Covariantizing Phase Space

Abstract

We covariantize calculations over the manifold of phase space, establishing Stokes' theorem for differential cross sections and providing new definitions of familiar observable properties like infrared and collinear safety. Through the introduction of explicit coordinates and a metric we show phase space is isomorphic to the product space of a simplex and a hypersphere, and we identify geometric phenomena that occur when its dimensions are large. These results have implications for fixed order subtraction schemes, machine learning in particle physics and high-multiplicity heavy ion collisions.

arXiv comment6 pages, 1 figure; v2: PRD version, extended discussion of IRC safe and additive observables from Stokes' theorem

References in corpus (36)

• Machine learning and the physical sciences
• A General Algorithm for Calculating Jet Cross Sections in NLO QCD
• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• Identifying Boosted Objects with N-subjettiness
• Three-jet cross sections to next-to-leading order
• Antenna Subtraction at NNLO
• N-Jettiness: An Inclusive Event Shape to Veto Jets
• Energy Correlation Functions for Jet Substructure
• Deep Learning and its Application to LHC Physics
• A novel subtraction scheme for double-real radiation at NNLO
• Maximizing Boosted Top Identification by Minimizing N-subjettiness
• Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning
• Fully differential VBF Higgs production at NNLO
• $W$-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD
• Principles of general final-state resummation and automated implementation
• Jet Shapes and Jet Algorithms in SCET
• Substructure of high-p_T Jets at the LHC
• Event Shape/Energy Flow Correlations
• A new method for real radiation at NNLO
• Jet Shapes with the Broadening Axis
• New Angles on Energy Correlation Functions
• Nested soft-collinear subtractions in NNLO QCD computations
• Factorization for groomed jet substructure beyond the next-to-leading logarithm
• Energy flow polynomials: A complete linear basis for jet substructure
• Subtraction terms at NNLO
• The Metric Space of Collider Events
• Infrared Safe but Infinite: Soft-Gluon Divergences Inside the Physical Region
• A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of doubly-real emissions
• Measuring Multijet Structure of Hadronic Energy Flow Or What IS A Jet?
• Geometric IR subtraction for real radiation
• Constructing effective field theories via their harmonics
• The Hidden Geometry of Particle Collisions
• Rest Frame Subjet Algorithm With SISCone Jet For Fully Hadronic Decaying Higgs Search
• Subtraction Terms for Hadronic Production Processes at Next-to-Next-to-Leading Order
• Conformal-helicity duality & the Hilbert space of free CFTs
• Independently Parameterised Momenta Variables and Monte Carlo IR Subtraction

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