Transverse Nucleon Single-Spin Asymmetry for Single-Inclusive Hadron and Jet Production at NLO Accuracy

TL;DR

This work delivers a comprehensive NLO calculation of the transverse single-spin asymmetry in lepton–nucleon scattering for single-inclusive hadron and jet final states within collinear twist-3 factorization. It shows that cancellations of ultraviolet and infrared poles occur across all contributing partonic channels, establishing the validity of twist-3 factorization at one loop for truly single-inclusive observables, and reveals that NLO corrections can be large and strongly depend on the off-diagonal, two-variable twist-3 correlators F(x,x') and G(x,x'). The results, including jet-specific NLO terms via a small-cone approximation, highlight the crucial role of the full x,x' support of the nucleon correlations and point to the Electron-Ion Collider as a crucial facility to constrain these poorly known functions. The findings indicate significant sensitivity of the SSA to the detailed shape of F and G, motivating a global QCD analysis incorporating SIDIS, DIS, and RHIC/EIC data to extract the underlying multiparton correlations.

Abstract

We investigate the single-spin asymmetry for the single-inclusive production of hadrons and jets in collisions of transversely polarized nucleons and unpolarized leptons, $\ell N^\uparrow \to (h\,\mathrm{or\,jet})X$. We compute the spin-dependent cross section within collinear twist-3 factorization in perturbative QCD at next-to-leading order (NLO) accuracy. In this approach, multiparton correlations generate a non-vanishing effect. For the present paper, we focus on correlations in the nucleon initial-state rather than in the fragmentation process. We explicitly verify that collinear twist-3 factorization is valid at the one-loop level. Our analytical results show that at NLO the relevant multiparton correlation functions in the nucleon are probed on their full support in momentum fractions. Our numerical analysis for collisions at the Electron-Ion Collider indicates that the NLO corrections can be large and are sensitive to the functional form of the twist-3 correlation functions.

Figures (26)

• Figure 1: LO Feynman diagrams that are used for the calculation of Eq. \ref{['eq:LO']}. The black line indicates the lepton line, the blue line represents a quark line. Left:Kinematical twist-3 contribution, Right:Dynamical twist-3 contribution.
• Figure 2: NLO real-gluon emission diagrams in the $qg\to q$ channel relevant for the kinematical twist-3 contribution. One needs to compute the interference of the sum of these diagrams with itself.
• Figure 3: NLO virtual vertex correction relevant for the kinematical twist-3 contribution. The momenta of the external lines are denoted as in Fig. \ref{['fig:LO']} (left). This diagram comes in interference with the LO diagram in Fig. \ref{['fig:LO']} (left), with a non-zero $k_T$. Also the mirror diagram needs to be taken into account.
• Figure 4: NLO real-gluon emission diagrams in the $qg\to q$ channel relevant for the dynamical twist-3 contribution. One needs to compute the interference of the sum of these diagrams with with the sum of the diagrams in Fig. \ref{['fig:NLOkinqg2qreal']}, with $k_T=0$.
• Figure 5: NLO virtual box diagrams relevant for the dynamical twist-3 contribution. The momenta of the external lines are labeled as in Fig. \ref{['fig:LO']} (right). These diagrams come in interference with the LO diagram in Fig. \ref{['fig:LO']} (left), with $k_T=0$.