# QCD predictions for the azimuthal asymmetry in charm leptoproduction for the COMPASS kinematics

## TL;DR

This paper provides QCD-based predictions for the azimuthal $ ext{cos} 2 heta$ asymmetry in charm leptoproduction at COMPASS, showing it to be large, stable, and sensitive to gluon transverse momentum and charm fragmentation, with implications for understanding gluon polarization.

## Contribution

It offers the first detailed QCD predictions for the azimuthal asymmetry in charm leptoproduction at COMPASS, including estimates of radiative and nonperturbative effects, and discusses its potential to probe gluon polarization.

## Key findings

- Asymmetry predicted to be about 15%.
- Radiative corrections are less than 10%.
- Nonperturbative effects are sizable, around 30-40%.

## Abstract

We present the QCD predictions for the azimuthal $\cos 2\varphi$ asymmetry in charm leptoproduction for the kinematics of the COMPASS experiment at CERN. The asymmetry is predicted to be large, about 15%. The radiative corrections to the QCD predictions for the $\cos 2\varphi$ distribution are estimated to be small, less than 10%. Our calculations show that the azimuthal asymmetry in charm production is well defined in pQCD: it is stable both perturbatively and parametrically, and practically insensitive to theoretical uncertainties in the input parameters. We analyze the nonperturbative contributions to the $\cos 2\varphi$ distribution due to the gluon transverse motion in the target and the $c$-quark fragmentation. Because of the $c$-quark low mass, the nonperturbative contributions are expected to be sizable, about (30--40)%. We conclude that extraction of the azimuthal asymmetries from available COMPASS data will provide valuable information about the transverse momentum dependent distribution of the gluon in the proton and the $c$-quark hadronization mechanism. Finally, we discuss the $\cos 2\varphi$ asymmetry as a probe of the gluonic analogue of the Boer-Mulders function, $h_{1}^{\perp g}$, describing the linear polarization of gluons inside unpolarized proton.