(B–L) symmetry vs. neutrino seesaw

We compute the effective coupling of the Majoron to W bosons at by evaluating the matrix element of the ( B – L ) current between the vacuum and a W + W − state. The ( B – L ) anomaly vanishes, but the amplitude does not vanish as a result of a UV finite and non-local contribution which is entirely due to the mixing between left-chiral and right-chiral neutrinos. The result shows how anomaly-like couplings may arise in spite of the fact that the ( B – L ) current remains exactly conserved to all orders in ħ , lending additional support to our previous proposal to identify the Majoron with the axion.