Abstract
We point out that leptonic weak-basis invariants are an important tool for the study of the properties of lepton flavour models. In particular, we show that appropriately chosen invariants can give a clear indication of whether a particular lepton flavour model favours normal or inverted hierarchy for neutrino masses and what is the octant of θ23. These invariants can be evaluated in any conveniently chosen weak-basis and can also be expressed in terms of neutrino masses, charged lepton masses, mixing angles and CP violation phases.
Highlights
Introductory remarksIn the SM, the flavour structure of Yukawa couplings, in both the lepton and quark sectors, is not constrained by gauge symmetry
On the theoretical side there have been many attempts at understanding the pattern of leptonic masses and mixing, through the introduction of family symmetries at the Lagrangian level or as symmetries of the leptonic mass matrices
We show how weak basis (WB) invariants provide a simple way of determining whether a given model favours normal or inverted neutrino mass ordering and what it predicts for the θ23 octant
Summary
In the SM, the flavour structure of Yukawa couplings, in both the lepton and quark sectors, is not constrained by gauge symmetry. Let us consider the SM and assume that lepton number is violated by some physics beyond the SM, leading at low energies to an effective Majorana neutrino mass matrix. Under rephasing of the charged lepton fields, the leptonic Dirac triangles rotate and the direction of their sides have no physical meaning They correspond to quantities like arg(Ue1Uμ∗1) which are not rephasing invariant. The phases which are physically meaningful in these Dirac triangles are the internal angles of the triangles which analytically correspond to the arguments of invariant leptonic quartets like (Ue2Uμ3Ue∗3Uμ∗2). In the Majorana triangles, one encounters a very different situation [13] In these triangles the directions of the sides are physically meaningful and do not change under the rephasing of the charged lepton fields. It has been shown that from the knowledge of six independent Majorana phases one can construct the full PMNS matrix, including moduli and phases [14]
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