Lepton mixing predictions including Majorana phases fromΔ(6n2)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, ∆(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. *

Lepton mixing in A 5 family symmetry and generalized CP

“…In the case that G ν = K 4 and G l is capable of distinguishing the three generations (i.e.,G l can not be smaller than Z 3 ), all lepton mixing parameters including the Majorana phases would be completely fixed by residual symmetries once the CP symmetry is considered. In this way, both Dirac and Majorana CP violating phases are found to be conserved in the context of ∆(6n 2 ) family symmetry combined with generalized CP [43]. Recently a bottom up analysis of the remnant K 4 flavor symmetry and CP symmetry in the neutrino sector has been performed [29].…”

Unified models of neutrinos, flavour andCPViolation

“…The phenomenological predictions and model building of combining discrete flavour symmetry with generalized CP have already been studied for a number of discrete groups in the literature, e.g. A 4 [112], S 4 [52,92,[113][114][115][116], A 5 [117][118][119][120], ∆ (27) [93,121], ∆(48) [122,123], ∆(96) [124] and the infinite series of finite groups ∆(3n 2 ) [125,126], ∆(6n 2 ) [125,127,128] and D (1) 9n,3n [129]. Recently leptogenesis has been considered in this approach [130,131].…”

A to Z of Flavour with Pati-Salam

“…CP violation has also been considered in a variety of other discrete groups [46][47][48][49][50][51]. With the above definition of CP, all coupling constants g and explicit masses m are real due to CP conservation and the only source of phases can be the VEVs of fields which break A 4 × Z 5 .…”