We can apply the above recoupling relations to write down the amplitude at each vertex of the decay tree. Connecting the these amplitudes are Lorentz transformations between rest frames: calculating the decay amplitude of a daughter particle requires a rotation into its direction and a boost into its rest frame. The coordinate system is preserved. This procedure results in the decay particle's quantization axis being the same as the momentum direction in the parent's frame, thus forcing the ''m'' quantum number to be equal to its helicity ''λ'' used in the parent's frame.
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We can apply the above recoupling relations to write down the amplitude at each vertex of the decay tree. Connecting the these amplitudes are Lorentz transformations between rest frames: calculating the decay amplitude of a daughter particle requires a rotation toward its direction and a boost into its rest frame. The coordinate system is preserved. This procedure results in the decay particle's quantization axis being the same as the momentum direction in the parent's frame, thus forcing the ''m'' quantum number to be equal to its helicity ''λ'' used in the parent's frame.
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Substitutions of known quantum numbers are made as necessary below: pions in the final state are given zero helicities and spin of b_<sub>1</sub> and ω are put in from the start.
<math>
<math>
Line 140:
Line 142:
a_{L_X 1}^{J_X}
a_{L_X 1}^{J_X}
</math>
</math>
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<math>
<math>
Line 181:
Line 184:
f_{J_\rho\,0}^{J_\rho}
f_{J_\rho\,0}^{J_\rho}
</math>
</math>
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Note that the ω decay is modeled as a two-stage process, with a quasi-ρ in the intermediate state: actual &rho meson quantum numbers are not forced but a sum over its possible spins and a broad phase space is given.