Single transverse-spin asymmetry in high transverse momentum pion production in pp collisions

TL;DR

The paper develops a twist-3 collinear-factorization framework to describe the left-right single-spin asymmetry $A_N$ in high-$p_T$ pion production in $pp$ collisions. It extends prior derivative-only treatments by deriving and incorporating non-derivative twist-3 contributions through a master formula, revealing a simple universal structure with a common hard-scattering function multiplying $T_{a,F}(x,x) - x T'_{a,F}(x,x)$. The LO hard-scattering functions are calculated for relevant partonic channels, with phases arising from soft-gluon poles enabling the asymmetry. Phenomenological analysis uses LO inputs and models for twist-3 functions, fitting to fixed-target and RHIC data to show that the framework can describe observed asymmetries and to make predictions for future experiments at RHIC.

Abstract

We study the single-spin (left-right) asymmetry in single-inclusive pion production in hadronic scattering. This asymmetry is power-suppressed in the transverse momentum of the produced pion and can be analyzed in terms of twist-three parton correlation functions in the proton. We present new calculations of the corresponding partonic hard-scattering functions that include the so-called "non-derivative" contributions not previously considered in the literature. We find a remarkably simple structure of the results. We also present a brief phenomenological study of the spin asymmetry, taking into account data from fixed-target scattering and also the latest information available from RHIC. We make additional predictions that may be tested experimentally at RHIC.

Figures (5)

• Figure 1: Generic Feynman diagram contributing to the single transverse-spin asymmetry for inclusive pion production in proton-proton scattering at leading twist (twist-three). The polarized cross section can be factorized into convolutions of the following terms: twist-three quark-gluon correlation functions for the transversely polarized proton, parton distributions for the unpolarized proton, pion fragmentation functions, and hard-scattering functions calculable in QCD perturbation theory.
• Figure 2: Factorization of hard part and twist-three matrix element: (a) before and (b) after separation of spinor trace and Lorentz indices. For simplicity we have omitted the unpolarized parton distribution and the fragmentation function. $n\sim P'$ is a light-like vector with spatial components in direction opposite to those of the initial momentum $P$.
• Figure 3: Three classes of quark-gluon scattering diagrams contributing to the spin-dependent cross section $\Delta\sigma(\vec{s}_T)$: (a) diagrams with an initial-state pole, (b) and (c) diagrams with a final-state pole. Symbols $B$ and $ij$ are color indices for the gluon and the quarks. The propagator that provides the pole is indicated by a bar. All poles shown are "soft-gluon" poles, contributing at $x_1=x_2$ (see text).
• Figure 4: Specific examples of diagrams for generic (a) initial-state and (b) final-state interactions, along with simplified notation of external momenta.
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