(B-L) Symmetry vs. Neutrino Seesaw

Abstract

We compute the effective coupling of the Majoron to W bosons at $\text{cO}(\hslash )$ 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 $\hslash$, lending additional support to our previous proposal to identify the Majoron with the axion.

Comments: 13 pages, 1 figure, with additional explanations and clarifications