Rate ofA1→ϱπfrom Asymptotic Chiral Symmetry

Abstract

By assuming that $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$ symmetry is approached at large momentum transfer and using a crude pole approximation, we determine the $A_1\to \rho \pi$ decay amplitude. The ratio of $\Gamma (A_1\to \rho \pi )$ to $\Gamma (\rho \to \pi \pi )$ is predicted to be about 2 or $\frac{1}{3}$, depending on a further assumption. However, as pointed out by Schwinger, it is conceivable that the total $A_1$ width may be considerably smaller than the width for $A_1\to \rho \pi$. The ratio of $s$- to $d$-wave decay is different for the various known approaches and may be decided on by polarization and angular measurements. We briefly remark upon the relationship of asymptotic chiral symmetry to current algebra.