Polynomials, Riemann surfaces, and reconstructing missing-energy events

Abstract

We consider the problem of reconstructing energies, momenta, and masses in collider events with missing energy, along with the complications introduced by combinatorial ambiguities and measurement errors. Typically, one reconstructs more than one value and we show how the wrong values may be correlated with the right ones. The problem has a natural formulation in terms of the theory of Riemann surfaces. We discuss examples including top quark decays in the Standard Model (relevant for top quark mass measurements and tests of spin correlation), cascade decays in models of new physics containing dark matter candidates, decays of third-generation leptoquarks in composite models of electroweak symmetry breaking, and Higgs boson decay into two tau leptons.

28 pages, 6 figures; version accepted for publication, with discussion of Higgs to tau tau decay

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• Using Energy Peaks to Measure New Particle Masses
• Mixing It Up With MT2: Unbiased Mass Measurements at Hadron Colliders
• Improved mass measurement using the boundary of many-body phase space
• Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events
• Higgs boson to di-tau channel in Chargino-Neutralino searches at the LHC
• Identifying Phase Space Boundaries with Voronoi Tessellations
• Determining the helicity structure of third generation resonances
• Singularity Variables for Missing Energy Event Kinematics
• Reconstruction of Higgs bosons in the di-tau channel via 3-prong decay
• Multi-Dimensional Phase Space Methods for Mass Measurements and Decay Topology Determination
• Extracting gluino endpoints with event topology patterns
• Kinematic Focus Point Method for Particle Mass Measurements in Missing Energy Events
• Energy spectra of massive two-body decay products and mass measurement
• Applying Machine Learning Techniques To Intermediate-Length Cascade Decays