Abstract:We perform a detailed analysis of ∆(6n 2 ) family symmetry combined with a generalised CP symmetry in the lepton sector, breaking to different remnant symmetries G ν in the neutrino and G l in the charged lepton sector, together with different remnant CP symmetries in each sector. We discuss the resulting mass and mixing predictions for G ν = Z 2 with G l = K 4 , Z p , p > 2 and G ν = K 4 with G l = Z 2 . All cases correspond to the preserved symmetry smaller than the full Klein symmetry, as in the semi-direct approach, leading to predictions which depend on a single undetermined real parameter, which mainly determines the reactor angle. We focus on five phenomenologically allowed cases for which we present the resulting predictions for the PMNS parameters as a function of n, as well as the predictions for neutrinoless double beta decay.

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, ∆(6n 2 ) = (Z n × Z n ) S 3 . In direct models the mixing angles and Dirac CP phase are solely predicted from symmetry. ∆(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 π. The Majorana phases are predicted from residual flavour and CP symmetries where α 21 can take several discrete values for each n and the Majorana phase α 31 is a multiple of π. 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. *

We propose a model for CP violating oscillations of neutral, heavy-flavored baryons into antibaryons at rates which are within a few orders of magnitude of their lifetimes. The flavor structure of the baryon violation suppresses neutron oscillations and baryon number violating nuclear decays to experimentally allowed rates. We also propose a scenario for producing such baryons in the early Universe via the out-of-equilibrium decays of a neutral particle, after hadronization but before nucleosynthesis. We find parameters where CP violating baryon oscillations at a temperature of a few MeV could result in the observed asymmetry between baryons and antibaryons. Furthermore, part of the relevant parameter space for baryogenesis is potentially testable at Belle II via decays of heavy flavor baryons into an exotic neutral fermion. The model introduces four new particles: three light Majorana fermions and a colored scalar. The lightest of these fermions is typically long lived on collider timescales and may be produced in decays of bottom and possibly charmed hadrons.

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