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

Abstract

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. $\mathrm{CP}$ invariance is assumed throughout the discussion.