Weak-Coupling Currents and Symmetries of Strong Interactions

Abstract

The general isotopic properties of bilinear currents which will lead to the $|\ensuremath{\Delta}S|\ensuremath{\le}1$ and $|\ensuremath{\Delta}I|=\frac{1}{2}$ rules for weak decay processes are examined. The latter rule is re-expressed in terms of an equivalent mathematical statement which permits one to obtain the usual predictions in a simple manner. In general, when the strangeness-conserving part of such a current is an isotopic vector, the strangeness-changing part can be a linear combination of $I=\frac{1}{2}$ and $I=\frac{3}{2}$ currents. The existence of an $I=\frac{3}{2}$ current could be established by experiments on the decays $K\ensuremath{\rightarrow}\ensuremath{\pi}+\mathrm{leptons}$, or on high-energy neutrino capture, $\ensuremath{\nu}+N\ensuremath{\rightarrow}\ensuremath{\mu}+\ensuremath{\Sigma}$. Experiments on ${K}_{e4}$ decays could test the bilinearity of the current.The assumption that the vector part of such a current, both strangeness changing and nonchanging, is quasi-conserved (i.e., neglecting certain mass differences) in the presence of the strong interactions fixes the specific form of the current and further implies symmetries for the strong couplings. The various transformations which leave invariant a Yukawa-type strong interaction as well as their associated currents are found. A new possible symmetry group of the strong interactions is examined: a 14 parameter group usually denoted as $G2$. In the presence of both $\ensuremath{\pi}$ and $K$ couplings, it is found that $I=\frac{1}{2} \mathrm{and} \frac{3}{2}$ currents are quasi-conserved when the strong Lagrangian has a 7-dimensional rotational symmetry, while for the $I=\frac{3}{2}$ alone, the symmetry required is $G2$. In the presence of only $\ensuremath{\pi}$-baryon couplings, only $I=\frac{1}{2}$ currents can be quasi-conserved. Certain predictions for the ${K}_{e3}$ and ${K}_{e4}$ modes of decay and for ${\ensuremath{\Sigma}}^{\ensuremath{-}}\ensuremath{\rightarrow}n+{e}^{\ensuremath{-}}+\ensuremath{\nu}$ follow from the weak currents determined in this way.