Lower bounds on the smallest lepton mixing angle

Abstract

We give minimal values for the smallest lepton mixing parameter jU e3 j, applying 2-loop renormalization group equations in an effective theory approach. This is relevant in scenarios that predict an inverted neutrino mass spectrum with the smallest mass and jU e3 j being zero at tree level, a situation known to be preserved at 1-loop order. At 2-loop, jU e3 j is generated at a level of 10 À12 -10 À14 . Such small values are of interest in supernova physics. Corresponding limits for the normal mass ordering are several orders of magnitude larger. Our results show that jU e3 j can in general be expected to be nonzero.

The smallest neutrino mass revisited

“…First, the size of the Dirac Yukawa coupling O(Y ν ) ∼ m 3 M/(v sin β) 2 ≈ 0.167 is small for the adopted values m 3 = 50.1 meV and M = 10 14 GeV. If M = 10 15 GeV is chosen, the perturbativity constraint O(Y ν ) < √ 4π is still satisfied while m 1 will be enhanced by two orders of magnitude, i.e., m 1 ∼ 5.6 × 10 −9 eV. Second, the CP-violating phase δ could even be maximal at the seesaw scale such that sin 2 δ = 1, leading to the enhancement of m 1 by another order of magnitude.…”

“…[14]. In this connection, it is interesting to notice that a lower bound on the smallest leptonic mixing angle can also be derived [15]. Notice also that the smallest neutrino mass is denoted here by m L , which is actually m 1 in the NO case or m 3 in the IO case.…”