Asymptotic Behavior of Weak Spectral Functions and Hadronic Decays of theWBoson

Models of current algebra are employed to study the asymptotic properties of the spectral functions of weak currents. Asympotically it is found that they all approach constant values closely related to each other. As an application, we use our results to estimate the hadronic decay of the intermediate vector boson. The branching ratio of the $W$ decay into hadrons to the decay into leptons is of order unity, provided that the electron-positron annihilation total cross section is pointlike and predominantly isovector in character. Another contribution of this paper is a consequence of partial conservation of axial-vector current, which relates the decay rate of the $W$ boson into a soft pion plus any number of bosons to the decay into all bosons through a known constant independent of the $W$ mass.