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

Abstract

We re-examine the kinematic variable mT 2 and its relatives in the light of recent work by Cheng and Han. Their proof that mT 2 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 (mT , the transverse mass) and to more complex cases (mT Gen). 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 mT 2) 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 mT 2 to the case in which the parent or daughter particles are not identical, and (b) the inverses of mT and mT 2 -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.

Search for top squarks in final states with one isolated lepton, jets, and missing transverse momentum ins=13 TeVppAaboud1, Bergeås2, Brenner3 et al. 2016Phys. Rev. D540320View full textAdd to dashboardCite

“…[29], are used to discriminate between these backgrounds and the signal processes. The asymmetric m T2 (am T2 ) [116][117][118][119] and m τ T2 are both variants of the variable m T2 [120], a generalization of the transverse mass applied to signatures where two particles are not directly detected. Like the transverse mass, m T2 is the minimum mass consistent with the observed transverse momenta and is bounded by the parent particle mass for particular topologies.…”

Identifying the production process of new physics at colliders; symmetric or asymmetric?

“…total center-of-mass energy √ŝ of colliding partons are supplied [18,33]. Without such extreme kinematic conditions, the endpoint should be interpreted cautiously.…”

“…Therefore, we need special treatment for studying asymmetric mass spectrum within a framework of min-max type mass variables. Studies of generalized M T 2 with a hypothetical ratio of parents masses [33] and subsystem M T 2 for gluino-squark co-production [34] are examples of the non-trivial treatment.…”

“…While in the introduction, we mentioned two non-trivial extensions of M T 2 for asymmetric parent masses, such as M T 2 with a ratio of parents masses [33] and subsystem M T 2 [34]. These extensions inherit property of M T 2 .…”

“…To use this generalized M T 2 for mass measurement, choosing a correctm A 2 /m A 1 is very important. We may leave this problem by comparing data to templates as mentioned in [33] at a cost of model-dependent interpretation of the data. Without a template or a model assumption, we cannot interpret the kinematic endpoint of the generalized M T 2 directly, because we don't know that used m A 2 /m A 1 is correct or not.…”