Transverse single-spin asymmetries in $p^\uparrow p \to γX$ from quark-gluon-quark correlations in the proton

TL;DR

The paper analyzes transverse single-spin asymmetries in direct photon production p^up p -> gamma X using collinear twist-3 factorization. It provides a complete calculation of the unpolarized proton's quark-gluon-quark correlator contribution via E_F(x1,x2), including soft-gluon and soft-fermion poles, and summarizes the existing twist-3 contributions from the polarized proton. The numerical analysis shows the asymmetry is dominated by the chiral-even SGP term related to the Qiu-Sterman function G_F(x,x), with chiral-odd and SFP contributions negligible; using SIDIS Sivers inputs yields sizable, negative A_N^gamma in the forward region at RHIC, and error bands reflect uncertainties in the Sivers function. The results indicate A_N^gamma could enable a clean extraction of G_F(x,x), test the process dependence of the Sivers function, and help discriminate between twist-3 and generalized parton model predictions.

Abstract

We analyze the transverse single-spin asymmetry in direct photon production from proton-proton collisions, denoted $A_N^γ$, within collinear twist-3 factorization. We provide a calculation of the contribution due to quark-gluon-quark correlations in the unpolarized proton as well as summarize previous studies on those effects in the polarized proton. Both soft-gluon poles and soft-fermion poles are considered. From this complete result we then estimate $A_N^γ$, including error bands due to uncertainties in the non-perturbative inputs, at kinematics relevant for planned measurements of this observable at the Relativistic Heavy Ion Collider. We find $A_N^γ$ can allow for a "clean" extraction of the Qiu-Sterman function, which could lead to a definitive solution to the so-called "sign mismatch" crisis. Since we use the Sivers function extracted from semi-inclusive deep-inelastic scattering to develop our input for the Qiu-Sterman function, this reaction can also make a statement about the process dependence of the Sivers function.

Figures (6)

• Figure 1: Generic diagrams giving rise to $A_N^\gamma$ from the chiral-odd twist-3 function $E_F(x_1,x_2)$ in the unpolarized proton are shown in (a), (b). The mirror diagrams also contribute to the asymmetry.
• Figure 2: Feynman diagrams that produce SGPs are shown in (a), (b). The circle represents the sum of the $t$-channel and $u$-channel diagrams for the partonic subprocess.
• Figure 3: Feynman diagrams that produce SFPs are shown in (a)--(f) . A coherent gluon line from the unpolarized proton attaches to each dot. The mirror diagrams also contribute. Graphs producing SFPs that cancel one another are not shown. See Kanazawa:2011er for details.
• Figure 4: $A_N^\gamma$ vs. $x_F$ at a fixed $q_T = 2\,{\rm GeV}$ for a range $|x_F| < 0.8$. The center-of-mass energy is set at $\sqrt{S} = 200\,{\rm GeV}$. The SGP pieces are given by the long-dashed curve for chiral-even and the short-dashed curve for chiral-odd. The chiral-even SFP part is shown by the dot-dashed curve. Note again that the chiral-odd SFP term vanishes. The sum of all contributions is the solid curve. The shaded area gives the error band in the calculation as described in the text.
• Figure 5: $A_N^\gamma$ vs. $x_F$ at fixed $\eta$ for $\eta = 3.0,\,3.5$ and $\sqrt{S} = 200,\,510\,{\rm GeV}$. The curve labels are the same as in Fig. \ref{['pt2']}.