Determination of coupling constants and helicity amplitudes in decay processes

Abstract

The two coupling constants and the helicity amplitudes of the decay processes [(1) a spin-$J$ baryon decaying into a pseudoscalar meson and a spin-$\frac{3}{2}$ baryon, and (2) a spin-$J$ boson decaying into a pseudoscalar meson and a spin-1 boson with normality opposite to that of the decaying boson] are expressed in terms of the partial-wave amplitudes. The expressions are exact, without involving any kinematical and dynamical assumptions except Lorentz invariance. The values of the coupling constants and the helicity amplitudes are then calculated for baryons of spin $\frac{3}{2}$, $\frac{5}{2}$, and $\frac{7}{2}$ and for bosons of spin 1 by ignoring the high-partial-wave contribution. Under the above approximation, simple relations between the coupling constants and between the helicity amplitudes are obtained. The results are found to be exactly the same as those predicted by $\mathrm{SU}{(2)}_{W}$ as long as $\mathrm{SU}{(2)}_{W}$ does not forbid any helicity amplitude.