Abstract
We consider a class of on-shell constrained mass variables that are 3+1 dimensional generalizations of the Cambridge $M_{T2}$ variable and that automatically incorporate various assumptions about the underlying event topology. The presence of additional on-shell constraints causes their kinematic distributions to exhibit sharper endpoints than the usual $M_{T2}$ distribution. We study the mathematical properties of these new variables, e.g., the uniqueness of the solution selected by the minimization over the invisible particle 4-momenta. We then use this solution to reconstruct the masses of various particles along the decay chain. We propose several tests for validating the assumed event topology in missing energy events from new physics. The tests are able to determine: 1) whether the decays in the event are two-body or three-body, 2) if the decay is two-body, whether the intermediate resonances in the two decay chains are the same, and 3) the exact sequence in which the visible particles are emitted from each decay chain.
Highlights
The best known example is the invariant mass of visible particles observed in the detector
We study the mathematical properties of these on-shell constrained M2 kinematic variables and propose several novel techniques for mass measurements and for disambiguating alternative event topologies
We find that differential distributions of the constrained M2 variables exhibit sharper kinematic endpoints, making them easier to measure in the presence of backgrounds
Summary
In this paper we shall consider the generic processes depicted in figure 1. The process (2.1) depicted in figure 1 covers a large class of physically interesting and motivated scenarios, including dilepton events from top pair production and decay, stop decays in supersymmetry (t → b ν ), and many more. We shall assume that all four visible particles ai and bi in figure 1 are distinguishable. Another question is, which visible particles belong to the first decay chain (a1, b1) and which belong to the second (a2, b2). 3. when ai is distinguishable from bi, one could ask which of these two particles was emitted first and which came second. When ai is distinguishable from bi, one could ask which of these two particles was emitted first and which came second The answer to this question will be the subject of section 5.2
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