Current Algebras and Meson Form Factors

Abstract

Relations between the weak form factors of mesons are derived by employing the following methods of current algebras: (a) the Oehme approximation without Hamiltonian, (b) saturation of commutators by allowed single-particle and disconnected pair states, (c) the Ward-Takahashi method, and (d) the generalized Ward-Takahashi method with the hypothesis of partially conserved axial-vector current (PCAC). These relations of meson form factors in various limits and their pole-model solutions are then discussed and compared. The information about meson form factors thus extracted indicates that the renormalization effects are small and the suppression of the $\left|\Delta S\right|=1\mathrm{}$ semileptonic decays cannot be due to the symmetry-breaking effects. It is shown that the generalized Ward-Takahashi method with the PCAC hypothesis and the Ward-Takahashi method alone give equivalent results, as far as the meson vertex functions of the conserved vector currents are concerned. However, in the case of nonconserved currents, there are important differences involving contributions from possible scalar mesons. Within the framework of pole models, it is found that the methods (a) and (d), and the methods (b) and (c), give equivalent results.