Implications of second-class currents for neutral weak currents and gauge models

Exploiting the Hermiticity of hadronic neutral weak currents, we investigate implications of second-class charged currents for hadronic neutral weak currents. The main result is that if second-class charged currents exist, the isospin I=1 axial-vector neutral current must be a "new" current, or it must contain a "new" I=1 piece. Another result is that if the I=1 axial-vector neutral current is "old" (that is, it is proportional to the third component of the charged current), then the proportionality constant is real. In this case second-class charged currents are excluded. CP invariance is assumed throughout the discussion.