A systematic phenomenological study of the $\cos 2 φ$ asymmetry in unpolarized semi--inclusive DIS

TL;DR

This paper systematically analyzes the $\cos 2\phi$ azimuthal asymmetry in unpolarized SIDIS by separating perturbative and nonperturbative sources, including the Cahn effect and the Boer–Mulders mechanism coupled to Collins fragmentation, along with order-$\alpha_s$ processes. By relating $h_1^{\perp}$ to the Sivers function via the Burkardt impact-parameter framework and employing Collins and Sivers fits from SIDIS and $e^+e^-$ data, the authors produce predictions for HERMES, COMPASS, and JLab across kinematic regimes. They find the asymmetry to be typically a few percent, dominated by kinematic higher-twist at moderate $Q^2$, with a distinct signature: $\pi^-$ asymmetries larger than $\pi^+$ due to the Boer–Mulders effect. The work provides a practical roadmap for extracting $h_1^{\perp}$ from future measurements and emphasizes the complementary role of multiple experiments in mapping the nucleon's transverse structure.

Abstract

We study the $\cos 2 φ$ azimuthal asymmetry in unpolarized semi-inclusive DIS, taking into account both the perturbative contribution (gluon emission and splitting) and the non perturbative effects arising from intrinsic transverse motion and transverse spin of quarks. In particular we explore the possibility to extract from $<\cos 2 φ>$ some information about the Boer--Mulders function $h_1^{\perp}$, which represents a transverse--polarization asymmetry of quarks inside an unpolarized hadron. Predictions are presented for the HERMES, COMPASS and JLab kinematics, where $<\cos 2 φ>$ is dominated by the kinematical higher--twist contribution, and turns to be of order of few percent. We show that a larger asymmetry in $π^-$ production, compared to $π^+$ production, would represent a signature of the Boer--Mulders effect.

Figures (12)

• Figure 1: Lepton and hadron planes in semi-inclusive deep inelastic scattering.
• Figure 2: Feynman diagrams corresponding to $\ell q$ and $\ell g$ elementary scattering at first order in $\alpha_s$.
• Figure 3: Our prediction for $\langle \cos 2\phi \rangle$ in charged pion production at ZEUS, compared with the data. The asymmetry is completely dominated by the perturbative contribution.
• Figure 4: Our prediction for the $\cos 2\phi$ asymmetry at HERMES. The dot--dashed line is the ${\cal O}(\alpha_s)$ QCD contribution, the dotted line is the Boer-Mulder contribution, the dashed line is the higher--twist Cahn contribution. The continuous line is the resulting asymmetry taking all contributions into account.
• Figure 5: Our prediction for the $\cos 2\phi$ asymmetry at HERMES, with three different assumptions for $h_1^{\perp u}$. The solid line corresponds to the Ansatz adopted here.