Abstract
The cross section for back-to-back hadron pair production in $e^+e^-$ annihilation provides access to the dihadron fragmentation functions (DiFF) needed to extract nucleon parton distribution functions from the semi-inclusive deep inelastic scattering (SIDIS) experiments with two detected final state hadrons. Particular attention is given to the so-called interference DiFF (IFF), which makes it possible to extract the transversity parton distribution of the nucleon in the collinear framework. However, previously unnoticed discrepancies were recently highlighted between the definitions of the IFFs appearing in the collinear kinematics when reconstructed from DiFFs entering the unintegrated fully differential cross sections of SIDIS and $e^+e^-$ annihilation processes. In this work, to clarify this problem we rederive the fully differential cross section for $e^+e^-$ annihilation at the leading-twist approximation. We find a mistake in the definition of the kinematics in the original expression that systematically affects a subset of terms and that leads to two significant consequences. First, the discrepancy between the IFF definitions in the cross sections for SIDIS and $e^+e^-$ annihilation is resolved. Second, the previously derived azimuthal asymmetry for accessing the helicity dependent DiFF $G_1^\perp$ in $e^+e^-$ annihilation vanishes, which explains the nonobservation of this asymmetry in the recent experimental searches by the ${\tt BELLE}$ Collaboration. We discuss the recently proposed alternative option to extract $G_1^\perp$.
Highlights
The understanding of the complete spin-dependent structure of the nucleon has been at the forefront of studies in nuclear physics in recent decades
Previously unnoticed discrepancies were recently highlighted between the definitions of the interference DiFF (IFF) appearing in the collinear kinematics when reconstructed from dihadron fragmentation functions (DiFF) entering the unintegrated fully differential cross sections of semi-inclusive deep inelastic scattering (SIDIS) and eþe− annihilation processes
The information about the DiFFs extracted from the two back-to-back hadron pair semi-inclusive production in eþe− annihilation plays an absolutely vital role in these studies
Summary
The understanding of the complete spin-dependent structure of the nucleon has been at the forefront of studies in nuclear physics in recent decades. To the previous method, here again the SIDIS process with two final state hadrons being measured is used to access a structure function containing the transversity PDF and an IFF [9,10,11,12], while the semi-inclusive production of two back-to-back hadron pairs in eþe− annihilation provides access to IFFs [13,14,15]. The advantage of the dihadron method compared to using the Collins effect is that it is possible to work in the collinear framework where the corresponding SIDIS structure function factorizes in a simple product of the transversity PDF and the IFF, while for the single hadron case the transversity is convoluted with the Collins function via an integral involving their transverse momentum dependences.
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