From correlation functions to event shapes

Abstract

We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and describe the angular distribution of global charges in outgoing radiation created from the vacuum by some source. The charge flow correlations can be expressed in terms of Wightman correlation functions in a certain limit. We explain how to compute these quantities starting from their Euclidean analogues by means of a non-trivial analytic continuation which, in the framework of CFT, can elegantly be performed in Mellin space. The relation between the charge flow correlations and Euclidean correlation functions can be reformulated directly in configuration space, bypassing the Mellin representation, as a certain Lorentzian double discontinuity of the correlation function integrated along the cuts. We illustrate the general formalism in N=4 SYM, making use of the well-known results on the four-point correlation function of half-BPS scalar operators. We compute the double scalar flow correlation in N=4 SYM, at weak and strong coupling and show that it agrees with known results obtained by different techniques. One of the remarkable features of the N=4 theory is that the scalar and energy flow correlations are proportional to each other. Imposing natural physical conditions on the energy flow correlations (finiteness, positivity and regularity), we formulate additional constraints on the four-point correlation functions in N=4 SYM that should be valid at any coupling and away from the planar limit.

40 pages, 1 figure; v2: typos corrected

References in corpus (16)

• Viscosity Bound and Causality Violation
• Asymptotic Symmetries of Yang-Mills Theory
• Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
• The $(2,0)$ superconformal bootstrap
• Form factors at strong coupling via a Y-system
• Local bulk S-matrix elements and CFT singularities
• Factorization of e+e- Event Shape Distributions with Hadronic Final States in Soft Collinear Effective Theory
• Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Event shapes in N=4 super-Yang-Mills theory
• Energy-energy correlations in N=4 SYM
• Eikonal Methods in AdS/CFT: Regge Theory and Multi-Reggeon Exchange
• Aspects of the UV/IR correspondence : energy broadening and string fluctuations
• On Conformal Field Theories With Extremal a/c Values
• Direct test of the AdS/CFT correspondence by Monte Carlo studies of N=4 super Yang-Mills theory
• Correlation functions of local composite operators from generalized unitarity

Cited by in corpus (73)

• The Collinear Limit of the Energy-Energy Correlator
• Rethinking Jets with Energy Correlators: Tracks, Resummation and Analytic Continuation
• Energy flow polynomials: A complete linear basis for jet substructure
• Event shapes in N=4 super-Yang-Mills theory
• The Energy-Energy Correlation at Next-to-Leading Order in QCD, Analytically
• Analyzing N-point Energy Correlators Inside Jets with CMS Open Data
• Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation
• Shocks, Superconvergence, and a Stringy Equivalence Principle
• Quantum Interference in Jet Substructure from Spinning Gluons
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• Resolving the Scales of the Quark-Gluon Plasma with Energy Correlators
• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
• Four-point correlation function of stress-energy tensors in N=4 superconformal theories
• The Transverse Energy-Energy Correlator in the Back-to-Back Limit
• Energy-energy correlations at next-to-next-to-leading order
• Analytic Next-To-Leading Order Calculation of Energy-Energy Correlation in Gluon-Initiated Higgs Decays
• Energy correlations in the end-point region
• The Four Loop QCD Rapidity Anomalous Dimension
• Probing the Short-Distance Structure of the Quark-Gluon Plasma with Energy Correlators
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• Momentum-space conformal blocks on the light cone
• Extending Precision Perturbative QCD with Track Functions
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• The Nucleon Energy Correlators
• Nucleon Energy Correlators for the Color Glass Condensate
• A New Paradigm for Precision Top Physics: Weighing the Top with Energy Correlators
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• Spinning Gluons from the QCD Light-Ray OPE
• Three Point Energy Correlators in the Collinear Limit: Symmetries, Dualities and Analytic Results
• Conformal Field Theories and Deep Inelastic Scattering
• On super form factors of half-BPS operators in N=4 super Yang-Mills
• The Hidden Geometry of Particle Collisions
• On Conformal Field Theories With Extremal a/c Values
• Celestial Blocks and Transverse Spin in the Three-Point Energy Correlator
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
• Energy-energy correlators in Deep Inelastic Scattering
• Conformal 3-point functions and the Lorentzian OPE in momentum space
• Renormalization Group Flows for Track Function Moments
• Measurement of energy correlators inside jets and determination of the strong coupling ${\alpha }_{\mathrm{S}}(m_{\mathrm{Z}})$
• Three-point energy correlators and the celestial block expansion
• Conformal Colliders Meet the LHC
• Transverse-Energy-Energy Correlations in Deep Inelastic Scattering
• Ultraviolet divergences and factorization for coordinate-space amplitudes
• On the light-ray algebra in conformal field theories
• Energy-energy correlation in hadronic Higgs decays: analytic results and phenomenology at NLO
• Scaling violation in power corrections to energy correlators from the light-ray OPE
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Light-ray operators, detectors and gravitational event shapes
• Nonperturbative Effects in Energy Correlators: From Characterizing Confinement Transition to Improving ${\alpha }_s$ Extraction
• Probing Transverse Momentum Dependent Structures with Azimuthal Dependence of Energy Correlators
• Generalizing event shapes: In search of lost collider time
• Non-Gaussianities in Collider Energy Flux
• From correlation functions to event shapes in QCD
• Celestial Conformal Colliders
• Soft Fragmentation on the Celestial Sphere
• SHAPER: Can You Hear the Shape of a Jet?
• Energy Correlators of Hadronically Decaying Electroweak Bosons
• Exploring Perturbative Conformal Field Theory in Mellin space
• Detector Operators for Celestial Symmetries
• Inclusive Production Through AdS/CFT
• Quantum Computing for Energy Correlators
• Wave scattering event shapes at high energies
• Shedding Light on Hadronization by Quarkonium Energy Correlator
• Probing cold nuclear matter with energy correlators
• OPE inversion in Mellin space
• Two Lectures on QCD at Short Distances: Jets and Factorization
• Energy Correlators Beyond Angles
• Dihadron fragmentation framework for near-side energy-energy correlators
• Observable Optimization for Precision Theory: Machine Learning Energy Correlators
• Energy-Energy Correlator from the AdS Virasoro-Shapiro Amplitude
• On the Stress Tensor Light-ray Operator Algebra
• Energy Flow in Particle Collisions
• QCD Beyond Leading Power