Energy-Energy Correlators in $e^+e^-$ and Deep Inelastic Scattering

TL;DR

This work develops a unified, universal description of energy-energy correlators (EECs) in $e^+e^-$ annihilation and deep-inelastic scattering (DIS) through EEC jet functions constructed from di-hadron fragmentation functions. It provides both integrated and unintegrated (transverse-momentum dependent) jet functions, derives one-loop IR structures, and formulates a $b_T$-space evolution with resummation and a matching scheme to connect perturbative and nonperturbative regimes. The framework yields explicit NLO coefficients and a minimal nonperturbative input, delivering good agreement with $e^+e^-$ data and PYTHIA simulations, and it makes concrete predictions for SIDIS at the future EIC. The results illuminate hadronization effects in EECs and establish a path toward NNLO corrections and full evolution, with potential impact on precision QCD studies and hadron structure analyses.

Abstract

We study energy-energy correlators (EECs) in $e^+e^-$ annihilation and deep inelastic lepton-hadron scattering (DIS), focusing on aspects of nonperturbative physics in these observables. We introduce the EEC jet functions and investigate the infrared (IR) behavior of both small-angle EECs and angle-integrated EECs by performing explicit one-loop calculations. The factorization and universality of the EECs in these processes are demonstrated. A matching scheme is proposed to smoothly connect kinematic regions where different scaling behaviors with jet energy are observed. In combination with the next-to-leading order correction, this matching provides a good description of the EEC data and PYTHIA simulations in high-energy $e^+e^-$ annihilation. Predictions for DIS processes for future electron-ion collider kinematics are also presented.

Figures (9)

• Figure 1: Homogeneous contributions at one-loop order. The transverse momentum difference between the hadrons with respect to the initial quark's momentum, $q_T=|\left(\frac{\vec{p}_{1T}}{z_1}-\frac{\vec{p}_{2T}}{z_2}\right)|$, remains unchanged. However, with respect to the daughter quark or gluon, $q_T'=xq_T$, where $x$ is the momentum fraction carried by the daughter parton.
• Figure 2: Inhomogeneous contributions at one-loop order.
• Figure 3: Scaling behaviors for the improved unintegrated EEC jet function $\Gamma_q(\mu,q_T)$ in the non-perturbative and perturbative regions with different transverse momenta, $q_T=1,20$ GeV. To illustrate the scaling behavior, both curves are normalized to those at $\mu=50~\rm GeV$.
• Figure 4: Integrated EEC in $e^+e^-$ annihilation: theory predictions compared to PYTHIA8 simulations.
• Figure 5: Comparison of $\text{d}\Sigma_2^{e^+e^-}/(\theta\text{d}\theta)$ in Eq. (\ref{['eq:eefinalimproved']}) to PYTHIA8 simulations. We have imposed a normalization factor $N_{\rm{PY}}=0.85$ to our results, which reflects the fact that the PYTHIA8 simulations are about 15% lower than the experimental data.