Once-Subtracted Dispersion Relations, Current Algebra, and Nonleptonic Weak Decays of Hyperons

Abstract

Nonleptonic weak decays of hyperons and the ${K}_{1}\ensuremath{\rightarrow}2\ensuremath{\pi}$ decay are carefully analyzed using current algebra, partial conservation of axial-vector current, and once-subtracted dispersion relations, a method suggested by Okubo, Mathur, and Marshak. We have calculated the dispersion integral by assuming it to be saturated by the low-mass intermediate states of the nucleon octet, of the ${\frac{3}{2}}^{+}$ decuplet of $\ensuremath{\Delta}(1236)$, and of the ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$ ${\mathrm{SU}}_{3}$ singlet ${Y}_{0}^{*}(1405)$, in the case of hyperon decays, and by the intermediate states of vector mesons and a possible ${0}^{+}$ scalar-meson nonet, in the case of ${K}_{1}\ensuremath{\rightarrow}2\ensuremath{\pi}$ decay. The matrix element of the parity-violating weak Hamiltonian density between two baryons (which is required to evaluate the hyperon decay amplitudes) is related to the ${K}_{1}\ensuremath{\rightarrow}2\ensuremath{\pi}$ decay amplitude by the ${K}_{1}$ tadpole mechanism. With pseudovector ${\mathrm{SU}}_{3}$-symmetric coupling among the nucleon and pseudoscalar-meson octets, we are able to obtain a good fitting of all the hyperon decay amplitudes in terms of four parameters. We also find that the corrections to the soft-pion values are very important not only for $P$-wave hyperon decay amplitudes, but also for $S$-wave amplitudes. They are also extremely important for ${K}_{1}\ensuremath{\rightarrow}2\ensuremath{\pi}$ decays. Furthermore, we find that, contrary to the findings of Hara and Nambu, there is no evidence for the concept of a "universal parityconserving spurion" in hyperon and ${K}_{1}\ensuremath{\rightarrow}2\ensuremath{\pi}$ weak decays.