Single spin asymmetries and gauge invariance in hard scattering processes

TL;DR

This thesis develops a field-theoretic framework to study single spin asymmetries in hard scattering, emphasizing intrinsic transverse momentum and color gauge invariance via Wilson lines (gauge links). By employing a diagrammatic expansion, it derives gauge-link structures for quark distribution and fragmentation correlators across SIDIS, Drell–Yan, and e+e− annihilation, revealing process- and subprocess-dependent T-odd effects and sign changes (notably between SIDIS and Drell–Yan). It introduces the concept of gluonic-pole cross sections, enabling a compact expression of asymmetries as convolutions of standard parton distributions with process-dependent weights, while addressing factorization and universality questions including complexities in fragmentation. The work also explores higher-twist and M/Q corrections, unitarity checks in multi-gluon scenarios, and discusses the open status of small-q_T factorization for Drell–Yan and SIDIS. Overall, it provides a comprehensive, gauge-invariant treatment of transverse-momentum dependent phenomena central to interpreting single-spin observables in QCD.

Abstract

In this PhD-thesis effects from intrinsic transverse momentum are studied in several hard scattering processes with an emphasis on color gauge invariance. The thesis is intended for beginning PhD-students as well as for the experts.

Figures (36)

• Figure 1: The schematic setup of an Aharonov-Bohm like experiment. S represents a source of electrons producing an interference pattern on the screen owing to the two slits. The interference pattern shifts in a particular direction if the solenoid in B, pointing out of the plane, is given a current. If the screen is far away from the two slits then the shift is proportional to $\oint \text{d} {\textbf{x}}\cdot {\textbf{A}}({\textbf{x}})$. The path of the integral is the closed path formed by the two dashed lines and ${\textbf{A}}({\textbf{x}})$ is the potential field. One can call this shift of interference pattern an asymmetry because the direction of the shift depends on the direction of the magnetic field.
• Figure 2: An illustration of the interactions between the quark-jet and the target-remnant (Sivers effect). These interactions, which are on the amplitude level and lead to phases as we will see in chapter \ref{['chapter3']}, give rise to interference contributions in the cross section and could produce single spin asymmetries in the idealized jet-production in semi-inclusive deep-inelastic scattering.
• Figure 3: A nonzero transverse single target-spin asymmetry for $\pi^+$ and $\pi^-$ in electron-proton scattering measured by the HERMES collaboration. As will be explained in chapter \ref{['chapter3']}, the asymmetry is in the scaling limit proportional to the phase picked up by the outgoing quark and is also called the Sivers effect. The plot was taken from Ref. Airapetian:2004tw.
• Figure 4: Semi-inclusive DIS. Figure (a) illustrates the process in leading order in $\alpha_\text{e.m.}$. Figure (b) presents the definition of the Cartesian basis, except for the vectors $e_y$ and $P_h$ all vectors lie in the plane shown.
• Figure 5: Two examples of fixed frames. Only the momentum $P_h$ has a nonzero $y$-component and lies in the dashed planes.