The stransverse mass, MT2, in special cases

TL;DR

This paper explores special cases of the MT2 variable in particle physics, providing non-iterative calculation methods, new analytic solutions, and insights into its geometric properties, relevant for collider experiments like the LHC.

Contribution

It introduces non-iterative algorithms for calculating MT2 in specific cases, including massless particles and aligned momentum scenarios, and offers new derivations maintaining boost invariance.

Findings

Analytic solution for massless case of MT2

Non-iterative algorithms for special MT2 cases

New geometric insights into MT2 and related variables

Abstract

This document describes some special cases in which the stransverse mass, MT2, may be calculated by non-iterative algorithms. The most notable special case is that in which the visible particles and the hypothesised invisible particles are massless -- a situation relevant to its current usage in the Large Hadron Collider as a discovery variable, and a situation for which no analytic answer was previously known. We also derive an expression for MT2 in another set of new (though arguably less interesting) special cases in which the missing transverse momentum must point parallel or anti parallel to the visible momentum sum. In addition, we find new derivations for already known MT2 solutions in a manner that maintains manifest contralinear boost invariance throughout, providing new insights into old results. Along the way, we stumble across some unexpected results and make conjectures relating to geometric forms of M_eff and H_T and their relationship to MT2.