Transverse momentum asymmetry in the semi-inclusive electron positron annihilation process

TL;DR

The paper develops a twist-3 framework to study hadronization in semi-inclusive $e^+e^-$ annihilation by introducing the transverse momentum asymmetry of the fragmenting quark or jet relative to the observed hadron direction. It derives the hadronic tensor and differential cross section up to twist-3 within the parton model, incorporating both electromagnetic and weak interactions, and expresses the twist-3 observables in terms of transverse momentum dependent fragmentation functions. Using a Gaussian ansatz for TMD FFs, it provides numerical estimates showing that the asymmetry decreases with the center-of-mass energy and grows with the jet transverse momentum, with a periodic dependence on the lepton-hadron kinematics, suggesting the observable is a robust probe of twist-3 FFs. The results indicate that the transverse momentum asymmetry offers a measurable pathway to determine twist-3 TMD FFs, deepening our understanding of jet distributions and hadronization dynamics.

Abstract

Hadronization, a nonperturbative process, cannot be calculated from first principles. It can be investigated either by using phenomenological models or by examining the behavior of produced hadrons or through fragmentation functions. These fragmentation functions are nonperturbative quantities whose determination relies entirely on experimental data. However, higher-twist fragmentation functions present significant challenges for their determination due to power suppression. In this paper, we propose an asymmetry to study twist-3 fragmentation functions. This asymmetry is defined as the transverse momentum asymmetry of the fragmenting quark and/or the produced jet with respect to the observed hadron direction within the semi-inclusive electron positron annihilation process. As a twist-3 effect, this asymmetry is sensitive to the distribution of the jet relative to the produced hadron direction during hadronization. Furthermore, it is closely related to twist-3 transverse momentum dependent fragmentation functions and provides a set of measurable quantities for their determination.

Figures (5)

• Figure 1: The center-of-mass frame of leptons of the semi-inclusive electron positron annihilation process.
• Figure 2: Numerical estimates of transverse momentum asymmetry $A_{U}^x$ with respect to $Q$. In this case $z=0.2$ and $y=0.4$.
• Figure 3: Numerical estimates of transverse momentum asymmetry $A_{U}^x$ with respect to $k_\perp$. In this case $z=0.2$ and $Q=10$ GeV.
• Figure 4: Numerical estimates of transverse momentum asymmetry $A_{U}^x$ with respect to $y$. In this case $z=0.2$ and $Q=10$ GeV.
• Figure 5: Numerical estimates of transverse momentum asymmetry $A_{U}^x$ with respect to $z$. In this case $Q=10$ GeV and $k_\perp=0.7$ GeV.