Abstract
Information on the Sivers distribution and the Collins fragmentation functions and their transverse momentum dependence is mainly based on fitting single spin asymmetry data from semi-inclusive deep inelastic scattering (SIDIS). Independent information, respectively on the Sivers distribution and the Collins fragmentation, can be obtained from Drell-Yan and $e^+e^-$ annihilation processes. In the SIDIS case, the transverse momentum of the final observed hadron, which is the quantity measured, is generated both by the average transverse momentum in the distribution and in the fragmentation functions. As a consequence, these are strongly correlated and a separate extraction is made difficult. In this paper we investigate, in a simple kinematical Gaussian configuration, this correlation, its role on the transverse single spin asymmetries in SIDIS and the consequences for predictions of the Sivers asymmetry in Drell-Yan processes and for the Collins asymmetry in $e^+e^-$ annihilation. We find that, in some cases, these effects can be relevant and must be carefully taken into account.
Highlights
Transverse-momentum-dependent parton distribution and fragmentation functions are important tools for investigating the nucleon and its threedimensional structure
In the Sivers case discussed in the previous section, we investigated how the freedom left on the parameters ξ1 and ρS by semi-inclusive deep inelastic scattering (SIDIS) data could affect the predictions for the Sivers asymmetry in DY processes
We have investigated to what extent the actual parametrizations of the most studied TMDs—the Sivers distribution and the Collins fragmentation function—can be fixed by data and what uncertainties could remain
Summary
Transverse-momentum-dependent parton distribution and fragmentation functions (respectively, TMD PDFs and TMD FFs, collectively denoted as TMDs) are important tools for investigating the nucleon and its threedimensional structure. We start by noticing that most of the available information on spin asymmetries—related to the Sivers and Collins functions—and on unpolarized TMDs, is obtained from SIDIS processes data In this case, the transverse momentum of the final observed hadron, PT, originates both from the transverse motion of the initial struck quark inside the nucleon, k⊥, and the transverse momentum of the final hadron with respect to the fragmenting quark, p⊥. In this paper we investigate this issue in more detail To this end, we consider in the TMD factorization approach of the first phase the Sivers and Collins transverse single-spin asymmetries, together with the corresponding unpolarized cross sections, in SIDIS and Drell-Yan processes and in eþe− annihilations. V we will summarize our main results and their possible consequences for future studies of azimuthal and single-spin asymmetries in Drell-Yan processes and eþe− annihilations
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