Identifying a minimal flavor symmetry of the seesaw mechanism behind neutrino oscillations

Abstract

In the canonical seesaw framework flavor mixing and CP violation in weak charged-current interactions of light and heavy Majorana neutrinos are correlated with each other and described respectively by the 3 × 3 matrices U and R. We show that the very possibility of |Uμi| = |Uτi| (for i = 1, 2, 3), which is strongly indicated by current neutrino oscillation data, automatically leads to a novel prediction |Rμi| = |Rτi| (for i = 1, 2, 3). We prove that behind these two sets of equalities and the experimental evidence for leptonic CP violation lies a minimal flavor symmetry — the overall neutrino mass term keeps invariant when the left-handed neutrino fields transform as νeL→ (νeL)c, νμL→ (ντL)c, ντL→ (νμL)c and the right-handed neutrino fields undergo an arbitrary unitary CP transformation. Such a generalized μ-τ reflection symmetry may help constrain the flavor textures of active and sterile neutrinos to some extent in the seesaw mechanism.

The µ–τ reflection symmetry of Majorana neutrinos *

“…Given U µi = U τ i for the unitary PMNS matrix U, the question is how to transform U µi to U τ i or U * τ i in a given flavor basis, in which U ei either stays unchanged or becomes its complex conjugate such that U ei keeps invariant. We find that there are two typical possibilities of this kind [74].…”

“…The parameters of U = P l AU 0 and R = P l R can then be constrained, but the exact constraint relations are too complicated to be useful. So it is more instructive to impose the µ-τ reflection symmetry on U ≃ P l U 0 and R ≃ P l R by neglecting the small non-unitary corrections to U 0 and keeping only the leading terms of R. In this case we obtain the approximate constraint conditions [74] e i2ϕ e ≃ e i2(ϕ e −δ 12 ) ≃ e i2(ϕ e −δ 13 ) ≃ 1 (A.6) from U ei ≃ U * ei (for i = 1, 2, 3), and…”

“…Given the fact that the canonical seesaw mechanism [15][16][17][18][19][20] is currently the most convincing and popular mechanism for interpreting the origin of tiny neutrino masses, we are going to combine it with the µ-τ reflection symmetry in a rather generic approach that has recently been developed in [74]. First of all, let us consider the SM extended by adding three righthanded neutrino fields N αR (for α = e, µ, τ ) and allowing for lepton number violation.…”

“…This result implies that the novel prediction R µi = R τ i is actually a natural consequence of U µi = U τ i in the canonical seesaw mechanism. Given a full Euler-like parametrization of the 3 × 3 matrices U, R, S and Q in equation (2.30) [92,93], the µ-τ reflection symmetry allows us to obtain some quite strong constraints on the relevant flavor mixing angles and CP-violating phases appearing in U and R (see appendix for a detailed discussion [74]).…”

On the Implications of |Uμi| = |Uτi| in the Canonical Seesaw Mechanism

“…|U µi | = |U τi | with i = 1, 2, 3, supported by a global analysis of the latest data on atmospheric, solar, reactor, and accelerator neutrino oscillations [38,42,43]. Recently, in [44], the author discusses the above-mentioned relation and claims that this relation necessarily implies |R µi | = |R τi | (with i = 1, 2, 3), in which R is a 3 × 3 sub-matrix of the full 6 × 6 neutrino mixing matrix in the context of the canonical seesaw mechanism. The author further claims that, in the scenario U = PU * with P =   1 0 0 0 0 1 0 1 0   , the relation R = P R * is a necessary consequence.…”