Abstract
We perform global fit to the quark Sivers function within the transverse momentum dependent (TMD) factorization formalism in QCD. We simultaneously fit Sivers asymmetry data from Semi-Inclusive Deep Inelastic Scattering (SIDIS) at COMPASS, HERMES, and JLab, from Drell-Yan lepton pair production at COMPASS, and from W/Z boson at RHIC. This extraction is performed at next-to-leading order (NLO) and next-to-next-to leading logarithmic (NNLL) accuracy. We find excellent agreement between our extracted asymmetry and the experimental data for SIDIS and Drell-Yan lepton pair production, while tension arises when trying to describe the spin asymmetries of W/Z bosons at RHIC. We carefully assess the situation, and we study in details the impact of the RHIC data and their implications through different ways of performing the fit. In addition, we find that the quality of the description of W/Z vector boson asymmetry data could be strongly sensitive to the DGLAP evolution of Qiu-Sterman function, besides the usual TMD evolution. We present discussion on this and the implications for measurements of the transverse-spin asymmetries at the future Electron Ion Collider.
Highlights
The transverse spin of the proton, has received considerable attention in recent years
We have performed extractions of the Sivers function for the first time at the next-to-leading order (NLO)+next-to-next-to leading logarithmic (NNLL) order
We find that while the Semi-Inclusive Deep Inelastic Scattering (SIDIS) and COMPASS Drell-Yan lepton pair production data is very well described by our extraction, that our theoretical curve is much smaller than the RHIC data
Summary
The differential cross section for SIDIS, e( ) + p (P, S⊥) → e ( ) + h (Ph) + X, where S⊥ is the transverse spin vector of the polarized nucleon, can be written as the following. × exp − 2Spert(b∗; μb∗ , μ2b∗ , Q, Q2) − SNs P(xB, b; Q0, Q) − SNDP(zh, b; Q0, Q) , where we have replaced μb by μb∗ = c0/b∗, and Q0 is the reference scale of the TMDs. The functions SNf P, SNDP, and SNs P are the corresponding non-perturbative Sudakov form factors for the unpolarized TMDPDF, TMDFF, and the Sivers function, respectively, and they will be given . The functions SNf P, SNDP, and SNs P are the corresponding non-perturbative Sudakov form factors for the unpolarized TMDPDF, TMDFF, and the Sivers function, respectively, and they will be given Note that in these expressions we have introduced the vector q⊥ = −Ph⊥/zh, while q⊥ = |q⊥| denotes its magnitude
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