A Complete Solution Classification and Unified Algorithmic Treatment for the One- and Two-Step Asymmetric S-Transverse Mass (MT2) Event Scale Statistic

The MT2 or "s-transverse mass" statistic was developed to associate a parent mass scale to a missing transverse energy signature, given that escaping particles are generally expected in pairs, while collider experiments are sensitive to just a single transverse momentum vector sum. This document focuses on the generalized extension of that statistic to asymmetric one- and two-step decay chains, with arbitrary child particle masses and upstream missing transverse momentum. It provides a unified theoretical formulation, complete solution classification, taxonomy of critical points, and technical algorithmic prescription for treatment of the MT2 event scale. An implementation of the described algorithm is available for download, and is also a deployable component of the author's selection cut software package AEACuS (Algorithmic Event Arbiter and Cut Selector). Appendices address combinatoric event assembly, algorithm validation, and a complete pseudocode.