A non-standard CP transformation leading to maximal atmospheric neutrino mixing

Abstract

We discuss a neutrino mass matrix M ν originally found by Babu, Ma, and Valle (BMV) and show that this mass matrix can be characterized by a simple algebraic relation. From this relation it follows that atmospheric neutrino mixing is exactly maximal while at the same time an arbitrary mixing angle θ 13 of the lepton mixing matrix U is allowed and-in the usual phase convention-CP violation in mixing is maximal; moreover, neither the neutrino mass spectrum nor the solar mixing angle are restricted. We put forward a seesaw extension of the Standard Model, with three right-handed neutrinos and three Higgs doublets, where the family lepton numbers are softly broken by the Majorana mass terms of the right-handed neutrino singlets and the BMV mass matrix results from a non-standard CP symmetry.

Consequences of minimal seesaw with complex μτ antisymmetry of neutrinos

“…However, this flavor symmetry leads to the prediction that θ 13 = 0 which has now been excluded at more than 5.2σ [41]. A way out was proposed [32][33][34] in terms of its complex (CP) extension (CP µτ ) with the postulate…”

“…This is what we aim to do in this paper by proposing a complex (CP) extension of µτ flavor antisymmetry CP µτ A and working out its various phenomenological implications. Complex extensions of µτ symmetry [32][33][34] and scaling symmetry [46][47][48] as well as their consequences have been worked out earlier. That is the direction of our thrust here for µτ antisymmetry.…”

“…Further, the formulation of a viable scheme of baryogenesis via leptogenesis within this scenario is a challenging task. There has also been a substantial amount of work with discrete flavor symmetries of the light neutrino Majorana mass matrix: specifically real µτ permutation symmetry [22][23][24][25][26][27][28][29][30][31] and its complex (CP) extension [32][33][34] as well as real µτ permutation antisymmetry [35] but not the complex (CP) extension of that. This last mentioned topic will be the subject of our attention in this paper with the aim of predicting the neutrino CP phases.…”

Mu-tau reflection symmetry with a texture-zero

“…One of the simplest symmetries that can predict all the CP phases and yet allow CP violation is the symmetry known as µτ -reflection symmetry or CP µτ symmetry where the neutrino sector is invariant by exchange of the muon neutrino with the tau antineutrino [4][5][6]. This symmetry ensures that the Dirac CP phase is maximal (δ = ±90 • ) while the Majorana phases are trivial allowing the possibility of discrete choices of the CP parities.…”

Maximal atmospheric neutrino mixing and the small ratio of muon to tau mass

“…[5] but also in those of Refs. [4,6]. It will become evident to which class of models the symmetry K can be applied.…”