A bottom-up approach to lepton flavor and CP symmetries

Abstract

We perform a model-independent analysis of the possible residual Klein and generalized CP symmetries associated with arbitrary lepton mixing angles in the case that there are three light Majorana neutrino species. This approach emphasizes the unique role of the Majorana phases and provides a useful framework in which to discuss the origin of the Dirac CP phase in scenarios with spontaneously broken flavor and generalized CP symmetries. The method is shown to reproduce known examples in the literature based on tribimaximal and bitrimaximal mixing patterns, and is used to investigate these issues for the case of a particular (GR1) golden ratio mixing pattern.

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

“…However, their inclusion clarifies the group theoretical properties at low energies of several quantities of interest for theoretical model-building, which can be obscured when these phases are set to zero. In particular, these phases have relevance for making connections of the family and generalized CP symmetry elements to explicit representations of specific discrete symmetry groups, and hence their inclusion provides a natural generalization of the bottom-up approach given in [40]. Our results provide a set of group theoretical relations that must be satisfied at low energies within any top-down flavor model-building scenario for three light Majorana neutrinos that leaves a residual Klein symmetry in the neutrino sector.…”

“…The utility of including unphysical phases in Eq. (5) can be seen by observing that Q e and Q ν can be related to their nondiagonal forms T e and S ν via the unitary transformations [40] …”

“…For example, in [40] we explicitly constructed the forms of the S ν in the case in which the four positive determinant choices of Q ν are preserved, while the charged leptons are taken to be diagonal. In this case, the mixing parameters of U ν have a direct connection to the measured mixing parameters of U MNSP , and thus the flavor symmetry elements can be given explicitly in terms of measurable quantities [40]. Here we will explore more general situations in which we allow for different possibilities for the choice and number of conserved symmetry elements.…”

“…1 With these studies in mind, is also worthwhile to take a bottom-up perspective, in which the goal is not to construct a specific top-down model, but instead to elucidate how and when preserving different residual CP and flavor symmetry elements affects the predictions for the lepton mixing parameters. To this end, in previous work [40] we constructed the general residual Klein and generalized CP symmetries in the neutrino sector as a function of the measured lepton mixing parameters. There the simplifying assumption was made that the charged lepton sector is diagonal, such that the neutrino sector mixing parameters are directly related to the experimentally measured (measurable) lepton mixing parameters.…”

“…In Section 3, we expand this discussion to include the ways in which such phases affect aspects of generalized CP symmetries. Section 4 provides a detailed exposition of the connections of this work to the bottom-up approach given in [40], including several examples. We present our conclusions and outlook in Section 5.…”