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We perform the global analysis of polarized semi-inclusive deep inelastic scattering (SIDIS), pion-induced polarized Drell-Yan (DY) process, and

The three-dimensional (3D) hadron structure is an important topic of theoretical, phenomenological, and experimental studies in nuclear physics. In the momentum space, the 3D nucleon structure is described in terms of transverse momentum dependent distributions and fragmentation functions, collectively called TMDs, which depend both on the collinear momentum fraction and the transverse momentum of parton. The TMD factorization theorem

The Sivers function arises from interaction of the initial or final state quark with the remnant of the nucleon and thus, many of its features reveal the gauge link structure that reflects the kinematics of the underlining process

In this work, we perform the global analysis of transverse spin asymmetries at next-to-next-to-next-to leading order (

The most precise experimental measurement related to the Sivers function comes from SIDIS on a transversely polarized target [

The relevant part of the differential cross section for DY reaction

Often, the experiment provides measurements related to

In addition to the Sivers function, SSAs

It is customary in the TMD phenomenology to match TMDs to collinear distributions at small

Notice that the absence of the small-

The TMD factorization theorems are derived in the limit of large

The Sivers asymmetry has been measured in SIDIS and DY reaction

The evaluation of the theory prediction for a given set of model parameters is made by

We performed several fits with different setups. In particular, we distinguish the fits with and without the inclusion of DY data. We found that the Sivers function extracted in the SIDIS-only fit nicely describes the DY data without extra tuning. Indeed, the

The combined

Examples of data description of

We have performed a fit without the sign change of the Sivers function from Eq.

The extracted Sivers functions in

The three-dimensional

The magnitude of

The Sivers function at small

Qiu-Sterman function at

In this Letter, we have presented the first extraction of the Sivers function that consistently utilizes previously extracted unpolarized proton and pion TMDs, and uses SIDIS, pion-induced Drell-Yan, and

Our results set a new benchmark and the standard of precision for studies of TMD polarized functions and are going to be important for theoretical, phenomenological, and experimental studies of the 3D nucleon structure and for the planning of experimental programs.

The authors are thankful to Gunar Schnell and Bakur Parsamyan for discussions of experimental data, and to John Terry for sharing results of ETK20

Our definition of the rapidity anomalous dimension corresponds to

The hard coefficient function is taken at

The numerical values of parameters and other subsidiary information will be presented in the following publication.