Re-interpreting the Oxbridge stransverse mass variable M _T2 in general cases

We extend the range of possible applications of M _T2 type analyses to decay chains with multiple invisible particles, as well as to asymmetric event topologies with different parent and/or different children particles. We advocate two possible approaches. In the first, we introduce suitably defined 3 + 1-dimensional analogues of the M _T2 variable, which take into account all relevant on-shell kinematic constraints in a given event topology. The second approach utilizes the conventional M _T2 variable, but its kinematic endpoint is suitably reinterpreted on a case by case basis, depending on the specific event topology at hand. We provide the general prescription for this reinterpretation, including the formulas relating the measured M _T2 endpoint (as a function of the test masses of all the invisible particles) to the underlying physical mass spectrum. We also provide analytical formulas for the shape of the differential distribution of the doubly projected M _T2⊥ variable for the ten possible event topologies with one visible particle and up to two invisible particles per decay chain. We illustrate our results with the example of leptonic chargino decays X̄⁺ → l⁺v X̄⁰in supersymmetry.