General partonic structure for hadronic spin asymmetries

TL;DR

The paper develops a leading-order, k_perp-dependent factorization framework for inclusive polarized hadronic processes, explicitly accounting for intrinsic parton transverse motion and noncollinear kinematics. It constructs a comprehensive set of soft, spin-dependent distributions and fragmentation functions (including Sivers, Boer-Mulders, and Collins-like terms) and derives explicit kernels for all LO partonic channels, showing how these feed into polarized cross sections. Numerical studies with saturated soft functions demonstrate strong cancellations from noncollinear phases, leaving the Sivers mechanism as the dominant contributor to transverse single-spin asymmetries, while unpolarized cross sections remain dominated by the conventional term. The approach provides a phenomenological yet predictive description of spin effects in hadronic collisions and offers pathways to extend to SIDIS and Drell-Yan processes.

Abstract

The high energy and large p_T inclusive polarized process, (A, S_A) + (B, S_B) --> C + X, is considered under the assumption of a generalized QCD factorization scheme. For the first time all transverse motions, of partons in hadrons and of hadrons in fragmenting partons, are explicitly taken into account; the elementary interactions are computed at leading order with noncollinear exact kinematics, which introduces many phases in the expressions of their helicity amplitudes. Several new spin and k_T dependent soft functions appear and contribute to the cross sections and to spin asymmetries; we put emphasis on their partonic interpretation, in terms of quark and gluon polarizations inside polarized hadrons. Connections with other notations and further information are given in some Appendices. The formal expressions for single and double spin asymmetries are derived. The transverse single spin asymmetry A_N, for p(transv. polarized) p --> pion + X processes is considered in more detail, and all contributions are evaluated numerically by saturating unknown functions with their upper positivity bounds. It is shown that the integration of the phases arising from the noncollinear kinematics strongly suppresses most contributions to the single spin asymmetry, leaving at work predominantly the Sivers effect and, to a lesser extent, the Collins mechanism.

Figures (5)

• Figure 1: Different contributions to the unpolarized cross section, plotted as a function of $x_F$, for $p \, p \to \pi^0 \, X$ processes and E704 kinematics, as indicated in the plot. The three curves correspond to: solid line = usual unpolarized contribution; dashed line = Boer-Mulders $\otimes$ Collins; dotted line = Boer-Mulders $\otimes$ Boer-Mulders.
• Figure 2: Different contributions to the unpolarized cross section, plotted as a function of $x_F$, for $p \, p \to \pi^0 \, X$ processes and STAR kinematics, as indicated in the plot. The 2 lines correspond to: solid line = usual unpolarized contribution; dashed line = Boer-Mulders $\otimes$ Collins. The Boer-Mulders $\otimes$ Boer-Mulders contribution is not even noticeable at the scale of the figure.
• Figure 3: Different contributions to $A_N$, plotted as a function of $x_F$, for $p^\uparrow p \to \pi^+ \, X$ processes and E704 kinematics. The different lines correspond to: solid line = quark Sivers mechanism alone; dashed line = gluon Sivers mechanism alone; dotted line = transversity $\otimes$ Collins. All other contributions are much smaller.
• Figure 4: Different contributions to $A_N$, plotted as a function of $x_F$, for $p^\uparrow p \to \pi^0 \, X$ processes and STAR kinematics. The different lines correspond to: solid line = quark Sivers mechanism alone; dashed line = gluon Sivers mechanism alone; dotted line = transversity $\otimes$ Collins. All other contributions are much smaller.
• Figure 5: Different contributions to $A_N$, plotted as a function of $x_F$, for $p^\uparrow \bar{p} \to \pi^+ \, X$ processes and PAX kinematics, as indicated in the plot. The different lines correspond to: solid line = quark Sivers mechanism alone; dashed line = gluon Sivers mechanism alone; dotted line = transversity $\otimes$ Collins. All other contributions are much smaller.