Lepton Mixing Predictions including Majorana Phases from $\Delta (6n^2)$ Flavour Symmetry and Generalised CP

Abstract

Generalised CP transformations are the only known framework which allows to predict Majorana phases in a flavour model purely from symmetry. For the first time generalised CP transformations are investigated for an infinite series of finite groups, $\Delta (6n^2)=(Z_n\times Z_n)⋊S_3$. In direct models the mixing angles and Dirac CP phase are solely predicted from symmetry. $\Delta (6n^2)$ flavour symmetry provides many examples of viable predictions for mixing angles. For all groups the mixing matrix has a trimaximal middle column and the Dirac CP phase is 0 or $\pi$. The Majorana phases are predicted from residual flavour and CP symmetries where ${\alpha }_{21}$ can take several discrete values for each $n$ and the Majorana phase ${\alpha }_{31}$ is a multiple of $\pi$. We discuss constraints on the groups and CP transformations from measurements of the neutrino mixing angles and from neutrinoless double-beta decay and find that predictions for mixing angles and all phases are accessible to experiments in the near future.

16 pages, 8 figures; references added; clarification in section 2.3 added; results are unchanged

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