Lepton sector phases and their roles in flavor and generalized CP symmetries

Abstract

We study the effects of considering nontrivial unphysical lepton sector phases on the group theoretical properties of the flavor and generalized CP symmetry elements in the case where there are three light, distinct Majorana neutrino species. We highlight the similarities and differences between the charged lepton and neutrino sectors and further elucidate the group properties of the flavor and generalized CP symmetry elements. We show how the inclusion of these leptonic phases affects the bottom-up constructions of these symmetry elements and discuss the implications for top-down model building based on discrete symmetry groups. *

Stitching an asymmetric texture with T13×Z5 family symmetry

“…The origin of the phase in the TBM matrix is still unknown. Perhaps it can be generated from a generalized CP symmetry [25].…”

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“…The residual CP transformation X ψ should be a symmetric and unitary matrix otherwise the mass spectrum would be partially or completely degenerate [16,17]. The restricted consistency condition between the residual flavor and CP symmetries reads [13,[16][17][18][19]27]…”

“…This approach turns out to be quite powerful and it allows for precise predictions of both lepton mixing angles and CP violating phases. It can lead to very predictive scenarios, where all the mixing angles and CP phases are related to a small number of input parameters [16][17][18][19][20][21][22][23][24]. Many models and analyses of CP and flavor symmetries have been studied so far, e.g.…”

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“…For example, one can build specific theories from scratch [21][22][23]. Alternatively, one can adopt a model-independent framework based on the imposition of residual symmetries, irrespective of how the mass matrices actually arise from first principles [24][25][26][27][28][29][30]. As a step in this direction one may consider complexified versions of the standard Tri-Bi-Maximal (TBM) neutrino mixing pattern.…”