Constraints on the gluon Sivers distribution via transverse single spin asymmetries at midrapidity in p(transv. polarized) p -> pi^0 X processes at BNL RHIC

TL;DR

The paper investigates how the gluon Sivers function contributes to transverse single-spin asymmetries in p↑p→π^0X at mid-rapidity using a generalized TMD factorization framework. By comparing PHENIX data with predictions that include unpolarized PDFs/FFs and a Gaussian k⊥ model, they show that A_N is effectively zero, which yields stringent upper bounds on the GSF, especially at small x. They explore how balancing the GSF with sea-quark Sivers contributions or enforcing Burkardt sum rule impacts these bounds, finding that the GSF remains modest within the probed x-range. The results favor valence-quark Sivers functions and demonstrate that PHENIX data provide a unique constraint on gluon spin-morbit correlations, with future measurements at different energies or processes expected to further refine these limits.

Abstract

We consider the recent RHIC data on the transverse single spin asymmetry (SSA) A_N, measured in p(transv. polarized) p -> pi^0 X processes at mid-rapidity by the PHENIX collaboration. The measurement is consistent with a vanishing SSA. We analyze this experimental information within a hard scattering approach based on a generalized QCD factorization scheme, with unintegrated, transverse momentum dependent (TMD), parton distribution and fragmentation functions. It turns out that, in the kinematical region of the data, only the gluon Sivers effect could give a large contribution to A_N; its vanishing value is thus an indication about the possible size of the gluon Sivers function (GSF). Approximate upper limits on its magnitude are derived. Additional constraints obtained combining available parameterizations of the quark Sivers function and the Burkardt sum rule (BSR) for the Sivers distributions are also discussed.

Figures (2)

• Figure 1: The SSA $A_N$, computed according to Eqs. (\ref{['defan']}) and (\ref{['sivgen']})-(\ref{['unpol']}) of the text, and compared with PHENIX data phe, with different choices for the gluon and sea-quark Sivers functions. The thin, red, solid line shows the results given by the valence $u$ and $d$ Sivers functions alone. The cyan, dot-dashed curve shows the contribution of the maximized GSF alone, $\Delta^N \hat{f}_{g/p^\uparrow} = -2\hat{f}_{g/p}$. The thick, red, solid curve is obtained by requesting results within one standard deviation from data in two different ways: no sea-quark contribution and maximized sea-quark contribution. In the latter case the blue, dotted curve shows the contribution of the sea (maximized) + valence quarks, while the green, dashed curve shows the contribution of the GSF. The valence quark Sivers distributions are taken from Ref. fu, while the unpolarized PDF's and FF's from Refs. MRST01 and KKP respectively. Further detail can be found in the text.
• Figure 2: The value of the normalized GSF, $|\Delta^N f_{g/p^\uparrow}(x)| /2 f_{g/p}(x)$, as obtained from fitting, within one standard deviation, the PHENIX data on $A_N$. The red, solid curve corresponds to the case of vanishing sea-quark contribution; the green, dashed curve shows the GSF corresponding to the extreme scenario in which the sea-quark contributions are all maximized and sum up to balance the negative GSF contribution. Further detail can be found in the text.