[Paper Review] Single Spin Asymmetries in l p(transv. pol.) --> h X processes and TMD factorisation

M. Anselmino, M. Boglione+4 more|arXiv (Cornell University)|Apr 25, 2014

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This paper investigates transverse single spin asymmetries (AN) in lepton-proton scattering (ℓp↑→hX) using transverse momentum dependent (TMD) factorisation, employing Sivers and Collins functions extracted from SIDIS data. It finds good agreement in sign and shape between theoretical predictions and HERMES experimental data, validating TMD factorisation for inclusive processes at large PT.

ABSTRACT

Some estimates for the transverse Single Spin Asymmetry, A_N, in the inclusive processes l p(transv. pol.) --> h X, given in a previous paper, are expanded and compared with new experimental data. The predictions are based on the Sivers distributions and the Collins fragmentation functions which fit the azimuthal asymmetries measured in Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes (l p(transv. pol.) --> l' h X). The factorisation in terms of Transverse Momentum Dependent distribution and fragmentation functions (TMD factorisation) -- i.e., the theoretical framework in which SIDIS azimuthal asymmetries are analysed -- is assumed to hold also for the inclusive process l p --> h X at large P_T. The values of A_N thus obtained agree in sign and shape with the data. Some predictions are given for future experiments.

Motivation & Objective

• To test the applicability of TMD factorisation in inclusive lepton-proton scattering with transversely polarised protons.
• To compare theoretical predictions of single spin asymmetries (AN) with new HERMES data.
• To assess the consistency of Sivers and Collins functions—fitted to SIDIS data—across different hard exclusive processes.
• To provide predictive benchmarks for future experiments at the Electron-Ion Collider (EIC).

Proposed method

• Applies TMD factorisation formalism to ℓp↑→hX processes, assuming the same framework used in SIDIS.
• Uses Sivers distribution functions (∆Nfq/p↑) and Collins fragmentation functions (Dh/q) extracted from SIDIS data.
• Computes AN using the ratio of spin-dependent to unpolarised cross sections, incorporating azimuthal and transverse momentum dependencies.
• Integrates over parton momenta (k⊥, p⊥) and uses delta functions to enforce momentum conservation in the partonic subprocess.
• Relies on the leading-twist TMD factorisation framework with twist-2 TMD distributions and fragmentation functions.
• Compares predictions with HERMES data at large PT, selecting kinematic regions consistent with the TMD framework.

Experimental results

Research questions

• RQ1 Does TMD factorisation hold for inclusive ℓp↑→hX processes at large transverse momentum?
• RQ2 Can Sivers and Collins functions extracted from SIDIS describe AN in ℓp↑→hX processes?
• RQ3 Do theoretical predictions for AN match the sign and shape of HERMES experimental data?
• RQ4 What are the implications for future measurements at the Electron-Ion Collider (EIC)?

Key findings

• Theoretical predictions for AN based on TMD factorisation and SIDIS-derived Sivers/Collins functions show good agreement in sign and shape with HERMES data.
• The predicted asymmetries are consistent with the observed left-right asymmetries in the transverse momentum distribution of hadrons.
• The model successfully describes AN across a range of PT values, validating the extension of TMD factorisation to inclusive processes.
• The results support the universality of TMD distributions across different hard processes like SIDIS and inclusive lepton-proton scattering.
• The study provides a predictive framework for future measurements at the EIC, particularly for testing TMD universality.
• The analysis confirms that the Sivers effect dominates the spin asymmetry in this kinematic regime, with minimal contribution from other twist-3 mechanisms.