How to measure the charm density in the proton

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 $\cos(2φ)$ asymmetry in DIS. Our approach is based on the following observations. First, the ratio $R(x,Q^2)=F_L/F_T$ and azimuthal $\cos(2φ)$ 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 $α_{s}\ln(Q^{2}/m^{2})$. 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.

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