Transverse spin effects in hard semi-inclusive collisions

TL;DR

This paper reviews transverse spin effects in hard semi-inclusive collisions as a path to 3D imaging of the nucleon. It outlines the experimental evidences requiring transverse momentum and spin correlations, and articulates the TMD framework (TMD-PDFs, TMD-FFs) together with GPDs and the more general GTMD/Wigner formalism. It synthesizes phenomenology across SIDIS, Drell–Yan, W/Z and e^+e^- processes, detailing how Sivers, Collins, and transversity are extracted and how they contribute to 3D momentum-space imaging and insights into orbital angular momentum. The discussion also covers theoretical issues such as factorisation, TMD evolution, and process dependence, and points to future experiments and the Electron-Ion Collider as essential to completing the nucleon phase-space map.

Abstract

The nucleons (protons and neutrons) are by far the most abundant form of matter in our visible Universe; they are composite particles made of quarks and gluons, the fundamental quanta of Quantum Chromo Dynamics (QCD). The usual interpretation of the nucleon dynamics in high energy interactions is often limited to a simple one-dimensional picture of a fast moving nucleon as a collection of co-linearly moving quarks and gluons (partons), interacting accordingly to perturbative QCD rules. However, massive experimental evidence shows that, in particular when transverse spin dependent observables are involved, such a simple picture is not adequate. The intrinsic transverse motion of partons has to be taken into account; this opens the way to a new, truly 3-dimensional (3D) study of the nucleon structure. A review of the main experimental data, their interpretation and understanding in terms of new transverse momentum dependent partonic distributions, and the progress in building a 3D imaging of the nucleon is presented.

Figures (23)

• Figure 1: Kinematics and definition of the variables of SIDIS processes in the $\gamma^* - N$ c.m. frame.
• Figure 2: The weighted transverse SSA $A_{UT}^{\sin(\phi_h - \phi_S)}$, as measured by the COMPASS and Hermes Collaborations is shown as a function of its kinematical variables (notice that $x = x_{_{\!B}}$, $z = z_h$ and $p^h_T = P_T$). This asymmetry is also denoted as $A_{\,Siv}^{\,p}$, because it will be interpreted as related to a TMD-PDF introduced by Sivers. Figure reprinted from Ref. Avakian:2019drf with kind permission of Società Italiana di Fisica, © Società Italiana di Fisica 2019.
• Figure 3: The weighted transverse SSA $A_{UT}^{\sin(\phi_h + \phi_S)}$, as measured by the COMPASS and Hermes Collaborations is shown as a function of its kinematical variables (notice that $x = x_{_{\!B}}$, $z = z_h$ and $p^h_T = P_T$). This asymmetry is also denoted as $A_{\,Col}^{\,p}$, because it will be interpreted as related to a TMD-FF introduced by Collins. Figure reprinted from Ref. Avakian:2019drf with kind permission of Società Italiana di Fisica, © Società Italiana di Fisica 2019.
• Figure 4: $x-Q^2$ coverage of the STAR Collaboration measuring the Collins asymmetry for the production of hadrons in jets, compared with the Collins asymmetry measurement in SIDIS experiments. Figure reprinted from Ref. Adamczyk:2017wld and available under a https://creativecommons.org/licenses/by/4.0/legalcode.
• Figure 5: Selection of world data on $A_N$ in $p\,p$ interactions for neutral and charged pions. In particular in the $\pi^0$ case, the so-called $x_F$ scaling is evident, which means that the asymmetry is almost independent of $\sqrt{s}$. In general, the dependence of $A_N$ on $x_F$ is almost linear. Data compiled by Oleg Eyser Aschenauer:2016our.