Higher-twist effect in inclusive electron-positron annihilation

TL;DR

This paper develops a theoretical framework for electron-positron annihilation that includes higher-twist effects up to twist-4, showing their significance at low energies and improving agreement with experimental data.

Contribution

It introduces a systematic collinear expansion including multi-parton correlators up to twist-4, and estimates their impact on hadronization analysis.

Findings

Higher-twist effects are significant at low energies.

Including twist-4 improves data description at low-$z$.

Power corrections dominate at intermediate energies.

Abstract

We establish a comprehensive theoretical framework for the electron-positron single-inclusive annihilation (SIA) process that incorporates higher-twist contributions up to twist-4 and demonstrate that these effects should be considered in low-energy reactions. Through a systematic collinear expansion of the hadronic tensor, we derive the complete set of structure functions in terms of collinear fragmentation functions (FFs), explicitly including multi-parton correlators up to the four-parton level. To evaluate the impact of these power corrections, we estimate the twist-4 unpolarized FF using a spectator model and compute the normalized differential cross section for $\pi^0$ production. Our numerical analysis reveals that the interplay between kinematic hadron mass corrections and dynamical twist-4 effects improves the theoretical description of recent BESIII data at relatively low-$z$ region. Furthermore, the $Q$-dependence confirms that higher-twist corrections are dominant at intermediate energy scales. These findings indicate that standard leading-twist global analyses must be extended to include these power corrections for precise studies of hadronization dynamics.