Renormalization of Vector Coupling Constants in Leptonic Decay of Hadrons

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Abstract
The renormalization of the vector coupling constant due to the strong interaction in the leptonic decay of hadrons is studied in the conventional field theory in which the time component of the weak vector current consists only of the terms which are bilinear in the usual way in the hadron field operators. It is shown that the renormalization of the vector coupling constant is negligible, even when the weak vector current is not conserved, and also completely independently of the transformation properties of the Hamiltonian and the weak vector current, as long as the off-mass-shell correction is negligible as regards the external mass continuation applied to the matrix element of the divergence of the weak vector current with respect to the initial and final hadrons in the respective leptonic decay. Essentially the same analysis applies also to the divergence of the weak axial-vector current. However, the assumption of negligible off-mass-shell correction implies in this case that axial-vector coupling is virtually absent, thus suggesting that the off-mass-shell correction is appreciable for the weak axial-vector current. The present analysis implies, when the weak vector and/or axial-vector currents are strictly conserved, that the baryons and the pseudoscalar bosons have, respectively, the same degenerate masses, as long as the respective fields appear explicitly in these weak currents.