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How to measure the charm content of the proton? Two challenging proposals for heavy quark physics at EIC 2. Test of the pQCD applicability to charm photoproduction: 1. Measurement of the charm content of the proton in DIS: N.Ya.Ivanov, Nucl. Phys. B 666 (2003), 88 L.N.Ananikyan and N.Ya.Ivanov, Nucl. Phys. B 762 (2007), 256 L.N.Ananikyan and N.Ya.Ivanov, Phys. Rev. D 75 (2007), 014010 N.Ya.Ivanov and B.A. Kniehl, Eur. Phys. J. C 59 (2009), 647 N.Ya.Ivanov, Nucl. Phys. B 814 (2009), 142 N.Ya.Ivanov, A.Capella, A.B.Kaidalov, Nucl. Phys. B 586 (2000), 382 N.Ya.Ivanov, Nucl. Phys. B 615 (2001), 266 N.Ya.Ivanov, P.E.Bosted, K.Griffioen, S.E.Rock, Nucl. Phys. B 650 (2003), 271

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1. Mass logarithms resummation and the charm content of the proton VFNS vs. FFNS: What series is more efficient? We propose two clean experimental ways to determine the heavy quark densities in the proton: using the Callan-Gross ratio R= F L / F T and azimuthal cos 2φ asymmetry, A=2xF A / F 2, in DIS: whereand are usual DIS observables Corresponding cross section is:

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The ratios R= F L / F T and A=2xF A / F 2 in heavy-quark leptoproduction are perturbatively stable within the FFNS. ln(Q 2 / m 2 The quantities F L / F T and 2xF A / F 2 are sensitive to resummation of the mass logarithms of the type α s ln(Q 2 / m 2 ) within the VFNS. Q 2 These facts together imply that (future) high- Q 2 data on the ratios R= F L / F T and A=2xF A / F 2 will make it possible to probe the heavy-quark densities in the nucleon, and thus to compare the convergence of perturbative series within the FFNS and VFNS. The approach is based on following observations: Remember that, within the VFNS, the heavy-quark content of the proton is due to resummation of the mass logarithms of the type ln(Q 2 / m 2 Q 2 α s ln(Q 2 / m 2 ) and, for this reason, closely related to behavior of asymptotic perturbative series for high Q 2.

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Brief description of the idea: Within the FFNS, the leading mechanism is which contributes to F 2, F L and F A. Within the VFNS, there is also the diagram which contributes only to F 2, but not to F L and F A ! ln(Q 2 / m 2 This is because F L and F A do not contain mass logarithms α s ln(Q 2 / m 2 ) So, the mass logarithms resummation (or heavy-quark densities) should reduce the pQCD predictions for R= F L / F T and A=2xF A / F 2.

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pQCD Predictions for F 2 and R Resummation for R= F L / F T Resummation for F 2 For F 2 the NLO and resummation contributions are very close CTEQ6M PDFs are used for estimates

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pQCD Predictions for F 2 and R Resummation for R= F L / F T Resummation for F 2 For F 2 the NLO and resummation contributions are very close CTEQ6M PDFs are used for estimates

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Resummation for A= 2xF A /F 2 pQCD Predictions for A

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2. Perturbative stability of QCD and the azimuthal asymmetry in charm photoproduction How to test the pQCD applicability? We propose to test the pQCD applicability to heavy flavor production with the help of azimuthal cos 2φ asymmetry in charm photoproduction where is the degree of linear polarization of the photon, and is the centre of mass energy of the reaction. Corresponding cross section is: is the angle between the photon polarization and quark ┴ momentum

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The azimuthal asymmetry is large: it is predicted to be about 20% for both charm and bottom; Contrary to the production cross sections, the cos 2φ asymmerty in azimuthal distributions of heavy quark is practically insensitive to soft- gluon radiation; pQCD predictions for A(S) are insensitive (to within few percent) to uncertainties in the QCD input parameters: and PDFs; The nonperturbative contributions are also small. The following mechanisms was considered: Gluon transverse motion in the target; Heavy quark fragmentation; The bound state effects due to Fermi motion of the c-quark inside the D-meson. We observe the following remarkable properties:

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Perturbative instability of the cross sections

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Perturbative stability of the asymmetry

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Bruell,Ent 3. A Remark on the Gluon Contribution to the Proton Spin RHIC-Spin Projected data on g/g with an EIC, via + p D 0 + X K - + + assuming vertex separation of 100 m. Measure 90% of G (@ Q 2 = 10 GeV 2 ) Open theoretical problem: At high Q 2 one should resum the mass logarithms in g 1. Since the signs of c(x, Q 2 ) and Δc(x, Q 2 ) are opposite, resummation can affect essentially predicted value ΔG/G ~ g 1 / F 2. N.Ya. Ivanov e.a., in preparation RHIC-Spin

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2. Contrary to the production cross section, the azimuthal cos 2φ asymmerty A in heavy quark photoproduction is well defined in QCD: it is stable, both perturbatively and parametrically, and practically insensitive to nonperturbative corrections. Measurements of the asymmerty would provide ideal test of pQCD. Conclusion Q 2 1. High- Q 2 data on the ratios R= F L / F T and A=2xF A / F 2 will make it possible to probe the heavy-quark densities in the nucleon, and thus to compare the convergence of perturbative series within the FFNS and VFNS. 3. The mass logarithms contributions to c(x, Q 2 ) and Δc(x, Q 2 ) have opposite signs, and their resummation can affect essentially predicted values of ΔG/G ~ g 1 / F 2.

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