The neutrino mixing matrix could (almost) be diagonal with entries ±1,” Phys

It is consistent with the measurement of θ13 ∼ 0.15 by Daya Bay to suppose that, in addition to being unitary, the neutrino mixing matrix is also almost hermitian, and thereby only a small perturbation from diag(+1,−1,−1) in a suitable basis. We suggest this possibility simply as an easily falsifiable ansatz, as well as to offer a potentially useful means of organizing the experimental data. We explore the phenomenological implications of this ansatz and parametrize one type of deviation from the leading order relation |Ve3 | ≈ |Vτ1|. We also emphasize the group-invariant angle between orthogonal matrices as a means of comparing to data. The discussion is purely phenomenological, without any attempt to derive the condition V † ≈ V from a fundamental theory. I A Phenomenological Ansatz The neutrino mixing matrix V is defined by να = Vαiνi, where α = e, µ, τ denotes the charged lepton mass basis (“flavor basis”), and i = 1, 2, 3 denotes the neutrino mass basis. The relevant part of the Lagrangian written in the flavor basis reads L = − α = e,µ,τ mαeαeα − 12να(Mν)αβνβ + h.c. (I.1) In this basis, the neutrino mass matrix is Mν = V ∗DνV †, where Dν ≡ diag(m1,m2,m3) with the mi real and positive. Assuming that the three light neutrinos of the Standard Model are Majorana, the mag-nitudes of the entries of V are constrained by data to b