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Large $N$-point energy correlator in the collinear limit

Lin Dai, Chul Kim, Adam K. Leibovich

TL;DR

The problem addressed is to characterize jet substructure using the $N$-point energy correlator (ENC) in the collinear limit, where the largest angle $R$ encodes the collinear core radius as $N\to\infty$. The authors develop a factorization theorem in soft-collinear effective theory (SCET) expressing the projected ENC cumulant in terms of fragmentation functions to a jet (FFJs) and their $N$-th moments, enabling simultaneous resummation of large logarithms in small $R$ and large $N$ to NLL. They show that the ENC jet function equals the $N$-th moment of the FFJ, derive one-loop results for massless and heavy-quark cases, and demonstrate deadcone effects in heavy-quark jets, with applications to $e^+e^-$ annihilation and comparisons to Pythia. Overall, the large-$N$ ENC provides a theoretically clean probe of the collinear jet core with reduced sensitivity to soft contamination, offering potential for improved heavy-flavor jet studies and quark/gluon discrimination.

Abstract

For the $N$-point energy correlator in the collinear limit, the largest projected angle $R$ in the large $N$ limit can be viewed as the radius of the jet that encompasses all the collinear core particles, while contributions from soft gluons to the radius are suppressed. We relate the $N$-point energy correlator in the large $N$ limit to the moments of the fragmentation functions to a jet, and, using previous work, we compare the difference between jets initiated by heavy quarks and light quarks. This comparison reveals the deadcone effect.

Large $N$-point energy correlator in the collinear limit

TL;DR

The problem addressed is to characterize jet substructure using the -point energy correlator (ENC) in the collinear limit, where the largest angle encodes the collinear core radius as . The authors develop a factorization theorem in soft-collinear effective theory (SCET) expressing the projected ENC cumulant in terms of fragmentation functions to a jet (FFJs) and their -th moments, enabling simultaneous resummation of large logarithms in small and large to NLL. They show that the ENC jet function equals the -th moment of the FFJ, derive one-loop results for massless and heavy-quark cases, and demonstrate deadcone effects in heavy-quark jets, with applications to annihilation and comparisons to Pythia. Overall, the large- ENC provides a theoretically clean probe of the collinear jet core with reduced sensitivity to soft contamination, offering potential for improved heavy-flavor jet studies and quark/gluon discrimination.

Abstract

For the -point energy correlator in the collinear limit, the largest projected angle in the large limit can be viewed as the radius of the jet that encompasses all the collinear core particles, while contributions from soft gluons to the radius are suppressed. We relate the -point energy correlator in the large limit to the moments of the fragmentation functions to a jet, and, using previous work, we compare the difference between jets initiated by heavy quarks and light quarks. This comparison reveals the deadcone effect.

Paper Structure

This paper contains 5 sections, 25 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Relation between the projected ENC and the jet cross section
  3. Refactorization in the large $N$ limit
  4. The projected ENC in $e^+e^-$-annihilation
  5. Conclusion and Outlook

Figures (3)

  • Figure 1: Illustration of the (projected) $N$-point energy correlator in the large $N$ limit. Here thick straight lines denote collinear particles and thin dotted lines are soft or collinear-soft particles. $R$ represents the largest angle between collinear particles.
  • Figure 2: Resummed results for the derivatives of the ENC jet functions to NLL accuracy. Here the dotted line for the light quark/gluon represents the nonperturbative domain, while the entire region for the bottom quark distribution can be described perturbatively.
  • Figure 3: The bottom and the light quark ENCs in $e^+e^-$-annihilation. In the upper panel, the blue and black solid smooth curves (associated with the blue and grey bands, respectively) are from analytic computations at NLL accuracy, and the step curves are from Pythia simulations. The lower panel shows the comparison between Pythia simulations with hadronization turned on and off.