Standard Model Gauging of the WZW Term: Anomalies, Global Currents and pseudo-Chern-Simons Interactions

The standard model $SU(2)_L\times U(1)_Y$ gauging of the Wess-Zumino-Witten term requires a modified counterterm when background fields, needed to generate the full set of currents, are introduced. The modified counterterm plays an essential role in properly defining covariant global currents and their anomalies. For example, it is required in order to correctly derive the gauge invariant baryon number current and its anomalous divergence. The background fields can also be promoted to a description of the physical spin-1 vector and axial-vector mesons in QCD and the counterterm leads to novel interactions. These are (pseudo-) Chern-Simons terms, such as $\epsilon^{\mu\nu\rho\sigma} \omega_\mu Z_\nu \partial_\rho A_\sigma$ and $\epsilon^{\mu\nu\rho\sigma} \rho^{\pm}_\mu W^{\mp}_\nu \partial_\rho A_\sigma$ that mediate new interactions between neutrinos and photons at finite baryon density.