Symmetry breaking in photonic matrix elements and the weak vector current

Abstract

An earlier suggestion of Majerotto and one of the authors (W.K.) to obtain relations for the electromagnetic symmetry-breaking in photonic matrix elements of the weak vector current, is generalized to similar matrix elements of an arbitrary local operator. This has been achieved by a formulation of a zero-momentum theorem for an auxiliary quantity. We make the only assumption—similar to the usual one in breaking the chiral symmetry—that the algebra of charges of the internal symmetry group remains the same after breaking the symmetry electromagnetically. As an example we apply this procedure to the vector currents of weak radiative reactions like π→eνγ, π+→π0evγ and radiative μ-capture and we find that requirements like gauge invariance and minimal electromagnetic coupling can be consistently incorporated. Because of the lack of sufficient experimental information concerning especially the last two afore-mentioned reactions, we take simple dispersion-theoretic models in order to show that the corrections from symmetry breaking are in general large entailing the complete breakdown of CVC in such matrix elements. At least in the kinematical range of the examples referred to above, however, the corrections are well determined by the soft-photon limit of the symmetry-breaking term.