Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form

doi:10.1088/1674-1137/34/10/001

Chinese Physics C> 2010, Vol. 34> Issue(10) : 1547-1555 DOI: 10.1088/1674-1137/34/10/001

Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form

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Abstract：
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_μ/m_τ)²)≈3.5×10^－3 from
their HPS values.

Assuming that (m_μ/m_τ)² can be neglected, we derive two simple constraints on the four parameters θ₁₂, θ₂₃, θ₃₁, and δ 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 μ parts of the mapping matrix have a definite form governed by two parameters α and β; any deviation of order m_μ/m_τ can be accommodated by adjusting these two parameters.

References

[1]

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Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form[J]. Chinese Physics C, 2010, 34(10): 1547-1555. doi: 10.1088/1674-1137/34/10/001

Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form[J]. Chinese Physics C, 2010, 34(10): 1547-1555. doi: 10.1088/1674-1137/34/10/001 shu

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Received: 2010-08-02
Revised: 2010-08-03

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form

Received Date: 2010-08-02

Accepted Date: 2010-08-03

Available Online: 2010-10-05

Abstract:

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_μ/m_τ)²)≈3.5×10^－3 from
their HPS values.

Assuming that (m_μ/m_τ)² can be neglected, we derive two simple constraints on the four parameters θ₁₂, θ₂₃, θ₃₁, and δ 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 μ parts of the mapping matrix have a definite form governed by two parameters α and β; any deviation of order m_μ/m_τ can be accommodated by adjusting these two parameters.

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Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form

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