Goldberger-Treiman Relation and the Elementarity of the Pion

概要

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After an argument to fix an arbitrary parameter characteristic of the pseudoscalar pion theory, the relation between the charged pion decay and the nucleon β-decay is discussed in connection with the elementarity of the pion, within the framework of the elastic unitarity model of n-p^^- scattering. The form factor and the vertex function for the pion decay are expressed in compact forms in terms of the pion propagator and Z(s). When the pion is elementary, the unsubtracted dispersion relation holds for the β-decay amplitude of n-p^^- pair in the ^<1>S_0 state, even if the proportionality <np^^-|∂_λJ_<λ^A>|0>∝<np^^-|φ_π|0> is not satisfied. The relations obtained from the proportionality hypothesis and from the unsubtracted dispersion relation for the decay vertex coincide with each other when Z_3 of the pion tends to zero.
理論物理学刊行会の論文
1967-08-25