How to measure the Charm Density in the Proton at EIC

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.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

On the polarization properties of the charmed baryon Lambda^+_c in the Lambda^+_c -> p + K^- + pi^+ + pi^0 decay

The polarization properties of the charmed Lambda^+_c baryon are investigated in weak non-leptonic four-body Lambda^+_c -> p + K^- + pi^+ + pi^0 decay. The probability of this decay and the angular distribution of the probability are calculated in the effective quark model with chiral U(3)XU(3) symmetry incorporating Heavy Quark Effective theory (HQET) and the extended Nambu-Jona-Lasinio model with a linear realization of chiral U(3)XU(3) symmetry. The theoretical value of the probability of the decay Lambda^+_c -> p + K^- + pi^+ + pi^0 relative to the probability of the decay Lambda^+_c -> p + K^- + pi^+ does not contain free parameters and fits well experimental data. The application of the obtained results to the analysis of the polarization of the Lambda^+_c produced in the processes of photo and hadroproduction is discussed.Comment: 10 pages, no figures, Late