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

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.