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NNLL Resummation for Projected Three-Point Energy Correlator

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arxiv 2307.07510 v1 pith:GN4AHZ3B submitted 2023-07-14 hep-ph hep-ex

classification hep-phhep-ex
keywords energycorrelatornnllprojectedresummationcollinearconstantdata
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

The projected energy correlator measures the energy deposited in multiple detectors as a function of the largest angular distance $x_L = (1 - \cos\chi_L)/2$ between detectors. The collinear limit $x_L\to 0$ of the projected energy correlator is particularly interesting for understanding the jet-substructures, while the large logarithms of $x_L$ could potentially spoil the perturbation theory and must be resummed. As a necessary ingredient for its resummation at next-to-next-to-leading logarithmic (NNLL) accuracy, we calculate the two-loop jet functions for the projected three-point energy correlator (E3C), using direct integration method and the parameter space Integration-by-Part (IBP) method. We then present the NNLL resummation for $e^+e^-$ annihilation and an approximate NNLL resummation for $pp\rightarrow jj$ process, where the two-loop hard constant is estimated in the latter case. The convergence is improved and the hadronization effect in the collinear limit is suppressed when considering the ratio of E3C distribution to two-point energy-energy correlator (EEC). Our results show potential in precision determination of strong coupling constant using energy correlators from both $e^+e^-$ data and $pp$ data.

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Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Photon-Tagged Energy Flow in Inclusive Endpoint $B$ Decays

    hep-ph 2026-07 accept novelty 7.0 of 10

    A new photon-tagged angular energy correlator in inclusive B→X_sγ factorizes at leading power into the standard shape function and a newly computed measured jet function, enabling angular tests of endpoint factorization.

  2. Energy Correlators of Spinning Sources

    hep-ph 2025-12 conditional novelty 7.0 of 10

    Spinning energy correlators classify the full Euler-angle dependence of N-point energy flux, obey generalized Hofman–Maldacena positivity bounds, and their ratios to inclusive correlators in QCD are largely insensitiv...

  3. Energy-Energy Correlator at Hadron Colliders: Celestial Blocks and Singularities

    hep-ph 2025-05 conditional novelty 7.0 of 10

    First analytic leading-order calculation of the full-angle energy-energy correlator in hadron collisions, with celestial block decomposition and Regge-limit factorization.

  4. Dissecting Parton Showers with Multi-Point Energy Correlators

    hep-ph 2026-07 accept novelty 6.0 of 10

    Projections of four-point energy correlators cleanly separate spin from kinematic azimuthal correlations inside jets; spin effects are subdominant in accessible LHC kinematics.

  5. Quantum Scaling in Energy Correlators Beyond the Confinement Transition

    hep-ph 2025-07 conditional novelty 6.0 of 10

    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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