How to Measure the Charm Density in the Proton at 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(2ϕ) 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(2ϕ) 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-flavornumber scheme of QCD. Second, both these quantities, R(x, Q 2 ) = F L /F T and cos(2ϕ) asymmetry, are sensitive to resummation of the mass logarithms of the type αs ln Q 2 /m 2 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.