Azimuthal Asymmetries in DIS as a Probe of Intrinsic Charm Content of the Proton

TL;DR

This work analyzes azimuthal asymmetries in heavy-quark leptoproduction as a probe of intrinsic charm (IC) in the proton. It derives and cross-checks partonic cross sections for the photon-quark scattering (QS) and photon-gluon fusion (GF) mechanisms at LO and NLO, and examines their hadron-level implications in fixed-flavor (FFNS) and variable-flavor (VFNS) schemes. The key finding is that the $\cos 2\varphi$ azimuthal asymmetry, $A(x,Q^{2})$, is perturbatively and parametrically stable in FFNS, with nonperturbative IC affecting mainly large-$x$ GF predictions, while in VFNS the perturbative IC (via charm PDFs) substantially reduces GF contributions across the entire $x$ range. Consequently, measurements of $A(x,Q^{2})$ at large $x$ can directly probe nonperturbative IC in FFNS and, in VFNS, reveal the impact of perturbative IC, offering a clean discriminator between schemes and informing the role of IC in nucleon structure. The predicted effects are within reach of current and planned experiments such as COMPASS, eRHIC, and LHeC, making azimuthal distributions a practical tool to quantify intrinsic charm.

Abstract

We calculate the azimuthal dependence of the heavy-quark-initiated ${\cal O}(α_{s})$ contributions to the lepton-nucleon deep inelastic scattering (DIS). It is shown that, contrary to the photon-gluon fusion (GF) component, the photon-quark scattering (QS) mechanism is practically $\cos2φ$-independent. We investigate the possibility to discriminate experimentally between the GF and QS contributions using their strongly different azimuthal distributions. Our analysis shows that the GF and QS predictions for the azimuthal $\cos2φ$ asymmetry are quantitatively well defined in the fixed flavor number scheme: they are stable, both parametrically and perturbatively. We conclude that measurements of the azimuthal distributions at large Bjorken $x$ could directly probe the intrinsic charm content of the proton. As to the variable flavor number schemes, the charm densities of the recent CTEQ and MRST sets of parton distributions have a dramatic impact on the $\cos2φ$ asymmetry in the whole region of $x$ and, for this reason, can easily be measured.

Figures (8)

• Figure 1: Definition of the azimuthal angle $\varphi$ in the nucleon rest frame.
• Figure 2: The LO (a) and NLO (b and c) photon-quark scattering diagrams.
• Figure 3: $c_{A,Q}^{(0,0)}(\eta,\lambda )$ and $c_{I,Q}^{(0,0)}(\eta,\lambda )$ coefficient functions at several values of $\lambda$.
• Figure 4: The LO photon-gluon fusion diagrams.
• Figure 5: The quantity $\bigl(\sigma^{(1)}_{A,QS}\,\bigl/\sigma^{(0+1)}_{2,QS}\bigr)(x,\lambda)$ in the FFNS with the HM HM charm density (left panel) and in the VFNS with the CTEQ5M charm distribution function (right panel).