Remark on the conservation of the axial vector current

Abstract

The conjecture is considered that: if the axial vector current were conserved in the V -- A theory of weak interactions, the absolute values of the Gamow-Teller constant (G/sub A/) and the Fermi constant (G/sub V/) would be exactly equal, and the Goldberger-Treiman relation between G/sub A/ and the charged pion decay constant would be valid. It is noted that attempts to verify this conjecture in field theoretical models depend on the assumptions that: there exists a pseudoscalar zero-mass meson that interants with the nucleon; and that in the limit of zero momentum transfer, a particular form factor must equal unity. It is shown by analysis of the properties of the chirality operator, and by consideration of the conservation of the axial vector current, that this form factor, which is an analog of the Gamow-Teller constant, must vanish in the limit of zero momentum transfer. This result implies that either the raass of the meson, if it exists, is non-zero, or its effective coupling with the nucleon is zero. (T.F.H.)