we shall show, it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than $O((m_\mu/m_\tau)^2) \simeq 3.5 \times 10^{-3}$ from their HPS values. Assuming that $(m_\mu/m_\tau)^2 $ can be neglected, we derive two simple constraints on the four parameters $\theta_{12}$, $\theta_{23}$, $\theta_{31}$, and $\delta$ of the mapping matrix. These constraints are independent of the details of the imaginary $T$-violating perturbation of the charged lepton mass matrix. We also show that the $e$ and $\mu$ parts of the mapping matrix have a definite form governed by two parameters $\alpha$ and $\beta$; any deviation of order $m_\mu/m_\tau $ can be accommodated by adjusting these two parameters.

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