$M_{TN}$ is all you need: production of multiple semi-invisible resonances at hadron colliders

The stransverse mass variable $M_{T2}$ was originally proposed for the study of hadron collider events in which $N=2$ parent particles are produced and then decay semi-invisibly. Here we consider the generalization to the case of $N\ge 3$ semi-invisibly decaying parent particles. We introduce the corresponding class of kinematic variables $M_{TN}$ and illustrate their mathematical properties. Many of the celebrated features of the $M_{T2}$ kinematic endpoint are retained in this more general case, including the ability to measure the mass of the invisible daughter particle from the stransverse mass kink. We describe and validate a numerical procedure for computing $M_{TN}$ in practice. We also identify the configurations of visible momenta which result in nontrivial ($M_{TN}\ne 0$) values, and derive a pure phase-space estimate for the fraction of such events for any $N$.