Sivers Effect Research Articles

Universality of T-odd effects in single spin and azimuthal asymmetries

We analyze the transverse-momentum-dependent distribution and fragmentation functions in space-like and time-like hard processes involving at least two hadrons, in particular, 1-particle inclusive leptoproduction, the Drell–Yan process and two-particle inclusive hadron production in electron–positron annihilation. As is well known, transverse momentum dependence allows for the appearance of unsuppressed single spin azimuthal asymmetries, such as Sivers and Collins asymmetries. Recently, Belitsky, Ji and Yuan obtained fully color-gauge-invariant expressions for the relevant matrix elements appearing in these asymmetries at leading order in an expansion in the inverse hard scale. We rederive these results and extend them to observables at the next order in this expansion. We observe that at leading order one retains a probability interpretation, contrary to a claim in the literature and show the direct relation between the Sivers effect in single spin asymmetries and the Qiu–Sterman mechanism. We also study fragmentation functions, where the process-dependent gauge link structure of the correlators is not the only source of T-odd observables and discuss the implications for universality.

Sivers vs. Collins effect in azimuthal single spin asymmetries in pion production in SIDIS

Recently it has been argued that the transverse momentum dependent twist-2 Sivers distribution function does not vanish in QCD. Therefore both, the Collins and Sivers effects, should be considered in order to explain the azimuthal single spin asymmetries AUL in pion production in semi-inclusive deeply inelastic lepton scattering of a longitudinally polarized target. On the basis of presently available phenomenological information on the Sivers function we estimate that for those asymmetries AUL in the kinematic region of the HERMES experiments the Sivers effect can be neglected with respect to the Collins effect. It is argued that the same feature holds also for the COMPASS and CLAS experiments. This justifies theoretical approaches to understand the HERMES data on the basis of the Collins effect only.

Transverse single-spin asymmetries in gauge boson production

Transverse single-spin asymmetries (SSA) in inclusive reactions are now considered to be directly related to the transverse momentum kT of the fundamental partons involved in the process. Several possible leading-twist QCD mechanisms have been proposed to explain the available data, in particular the Sivers effect which was resurrected recently. We show that from the measurement of transverse SSA in inclusive production of gauge bosons, one can learn more about the Sivers functions and possibly to achieve a reliable flavor separation.

Transverse single spin asymmetries in Drell-Yan processes

Recently, it has been shown, contrary to previous beliefs, that the k_T distribution of quarks in a transversely polarized proton can be asymmetric. This ``Sivers effect'' had already been used to explain transverse single spin asymmetries (SSA) observed in inclusive pion production, p(transv. polarized) p --> pion + X and p-bar(transv. polarized) p --> pion + X. In such channels, however, other mechanisms, like the ``Collins effect'' (a k_T asymmetric fragmentation of a transversely polarized quark into pions), may generate SSA. The Sivers asymmetry is used here to compute SSA in Drell-Yan processes; in this case, by considering the differential cross-section in the lepton-pair invariant mass, rapidity and transverse momentum, other mechanisms which may originate SSA cannot contribute. Estimates for RHIC experiments are given.

Initial-state interactions in the unpolarized Drell-Yan process

We show that initial-state interactions contribute to the $\cos 2 \phi$ distribution in unpolarized Drell-Yan lepton pair production $p p$ and $ p \bar p \to \ell^+ \ell^- X$, without suppression. The asymmetry is expressed as a product of chiral-odd distributions $h_1^\perp(x_1,\bm{p}_\perp^2)\times \bar h_1^\perp(x_2,\bm{k}_\perp^2) $, where the quark-transversity function $h_1^\perp(x,\bm{p}_\perp^2)$ is the transverse momentum dependent, light-cone momentum distribution of transversely polarized quarks in an {\it unpolarized} proton. We compute this (naive) $T$-odd and chiral-odd distribution function and the resulting $\cos 2 \phi$ asymmetry explicitly in a quark-scalar diquark model for the proton with initial-state gluon interaction. In this model the function $h_1^\perp(x,\bm{p}_\perp^2)$ equals the $T$-odd (chiral-even) Sivers effect function $f^\perp_{1T}(x,\bm{p}_\perp^2)$. This suggests that the single-spin asymmetries in the SIDIS and the Drell-Yan process are closely related to the $\cos 2 \phi$ asymmetry of the unpolarized Drell-Yan process, since all can arise from the same underlying mechanism. This provides new insight regarding the role of quark and gluon orbital angular momentum as well as that of initial- and final-state gluon exchange interactions in hard QCD processes.

Predictions for single spin asymmetries in $\ell p^{\uparrow} \to \pi X$ and $\gamma^* p^{\uparrow} \to \pi X$

Predictions for the single transverse spin asymmetry $A_N$ in semi-inclusive DIS processes are given; non-negligible values of $A_N$ may arise from spin effects in the fragmentation of a polarized quark into a final hadron with a transverse momentum $\vec k_\perp$ with respect to the jet axis, the so-called Collins effect. The elementary single spin asymmetry of the fragmenting quark has been fixed in a previous paper, by fitting data on $p^\uparrow p \to \pi X$ , and by assuming that the QCD factorization theorem holds also when transverse momenta are taken into account. The predictions given here are based on the assumption that the Collins effect is the only cause of the observed single spin asymmetries in $p^\uparrow p \to \pi X$ . Eventual spin and $\vec k_\perp$ dependences in the quark distribution functions, the so-called Sivers effect, are also discussed.

Predictions for single spin asymmetries in

Predictions for the single transverse spin asymmetry $A_N$ in semi-inclusive DIS processes are given; non-negligible values of $A_N$ may arise from spin effects in the fragmentation of a polarized quark into a final hadron with a transverse momentum $\vec k_\perp$ with respect to the jet axis, the so-called Collins effect. The elementary single spin asymmetry of the fragmenting quark has been fixed in a previous paper, by fitting data on $p^\uparrow p \to \pi X$ , and by assuming that the QCD factorization theorem holds also when transverse momenta are taken into account. The predictions given here are based on the assumption that the Collins effect is the only cause of the observed single spin asymmetries in $p^\uparrow p \to \pi X$ . Eventual spin and $\vec k_\perp$ dependences in the quark distribution functions, the so-called Sivers effect, are also discussed.