Higher-twist effect in inclusive electron-positron annihilation

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 $π^0$ 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.

Figures (6)

• Figure 1: The center-of-mass frame of leptons of the inclusive electron positron annihilation process. The produced hadron travels along with $z$ direction.
• Figure 2: The first few diagrams as examples of the considered diagram series with exchange of $j$-gluon(s) and different cuts. We see (a) $j=0$, (b) $j=1$, and (c) $j=2$, respectively.
• Figure 3: The first two diagrams correspond to the four-quark case without multiple gluon scattering. In Fig. (a), we have $k_1'=k_1-k$ and $k_2'=k_2-k$; in Fig. (b), we have the interchange of $k_1$ with $k_1'$.
• Figure 4: The model result by fitting MAPFF parametrization AbdulKhalek:2022laj at $Q=2.8$ GeV.
• Figure 5: Normalized differential cross sections from the twist-2 contribution, as well as those including hadron-mass and/or higher-twist corrections, are compared with the BESIII data for $e^+ e^- \rightarrow \pi^0 + X$BESIII:2022zit.