Global analysis of the Sivers functions at NLO+NNLL in QCD

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.

The Drell-Yan process with pions and polarized nucleons

“…where C F = 4/3, C A = 3, T F = 1/2 and n f is the number of active flavors. The NLL two-loop contribution forK [113,124], valid at small values of b T , is…”

The Sivers asymmetry in hadronic dijet production

“…As we have done for the unpolarized cross section, we also derive a similar resummation formula for the spin-dependent cross section , x a , µ b * ) and a different non-perturbative Sudakov factor S s NP . The relevant parametrization has been determined from a recent global analysis of the Sivers asymmetry of SIDIS and Drell-Yan processes [116]. The non-perturbative Sudakov factor is given by…”

“…In the forward region, the Sivers asymmetry can achieve O(0.01%), and size of our calculation is also around the same order of the data. Furthermore, we have also plotted the theoretical uncertainty which is related to the extraction of the Sivers function obtained in [116]. To generate this uncertainty, we have considered the 200 replicas from this reference.…”

“…In the right plot we show the Sivers asymmetry distribution within three different jet charge Q κ bins. The red and blue bands indicate the theoretical uncertainties using the 200 replicas of the quark Sivers function[116]. At each point in calculation of our theoretical prediction, we retain the middle 68% of the replicas.…”

Extraction of the Sivers function from SIDIS, Drell-Yan, and W±/Z boson production data with TMD evolution

“…The Sivers function attracted a lot of attention in the literature [19][20][21][22][23][24][25][26][27][28][29][30][31][32] since its invention in the early 90's [8,9], when it was suggested as a possible mechanism for generation of the transverse left-right asymmetry in inclusive pion production in polarized proton-proton scattering [33]. In the modern generation of polarized experiments, transverse single-spin asymmetries (TSSAs) related to the Sivers function have been measured in SIDIS, DY and W ± /Z production processes by HERMES [34,35], COMPASS SIDIS [36][37][38][39], COMPASS DY [40], JLab [41,42] and STAR [43].…”