Addendum to "Distinguishing Spins in Decay Chains at the Large Hadron Collider"

We extend our earlier study of spin correlations in the decay chain $D\to C q$, $C\to B l^{near}$, $B\to A l^{far}$, where $A,B,C,D$ are new particles with known masses but undetermined spins, $l^{near}$ and $l^{far}$ are opposite-sign same-flavour charged leptons and $A$ is invisible. Instead of looking at the observable 2- and 3-particle invariant mass distributions separately, we compare the full three-dimensional phase space distributions for all possible spin assignments of the new particles, and show that this enhances their distinguishability using a quantitative measure known as the Kullback-Leibler distance.