Application of Current Commutation Rules toΔQ=0,ΔS=1Decay Modes of Hadrons

Abstract

The reduction in strength of the order of $f^2\approx {10}^{-4\mathrm{}}$ due to the strong interactions that characterizes the $\Delta Q=0\mathrm{}$, $\left|\Delta S\right|=1\mathrm{}$ decay modes such as ${\Sigma }^{+}\to p+\gamma$ is obtained from the $S$-wave nonleptonic decay amplitudes. A weak-interaction Hamiltonian for nonleptonic $S$-wave decay that transforms like the 7th component of the space integral of the pseudoscalar quark density is assumed. Then, the algebra of current commutation relations of scalar, pseudoscalar, and axial-vector currents, and the partially conserved axial-vector current relation are used to relate the $S$-wave amplitude of ${\Sigma }^{+}\to p+{\pi }^0$ to the weak vertex ${\Sigma }^{+}\to p$. Extension of the present technique to the decay mode $K^{+}\to {\pi }^{+}+e^{+}+e^{-}$ is also discussed.