Celestial Blocks and Transverse Spin in the Three-Point Energy Correlator

Abstract

Quantitative theoretical techniques for understanding the substructure of jets at the LHC enable new insights into the dynamics of QCD, and novel approaches to search for new physics. Recently, there has been a program to reformulate jet substructure in terms of correlation functions, $⟨\mathcal{E}({\vec{n}}_1)\mathcal{E}({\vec{n}}_2)\cdots \mathcal{E}({\vec{n}}_k)⟩$, of light-ray operators, $\mathcal{E}(\vec{n})$, allowing the application of techniques developed in the study of Conformal Field Theories (CFTs). In this paper we further develop these techniques in the particular context of the three-point correlator $⟨\mathcal{E}({\vec{n}}_1)\mathcal{E}({\vec{n}}_2)\mathcal{E}({\vec{n}}_3)⟩$, using recently computed perturbative data in both QCD and $\mathcal{N}=4$ sYM. We derive the celestial blocks appearing in the light-ray operator product expansion (OPE) of the three-point correlator, and use the Lorentzian inversion formula to extract the spectrum of light-ray operators appearing in the expansion, showing, in particular, that the OPE data is analytic in transverse spin. Throughout our presentation, we highlight the relation between the OPE approach, and more standard splitting function based approaches of perturbative QCD, emphasizing the utility of the OPE approach for incorporating symmetries in jet substructure calculations. We hope that our presentation introduces a number of new techniques to the jet substructure community, and also illustrates the phenomenological relevance of the study of light-ray operators in the OPE limit to the CFT community.

75 pages, 16 figures

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Cited by in corpus (21)

• Resolving the Scales of the Quark-Gluon Plasma with Energy Correlators
• Probing the Short-Distance Structure of the Quark-Gluon Plasma with Energy Correlators
• The Nucleon Energy Correlators
• Nucleon Energy Correlators for the Color Glass Condensate
• Conformal Colliders Meet the LHC
• Scaling violation in power corrections to energy correlators from the light-ray OPE
• Nonperturbative Effects in Energy Correlators: From Characterizing Confinement Transition to Improving ${\alpha }_s$ Extraction
• Analytic Computation of Three-point Energy Correlator in QCD
• Non-Gaussianities in Collider Energy Flux
• Celestial Conformal Colliders
• Using the $W$ as a Standard Candle to Reach the Top: Calibrating Energy Correlator Based Top Mass Measurements
• Detector Operators for Celestial Symmetries
• Three-point Energy Correlators in Hadronic Higgs Decays
• Shedding Light on Hadronization by Quarkonium Energy Correlator
• Probing cold nuclear matter with energy correlators
• Two-loop anomalous dimensions for small-$R$ jet versus hadronic fragmentation functions
• Systematic Quark/Gluon Identification with Ratios of Likelihoods
• Energy Correlators Beyond Angles
• The Catchment Area of Groomed Jets at NNLL
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Observable Optimization for Precision Theory: Machine Learning Energy Correlators