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

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.