Sum Rules for Coupling Constants in Exact and BrokenSU(6)W

Abstract

The meson-baryon vertex and the decuplet decays are studied within the framework of the exact and the broken $\mathrm{SU}{(6)}_{W}$ group. The breaking is provided by a $W$-spin scalar spurion transforming like the $I=0$, $Y=0$ member of the 35-dimensional adjoint representation of $\mathrm{SU}{(6)}_{W}$. Twenty-one sum rules are obtained in the broken symmetry. One of these directly relates the ($p,p{\ensuremath{\pi}}^{0}$) and (${N}^{*++},p{\ensuremath{\pi}}^{+}$) couplings and yields a decay width $\ensuremath{\Gamma}({N}^{*++}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{+})=70$ MeV. Another relates the vertices ($Y_{1}^{}{}_{}{}^{*+},\ensuremath{\Lambda}{\ensuremath{\pi}}^{+}$) and ($Y_{1}^{}{}_{}{}^{*+},{\ensuremath{\Sigma}}^{+}{\ensuremath{\pi}}^{0}$), which seems to agree with the latest experiments on $Y_{1}^{}{}_{}{}^{*}$ decays. One more relation among the observable decuplet decays is the Gupta-Singh sum rule, which is very well satisfied experimentally. Some predictions of exact $\mathrm{SU}{(6)}_{W}$ seem to disagree with experiment. It is concluded that in the context of three-point functions the predictions of the broken $\mathrm{SU}{(6)}_{W}$ group are in very good agreement with experiments.