Colour Modification of Effective T-odd Distributions
Philip G. Ratcliffe, Oleg V. Teryaev
TL;DR
The paper demonstrates that soft-gluon twist-3 contributions to single-spin asymmetries can be recast as effective T-odd Sivers distributions with process-dependent color factors, extending the Sivers mechanism to large transverse momenta. It derives a direct link between the Sivers function and twist-3 gluonic poles by a k_T expansion and a master twist-3 formula, identifying the first moment f_S^{(1)}(x) with the gluonic-pole strength T(x,x) up to a color factor, with the sign determined by ISI versus FSI. Higher transverse moments correspond to higher twists, and the full k_T-dependent Sivers function resums an infinite tower of twists, indicating non-suppression in $Q^2$ and enabling Sivers-based descriptions in high-$p_T$ processes. The analysis clarifies the role of color factors in SIDIS and Drell–Yan, and provides a framework for predicting SSA across kinematic regimes using a non-perturbative Sivers function rather than a perturbative Sivers function. Overall, the work unifies twist-3 and TMD pictures of SSA and has implications for phenomenology at large $p_T$ where color-dependent pole contributions dominate.
Abstract
We show that soft-gluon twist-3 contributions to single-spin asymmetries (SSA) in hard processes may be expressed in the form of effective T-odd Sivers distributions, whose signs and scales are modified by process-dependent colour factors. We thus prove that the Sivers mechanism may also be applied at large transverse momenta. We stress that twist-3 SSA in semi-inclusive deeply inelastic scattering and Drell-Yan processes are suppressed by transverse momentum rather than a virtual-photon momentum transfer and thus naively correspond to twist two at the hadronic level. More rigorously, the transverse-momentum weighted averages of the Sivers function correspond to increasing twist (3, 5, 7, ...) while the full kT-dependent Sivers function (just as other transverse-momentum dependent distribution and fragmentation functions) corresponds to a resummed infinite tower of higher twists.