Radiative Corrections toβDecay and the Quantum Numbers of Fields Underlying Current Algebra

Abstract

It is shown that the second-order radiative corrections to ${\pi }^{\pm }\beta$ decay are finite, provided one assumes a $V-A$ interaction and a current algebra constructed from spin-½ SU(3) triplet fields with the quantum numbers of $\Lambda$, ${\Xi }^0$, and ${\Xi }^{-}$, or ${\Omega }^{-}$, ${\Xi }^0$, and ${\Xi }^{-}$, and $\frac{1}{3}$-integral hypercharge; or, equivalently, $V+A$ together with $p$, $n$, $\Lambda$ or $p$, $n$, ${\Omega }^{\prime +}$ triplets.