How to measure the charm density in the proton

TL;DR

This paper proposes experimental methods using the Callan-Gross ratio and azimuthal asymmetry in deep inelastic scattering to measure the charm quark content in the proton, emphasizing their stability and sensitivity to heavy-quark densities.

Contribution

It introduces a novel approach to determine the proton's heavy-quark content through stable and perturbatively reliable observables in high-Q^2 DIS data.

Findings

The ratios are stable within pQCD.

These observables are sensitive to mass logarithm resummation.

Potential to measure charm density at future colliders.

Abstract

We study two experimental ways to measure the heavy-quark content of the proton: using the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ and/or the azimuthal $\cos(2\varphi)$ asymmetry in DIS. Our approach is based on the following observations. First, the ratio $R(x,Q^2)=F_L/F_T$ and azimuthal $\cos(2\varphi)$ asymmetry in heavy-quark leptoproduction are stable, both parametrically and perturbatively, within pQCD. Second, both these quantities are sensitive to resummation of the mass logarithms of the type $\alpha_{s}\ln(Q^{2}/m^{2})$. We conclude that the heavy-quark densities in the nucleon can, in principle, be determined from high-$Q^2$ data on the Callan-Gross ratio and/or the azimuthal asymmetry. In particular, the charm content of the proton can be measured in future studies at the proposed Large Hadron-Electron (LHeC) and Electron-Ion (EIC) Colliders.