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

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 $\gamma^*(q) p \to \pi X$. 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; {\em 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 $J^z_p = \pm {1\over 2}$ 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.