Transverse masses and kinematic constraints: from the boundary to the crease

TL;DR

This paper revisits the kinematic variable m_T2, providing a new boundary-based definition that simplifies understanding, generalizes to complex cases, and offers explicit formulas useful for mass measurements and likelihood techniques.

Contribution

It generalizes the boundary definition of m_T2 and related variables, simplifying proofs and enabling new explicit formulas for non-identical particles and inverse calculations.

Findings

Reformulation of m_T2 as a boundary of kinematically consistent regions

Simplified proofs of properties like kink and crease structures

New explicit definitions and inverses for generalized mass variables

Abstract

We re-examine the kinematic variable m_T2 and its relatives in the light of recent work by Cheng and Han. Their proof that m_T2 admits an equivalent, but implicit, definition as the `boundary of the region of parent and daughter masses that is kinematically consistent with the event hypothesis' is far-reaching in its consequences. We generalize their result both to simpler cases (m_T, the transverse mass) and to more complex cases (m_TGen). We further note that it is possible to re-cast many existing and unpleasant proofs (e.g. those relating to the existence or properties of "kink" and "crease" structures in m_T2) into almost trivial forms by using the alternative definition. Not only does this allow us to gain better understanding of those existing results, but it also allows us to write down new (and more or less explicit) definitions of (a) the variable that naturally generalizes m_T2 to the case in which the parent or daughter particles are not identical, and (b) the inverses of m_T and m_T2 -- which may be useful if daughter masses are known and bounds on parent masses are required. We note the implications that these results may have for future matrix-element likelihood techniques.