Final-State Interactions and Single-Spin Asymmetries in Semi-Inclusive Deep Inelastic Scattering

TL;DR

The paper addresses the origin of large azimuthal single-spin asymmetries in SIDIS by proposing that final-state interactions between the struck quark and the spectator system generate a spin-dependent, infrared-finite phase difference between proton spin amplitudes, yielding a leading-twist SSA. Using a perturbative quark-diquark model and light-front perturbation theory, the authors compute tree and one-loop amplitudes for gamma* p -> q(qq)_0 and demonstrate that gluon exchange induces distinct phases for J^z_p = +1/2 and -1/2, producing an observable SSA that does not factorize into standard distribution and fragmentation functions. They extend the framework to QCD, showing the generalization with color factors and alpha_s, and provide predictions for A_UT sin phi that align with, and can describe, experimental observations after fragmentation. The work challenges conventional factorization for spin-dependent observables and offers a universal mechanism for SSAs with potential implications for other hadronic spin phenomena.

Abstract

Recent measurements from the HERMES and SMC collaborations show a remarkably large azimuthal single-spin asymmetries A_{UL} and A_{UT} of the proton in semi-inclusive pion leptoproduction. We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton-proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q^2 at fixed x_{bj}. The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with J^z_p = + 1/2 and -1/2 to the same final state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum L_z of the proton's constituents and is thus distinct for different proton spin amplitudes. The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution delta q(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.

Figures (4)

• Figure 1: The final-state interaction in the semi-inclusive deep inelastic lepton scattering $\ell p^\uparrow \to \ell^\prime \pi X$.
• Figure 2: The tree (a) and one-loop (b) graphs for $\gamma^* p \to q (qq)_0$. The interference of the two amplitudes with $J^z_p = \pm {1/2}$ provides the proton's single-spin asymmetry.
• Figure 3: The light-cone frame used is $p= (p^+,p^-,\vec{p}_\perp)=(P^+, M^2/P^+, \vec{0}_\perp)$ and $q = (q^+, q^-, \vec{q}_\perp)$ with $q^+ = 0$. The virtual photon and produced hadron define the production plane which we will take as the ${\hat{z}}-{\hat{x}}$ plane.
• Figure 4: Model predictions for the single spin asymmetry of the proton in electroproduction resulting from gluon exchange in the final state as a function of $\Delta = x_{bj}$ and quark transverse momentum $r_\perp$. The parameters are given in the text.