The three-photon vertex

Abstract

Owing to weak interactions, the three-photon vertex is non-zero. From gauge invariance and symmetry requirements, it is shown that the C=-1P=-1 vertex amplitudes are at least of order q7 in the limit of soft photon momentum q and that if any two photons are placed on mass shell the form factors vanish identically. To lowest order in q the effective current is in fact given by jrho =b epsilon kappa lambda mu nu ( delta 2(Fkappa lambda delta rho Fmu nu )- delta rho (Fkappa lambda delta 2Fmu nu )). b is estimated in certain models of weak interactions.