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

Understand

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.