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    How to measure the Charm Density in the Proton at EIC

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    We study two experimental ways to measure the heavy-quark content of the proton: using the Callan-Gross ratio R(x,Q2)=FL/FTR(x,Q^2)=F_L/F_T and/or the azimuthal cos⁑(2Ο•)\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,Q2)=FL/FTR(x,Q^2)=F_L/F_T and the azimuthal cos⁑(2Ο•)\cos(2\phi) asymmetry in heavy-quark leptoproduction are sufficiently stable, both parametricallly and perturbatively, in a wide region of variables xx and Q2Q^2 within the fixed-flavor-number scheme of QCD. Second, both these quantities, R(x,Q2)=FL/FTR(x,Q^2)=F_L/F_T and cos⁑(2Ο•)\cos(2\phi) asymmetry, are sensitive to resummation of the mass logarithms of the type Ξ±sln⁑(Q2/m2)\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-Q2Q^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.Comment: 9 pages, 4 figures, LaTeX. Talk given at the Workshop on Exclusive Reactions at High Momentum Transfer (IV), May 18-21, 2010, TJNAF, Newport News, VA and Electron-Ion Collider Collaboration Meeting, July 29-31, 2010, Catholic University of America, Washington, D
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