Probability Density Functions for CP-Violating Rephasing Invariants

Abstract

The implications of the anarchy principle on CP violation in the lepton sector are investigated. A systematic method is introduced to compute the probability density functions for the CP-violating rephasing invariants of the PMNS matrix from the Haar measure relevant to the anarchy principle. Contrary to the CKM matrix which is hierarchical, it is shown that the Haar measure, and hence the anarchy principle, are very likely to lead to the observed PMNS matrix. Predictions on the CP-violating Dirac rephasing invariant $|j_D|$ and Majorana rephasing invariant $|j_1|$ are also obtained. They correspond to $⟨|j_D|{⟩}_{\text{Haar}}=\pi /105\approx 0.030$ and $⟨|j_1|{⟩}_{\text{Haar}}=1/(6\pi )\approx 0.053$ respectively, in agreement with the experimental hint from T2K of $|j_D^{\text{exp}}|\approx 0.032\pm 0.005$ (or $\approx 0.033\pm 0.003$) for the normal (or inverted) hierarchy.

1+15 pages, 2 figures

References in corpus (10)

• Big-Bang Nucleosynthesis
• Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity
• Measurement of neutrino and antineutrino oscillations by the T2K experiment including a new additional sample of ${\nu }_e$ interactions at the far detector
• Rephasing Invariants of Quark and Lepton Mixing Matrices
• Neutrino Mass Priors for Cosmology from Random Matrices
• A composite parameterization of unitary groups, density matrices and subspaces
• Seesaw parametrization for n right-handed neutrinos
• Neutrino Mass Anarchy and the Universe
• Anarchy in the neutrino sector?
• A Probability Density Function for Neutrino Masses and Mixings

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• A Mellin Transform Approach to Rephasing Invariants
• ALP Anarchy