Abstract
We discuss singularity variables which are properly suited for analyzing the kinematics of events with missing transverse energy at the LHC. We consider six of the simplest event topologies encountered in studies of leptonic W -bosons and top quarks, as well as in SUSY-like searches for new physics with dark matter particles. In each case, we illustrate the general prescription for finding the relevant singularity variable, which in turn helps delineate the visible parameter subspace on which the singularities are located. Our results can be used in two different ways — first, as a guide for targeting the signal-rich regions of parameter space during the stage of discovery, and second, as a sensitive focus point method for measuring the particle mass spectrum after the initial discovery.
Highlights
Whose leptonic decays exhibit a classic MET signature, have long been considered promising probes of the electroweak symmetry breaking sector [5, 6], and more recently have rounded out the suite of Higgs discovery channels [7, 8]
The situation is analogous to the one already encountered in section 3.2.1 — there we saw that when PTISR = 0, the singularity variable for the event topology in figure 1(a) can be taken to be the pT of the visible particle, and a singularity occurs for any choice of test mass as shown in the upper left panels of figures 5–8
In this paper we outlined the general prescription for deriving a singularity variable for a given event topology with missing energy, i.e., where some of the final state particles are invisible in the detector
Summary
We define a singularity in the visible parameter space {pj} as a point where the event number density formally becomes infinite. 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 {qi, pj} (which does not exhibit any singularities) onto the visible subspace {pj}. We define a singularity in the visible parameter space {pj} 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 {qi, pj} (which does not exhibit any singularities) onto the visible subspace {pj}. Similar to the phenomenon of caustics in optics, astrophysics [14] or accelerator physics [15], singularities are formed at points where the visible projection onto {pj} of the allowed phase space in {qi, pj} gets folded This is expressed as the reduction in the rank of the Jacobian matrix of the coordinate transformation from the relevant set of kinematic constraints to {qi} (alternatively, from the generator-level event parameters to the visible space {pj}), which is why such singularities are sometimes known as Jacobian peaks
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