Dihadron fragmentation framework for near-side energy-energy correlators

Abstract

We establish an approach to analyze the free hadron and transition (nonperturbative) regions of near-side energy-energy correlators (EECs) based on dihadron fragmentation functions (DiFFs). We introduce a (nonperturbative) function we call the "EEC-DiFF" and explicitly show that expanding it for large relative transverse momentum between the two hadrons gives the $O(α_s)$ expression for the "EEC jet" function used in the quark/gluon (perturbative) region. This connection indicates that a formal theoretical matching will be able to bridge the free hadron, transition, and quark/gluon regions and allow all of them to be analyzed simultaneously. We further derive a result valid for near-side EECs in the free hadron and transition regions of $e^+e^-$ annihilation in terms of the EEC-DiFF. Using a simple model for the function, we perform the first fit within the dihadron framework to experimental data in this regime. We find reasonable agreement with the measurements and reproduce the salient features of near-side EECs in the free hadron and transition regions.

Figures (3)

• Figure 1: ${\rm EEC}(\chi)$ vs. $\chi$ for our theoretical central curve and $1\sigma$ error band compared to the data used in our analysis.
• Figure 2: $\mathcal{D}^i(z_\chi,Q^2;\mu)$ vs. $\chi Q$ with a $1\sigma$ error band for the quark (left) and gluon (right) at fixed $Q=91.2\,{\rm GeV}$ for various values of $\mu$. Note that the gluon curves have been multiplied by a factor of five and the inset zooms in on $0<\chi Q<2\,{\rm GeV}$.
• Figure 3: ${\rm EEC}(\chi)$ vs. $\chi Q$ with a $1\sigma$ error band for various values of $Q$.