Maximal CP Violation Hypothesis and a Lepton Mixing Matrix

TL;DR

This paper explores the maximal CP violation hypothesis applied to a lepton mixing matrix combining CKM and tribimaximal mixing, showing how phase conventions influence the predicted mixing angles.

Contribution

It demonstrates that the maximal CP violation hypothesis can restore the predicted lepton mixing angle to its tribimaximal value by choosing the Kobayashi-Maskawa phase convention.

Findings

The predicted b2  in tribimaximal mixing is affected by the CKM matrix.

Applying the hypothesis with the original phase convention recovers the b2  value.

The phase convention choice is crucial for the prediction accuracy.

Abstract

Maximal CP violation hypothesis is applied to a simple lepton mixing matrix form U=V_{CKM}^\dagger U_{TB}, which has recently been speculated under an ansatz that U becomes an exact tribimaximal mixing U_{TB} in a limit of the quark mixing matrix V_{CKM} \to {\bf 1}. The prediction \tan^2 \theta_{12} =1/2 in the case of the exact tribimaximal mixing U=U_{TB} is onsiderably spoiled in the speculated mixing U=V_{CKM}^\dagger U_{TB}. However, the application of the hypothesis to the lepton sector can again recover the spoiled value to \tan^2 \theta_{12} \simeq 1/2 if the original Kobayashi-Maskawa phase convention for V_{CKM} is adopted.