How to measure the Charm Density in the Proton at EIC

TL;DR

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

Contribution

It introduces a novel method to determine the heavy-quark densities in the proton using stable and perturbatively reliable ratios and asymmetries in high-Q^2 data.

Findings

Ratios and asymmetries are stable across a wide range of variables.

These quantities are sensitive to resummation effects of mass logarithms.

Potential to measure charm content at future colliders like LHeC and EIC.

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 $\cos(2\phi)$ asymmetry in deep inelastic lepton-nucleon scattering. Our approach is based on the following observations. First, unlike the production cross sections, the ratio $R(x,Q^2)=F_L/F_T$ and the azimuthal $\cos(2\phi)$ asymmetry in heavy-quark leptoproduction are sufficiently stable, both parametricallly and perturbatively, in a wide region of variables $x$ and $Q^2$ within the fixed-flavor-number scheme of QCD. Second, both these quantities, $R(x,Q^2)=F_L/F_T$ and $\cos(2\phi)$ asymmetry, are sensitive to resummation of the mass logarithms of the type $\alpha_{s}\ln\left(Q^{2}/m^{2}\right)$ within the variable-flavor-number schemes. These two facts together imply 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 heavy-quark leptoproduction. 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.