Transverse Polarisation of Quarks in Hadrons

TL;DR

This paper provides a comprehensive, field-theoretic treatment of quark transversity, the leading-twist, chirally-odd quark distributions $\Delta_T f(x)$, including their definitions, evolution, and nonperturbative foundations. It contrasts transversity with unpolarised and helicity distributions, explains why $\Delta_T f(x)$ cannot be probed in inclusive DIS, and develops its access through Drell–Yan and especially semi-inclusive leptoproduction (SIDIS) via Collins fragmentation $H_1^\perp$ and related $k_\perp$-dependent functions. The work presents LO and NLO QCD evolution, positivity bounds such as the Soffer inequality, and twist-3 connections, while detailing the full SIDIS formalism with fragmentation, transverse momentum dependence, and factorisation caveats. It further surveys nonperturbative calculations (quark models, lattice QCD, QCD sum rules) and the phenomenological implications for upcoming experiments (RHIC, HERMES, COMPASS). Overall, the paper consolidates the theoretical framework necessary to extract and interpret transversity in high-energy processes and highlights the pivotal role of Collins-like effects in enabling experimental access.

Abstract

We review the present state of knowledge regarding the transverse polarisation (or transversity) distributions of quarks. After some generalities on transverse polarisation, we formally define the transversity distributions within the framework of a classification of all leading-twist distribution functions. We describe the QCD evolution of transversity at leading and next-to-leading order. A comprehensive treatment of non-perturbative calculations of transversity distributions (within the framework of quark models, lattice QCD and QCD sum rules) is presented. The phenomenology of transversity (in particular, in Drell-Yan processes and semi-inclusive leptoproduction) is discussed in some detail. Finally, the prospects for future measurements are outlined.

Figures (66)

• Figure 1: (a) Representation of the chirally-odd distribution $\Delta_T{f}(x)$. (b) A handbag diagram forbidden by chirality conservation.
• Figure 2: Deeply-inelastic scattering.
• Figure 3: Lepton and spin planes. The lepton plane is taken here to coincide with the $xz$ plane, i.e., $\varphi=0$.
• Figure 4: The so-called handbag diagram.
• Figure 5: The $\gamma^*N$ collinear frame (note our convention for the axes).