Spin Effects on Triangle Graphs

It is shown that the triangle amplitude can be written as the scalar graph multiplied by a factor which contains only the characteristics of the external particles. In the case where the spins of the external particles are summed, their angles averaged, and only one partial-wave set (that is, a set of relative orbital angular momenta among the final-state particles) retained, this multiplicative factor is just a product of appropriate 3-momenta. The case $K^{+}p\to K\pi \pi \pi p$ at 3 $\frac{\mathrm{BeV}}{c}$ is considered; and it is demonstrated that the correct inclusion of threshold factors does not diminish the effect calculated in our earlier work, where the shape of the "$\kappa$ enhancement" was successfully described by a triangle graph.