Energy Correlators in Semi-Inclusive Electron-Positron Annihilation

TL;DR

This work introduces semi-inclusive energy correlators (SEC) in $e^+e^-$ annihilation as precision probes of hadronization dynamics. Using soft-collinear effective theory (SCET), it establishes factorization of SECs in two regimes: in the back-to-back limit, SECs factorize into hard, soft, and universal transverse-momentum dependent fragmentation functions (TMD FFs) with rapidity evolution governed by Collins-Soper kernels, while in the collinear limit, SECs map onto Fragmentation Energy Correlators (FECs) with a leading-twist operator definition and a modified DGLAP evolution. The work provides joint $\mathrm{N^3LL}$/NNLL RG-improved predictions for SECs in both Sudakov and jet fragmentation regions, enabling high-precision access to hadronization dynamics and informing future lepton-collider programs. It also clarifies the connection to standard collinear fragmentation functions through OPE matching of FECs and FFs, offering a robust framework to extract fragmentation information from energy-correlation observables across kinematic regimes.

Abstract

We investigate energy correlators in semi-inclusive electron-positron annihilation as precision probes of parton hadronization dynamics. Using soft-collinear effective theory (SCET), we analyze the correlation patterns between the examined hadron and the rest of QCD radiations in both large-angle and small-angle limits, which establishes a direct correspondence with Transverse-Momentum-Dependent Fragmentation Functions (TMD FFs) and Fragmentation Energy Correlators (FECs). The two complementary regimes encode the transition from perturbative parton branching to nonperturbative confinement, enabling a unified description of hadron formation across all kinematic regimes. Using renormalization group evolution, we obtain joint N3LL/NNLL quantitative predictions for energy correlations both in the sudakov and jet fragmentation region (JFR). Our results demonstrate that semi-inclusive ECs provide direct, theoretically controlled access to QCD dynamics underlying hadronization, opening new avenues for precision studies at future lepton colliders.

Figures (6)

• Figure 1: ECs back-to-back limit.
• Figure 2: Semi-inclusive ECs without $b_\ast$ prescription Collins:2014jpa in the back-to-back limit, with LHAPDF6Buckley:2014ana PDF dataset NPC23-PIsum-nloGao:2024nkzGao:2024dbv.
• Figure 3: ECs collinear limit.
• Figure 4: Mellin moments of FEC singlets renormalized at fragmented parton energy $\mu= E_a=m_Z$.
• Figure 5: NNLL prediction for semi-inclusive energy correlations in the collinear limit.