Cobimaximal lepton mixing from soft symmetry breaking

Abstract

Cobimaximal lepton mixing, i.e. ${\theta }_{23}=45^{\circ }$ and $\delta =\pm 90^{\circ }$ in the lepton mixing matrix $V$, arises as a consequence of $SV=V^{\ast }\mathcal{P}$, where $S$ is the permutation matrix that interchanges the second and third rows of $V$ and $\mathcal{P}$ is a diagonal matrix of phase factors. We prove that any such $V$ may be written in the form $V=URP$, where $U$ is any predefined unitary matrix satisfying $SU=U^{\ast }$, $R$ is an orthogonal, i.e. real, matrix, and $P$ is a diagonal matrix satisfying $P^2=\mathcal{P}$. Using this theorem, we demonstrate the equivalence of two ways of constructing models for cobimaximal mixing---one way that uses a standard $CP$ symmetry and a different way that uses a $CP$ symmetry including $\mu$--$\tau$ interchange. We also present two simple seesaw models to illustrate this equivalence; those models have, in addition to the $CP$ symmetry, flavour symmetries broken softly by the Majorana mass terms of the right-handed neutrino singlets. Since each of the two models needs four scalar doublets, we investigate how to accommodate the Standard Model Higgs particle in them.

16 pages, no figures

References in corpus (15)

• Theory and phenomenology of two-Higgs-doublet models
• Status of neutrino oscillations 2018: first hint for normal mass ordering and improved CP sensitivity
• Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity
• Mu-Tau Reflection Symmetry in Lepton Mixing and Neutrino Oscillations
• Global constraints on absolute neutrino masses and their ordering
• A precision constraint on multi-Higgs-doublet models
• A non-standard CP transformation leading to maximal atmospheric neutrino mixing
• Generalized $\mu$-$\tau$ symmetry and discrete subgroups of O(3)
• Origin of Constrained Maximal CP Violation in Flavor Symmetry
• Soft lepton-flavor violation in a multi-Higgs-doublet seesaw model
• Large CP Violation, Large Mixings of Neutrinos and Democratic-type Neutrino Mass Matrix
• Soft $A_4\to Z_3$ Symmetry Breaking and Cobimaximal Neutrino Mixing
• Cobimaximal Neutrino Mixing from $S_3\times Z_2$
• Large CP Violation, Large Mixings of Neutrinos and the $Z_3$ Symmetry
• A three-parameter model for the neutrino mass matrix

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