Higher-order induced axial-vector isoscalar neutral current in gauge theories

Abstract

We calculate the strength of the axial-vector isosinglet neutral hadronic current coupling to neutrinos and electrons in the one-loop approximation in a class of gauge theories that forbid such couplings at the tree level. These theories are based on the gauge group $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ and $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$, respectively. The coupling strength comes out the same in both classes of models and is small compared to the corresponding coupling strength for isovector hadronic neutral current which is present at the tree level. We compare our results with the gluon-induced heavy-quarks contribution and find that the latter dominate, except for the case in which hadronic axial-vector currents are coupled to the electron vector current so that strong-interaction effects are suppressed by $1-4{{sin}^2\theta }_W$ and our results are dominant. That case may provide a clear way of testing gauge theories of weak and electromagnetic interactions.