Re-interpreting the Oxbridge stransverse mass variable MT2 in general cases

TL;DR

This paper generalizes the MT2 variable for complex decay chains with multiple and asymmetric invisible particles, providing new analytical tools and reinterpretations for mass spectrum extraction in particle physics.

Contribution

It introduces 3+1-dimensional analogues of MT2 and a reinterpretation method for the endpoint, applicable to diverse event topologies with multiple invisible particles.

Findings

Derived analytical formulas for MT2 distribution shapes.

Provided a general prescription for endpoint reinterpretation.

Illustrated methods with supersymmetric chargino decay examples.

Abstract

We extend the range of possible applications of MT2 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 MT2 variable, which take into account all relevant on-shell kinematic constraints in a given event topology. The second approach utilizes the conventional MT2 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 MT2 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 MT2(perp) 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, (chargino to lepton, neutrino and LSP) in supersymmetry.