Kinematic focus point method for particle mass measurements in missing energy events

Abstract

We investigate the solvability of the event kinematics in missing energy events at hadron colliders, as a function of the particle mass ansatz. To be specific, we reconstruct the neutrino momenta in dilepton tt-like events, without assuming any prior knowledge of the mass spectrum. We identify a class of events, which we call extreme events, with the property that the kinematic boundary of their allowed region in mass parameter space

Singularity variables for missing energy event kinematics

“…In this paper, we define a singularity in the visible parameter space { p j } as a point where the event number density formally becomes infinite. 2 The origin of such singularities is very well understood [10][11][12][13]: they arise in the process of projecting the allowed region in the full phase space { q i , p j } (which does not exhibit any singularities) onto the visible subspace { p j }. Similar to the phenomenon of caustics in optics, astrophysics [14] or accelerator physics [15], singularities are formed at points where the visible projection onto { p j } of the allowed phase space in { q i , p j } gets folded.…”

“…(1.1) can be viewed as a constraint on the allowed values of the mass parameters for which the current event would be located on a singularity hypersurface. In a companion paper [13], this idea was formulated as a new mass measurement method 5 , called the "focus point method", which was inspired by previous related work in [29][30][31][32][33]. The analysis in [13] was illustrated with one specific event topology, dilepton tt events, and we shall now show that it is also applicable for the remaining 5 event topologies considered here.…”

“…The novice reader is perhaps best advised to first read Refs. [10][11][12][13] and be ready to consult a standard reference like [34,35] when necessary. Finally, in Section 8 we present our conclusions and outlook for future studies.…”

“…We are now ready to outline the general method for deriving a singularity variable [10][11][12][13]. The first step is to collect all kinematic constraints on the invisible momenta q (and Q, if applicable).…”

“…By now, the transverse mass is one of the standard kinematic variables, which has been widely used in precision measurements of the W -boson mass [45][46][47] as well as in new physics searches for W resonances [48][49][50][51]. The new element in our discussion will be the role of the focus point method of [13] and its connection to the kink method for mass measurements [52][53][54][55][56].…”