Fermion Number Conservation Isn't Fermion Conservation

TL;DR

The paper argues that a nonperturbative regularization of the Standard Model with an exact fermion number symmetry can still reproduce fermion nonconservation phenomena like sphaleron transitions, demonstrated in 1+1D axial QED.

Contribution

It shows that an exact global fermion number symmetry in regularization does not prevent fermion nonconservation effects in the Standard Model.

Findings

Exact fermion number symmetry does not inhibit sphaleron-induced fermion processes.

Massless axial QED in 1+1 dimensions illustrates the preservation of fermion nonconservation.

Theoretical argument supports nonperturbative regularizations maintaining desired physics.

Abstract

A nonperturbative regularization of the Standard Model may have a superficially undesirable exact global U(1) symmetry corresponding to exact fermion number conservation. We argue that such a formulation can still have the desired physics of fermion nonconservation, i.e. fermion particle creation and annihilation by sphaleron transitions. We illustrate our reasoning in massless axial QED in 1+1 dimensions.