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The Collinear Limit of the Energy-Energy Correlator
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abstract
The energy-energy-correlator (EEC) observable in $e^+e^-$ annihilation measures the energy deposited in two detectors as a function of the angle between the detectors. The collinear limit, where the angle between the two detectors approaches zero, is of particular interest for describing the substructure of jets produced at hadron colliders as well as in $e^+e^-$ annihilation. We derive a factorization formula for the leading power asymptotic behavior in the collinear limit of a generic quantum field theory, which allows for the resummation of logarithmically enhanced terms to all orders by renormalization group evolution. The relevant anomalous dimensions are expressed in terms of the timelike data of the theory, in particular the moments of the timelike splitting functions, which are known to high perturbative orders. We relate the small angle and back-to-back limits to each other via the total cross section and an integral over intermediate angles. This relation provides us with the initial conditions for quark and gluon jet functions at order $\alpha_s^2$. In QCD and in $\mathcal{N}=1$ super-Yang-Mills theory, we then perform the resummation to next-to-next-to-leading logarithm, improving previous calculations by two perturbative orders. We highlight the important role played by the non-vanishing $\beta$ function in these theories, which while subdominant for Higgs decays to gluons, dominates the behavior of the EEC in the collinear limit for $e^+e^-$ annihilation, and in $\mathcal{N}=1$ super-Yang-Mills theory. In conformally invariant $\mathcal{N}=4$ super-Yang-Mills theory, reciprocity between timelike and spacelike evolution can be used to express our factorization formula as a power law with exponent equal to the spacelike twist-two spin-three anomalous dimensions, thus providing a connection between timelike and spacelike approaches.
Forward citations
Cited by 27 Pith papers
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Photon-Tagged Energy Flow in Inclusive Endpoint $B$ Decays
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Projected Energy Correlators: Two-Loop Jet Functions and NNLL Resummation
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High precision heavy-boson-jet substructure with energy correlators
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Energy Correlators of Spinning Sources
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First analytic leading-order calculation of the full-angle energy-energy correlator in hadron collisions, with celestial block decomposition and Regge-limit factorization.
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Per-jet fluctuations of binned energy-energy correlators show a smaller covariance trace and larger neighboring-shell correlations at hadron level than at parton level in Pythia and Herwig across all tested configurations.
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Energy-Energy Correlators at Strong Coupling
The strong-coupling EEC in planar N=4 SYM is now known through λ⁻² for p=2 and through λ⁻³ᐟ² for all half-BPS operators O_p, derived independently from worldsheet and low-energy Wilson-coefficient methods.
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Benchmarking the Nearside Energy-Energy Correlators with Mellin Transform
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Dissecting Parton Showers with Multi-Point Energy Correlators
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OPEC in e+A collisions factorizes in TMD QCD and predicts ~0.3–0.4 nuclear suppression at small angles, growing with angle, as a probe of cold-nuclear-matter broadening.
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Heavy Quark Pair Energy Correlators: From Profiling Partonic Splittings to Probing Heavy-Flavor Fragmentation
Heavy-flavor energy-energy correlators isolate the gluon to heavy quark-antiquark splitting and are predicted to be sensitive to medium modifications and anisotropic quark-gluon plasma structure.
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Quantum Scaling in Energy Correlators Beyond the Confinement Transition
In the post-confinement regime the small-angle energy-energy correlator scales with the collision energy through the J=5 DGLAP anomalous dimension, and the light-ray OPE coefficients are moments of the dihadron fragme...
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Factorization and Resummation for the Nearside Energy-Energy Correlators
A new all-order resummation formula in Fourier b_T-space for the nearside energy-energy correlator, derived from di-hadron fragmentation functions, matches fixed-order calculations and predicts a small-angle turnover.
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In the critical O(N) model, renormalizing detector and distribution light-ray operators at leading order in 1/N yields Regge intercepts, the leading-twist splitting function, and a BFKL-type anomalous spin.
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Giving wake to energy-energy correlators: Hydrodynamic response on the celestial sphere
The medium response contribution to the jet energy-energy correlator scales as dSigma/dtheta proportional to theta at small angles and can qualitatively reproduce the large-angle enhancement seen in PbPb-to-pp EEC mea...
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Heavy quark mass effects in the Energy-Energy Correlation in the back-to-back region
Massive quark Sudakov resummation for e+e- energy-energy correlations is extended to NNLL accuracy, and the NLL dead cone angle is enlarged by sqrt(e).
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Simple Scaling Laws for Energy Correlators in Nuclear Matter
The leading nuclear modification of the two-point energy correlator in A-A and p-A collisions is a twist-4 light-ray operator contribution, giving an EEC ratio of 1 + a theta^2.
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Energy-Energy Correlator for jet production in $pp$ and $pA$ collisions
A TMD-inspired non-perturbative model plus leading-logarithm perturbative evolution describes the full angular energy-energy correlator in pp and pA jet production and attributes the observed pA suppression to medium-...
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Factorization of the Energy-Energy Correlation in the two-jet limit in the massive case
Authors introduce a partial two-jet event fraction for massive-quark EEC and an improved factorization scheme with χ-dependent coefficient function.
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Energy Correlators Resolving Proton Spin
The work establishes a correspondence between spin-dependent energy correlators and polarized TMDs/NECs using SCET, yielding N3LL/N2LL predictions for correlation patterns in current and target fragmentation regions.
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One-Point energy correlator inside jets
A TMD factorization and NNLL resummation is derived for a one-point energy correlator inside jets, and the normalized observable mainly depends on the jet scale, with sensitivity to gluon TMDFFs.
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