Effect of Mass Splittings on Symmetry Relations between Scattering Amplitudes

The question of the violation of relations predicted by $\mathrm{SU}\left(3\right)\mathrm{}$ invariance between scattering amplitudes that is due to the kinematical effect of mass splittings alone, with no other symmetry breaking in the Hamiltonian, is considered. On the basis of qualitative considerations and a simple potential scattering model, it is argued that these effects can be very severe, and can produce order-of-magnitude disagreements with the theoretical predictions unless the total center-of-mass energy is large compared with the masses of the particles involved. It seems likely that all existing disagreements between $\mathrm{SU}\left(3\right)\mathrm{}$ predictions and scattering experiments could be accounted for on the grounds of mass splittings alone. A study is also made of whether to compare cross sections at the same initial kinetic energies, or at the same $Q$ values, as has been done heretofore. It appears that there is comparatively little to choose between the two methods, or between either of them and other procedures which might be used. If the result depends sensitively on the method adopted for comparing the cross sections, this in itself is an indication that the effects of mass splittings are so large that agreement with theory cannot be expected.