How to measure the charm content of the proton? Two challenging proposals for heavy quark physics at EIC 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 2. Test of the pQCD applicability to charm photoproduction: 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

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= FL/ FT and azimuthal cos 2φ asymmetry, A=2xFA/ F2 , in DIS: Corresponding cross section is: where and are usual DIS observables

Charm density in the proton - a bit of history: 1. The intrinsic charm notion was introduced about 30 years ago in S.J.Brodsky, C.Peterson, and N.Sakai, Phys. Rev. D 23 (1981) , 2745 S.J.Brodsky, P.Hoyer, C.Peterson, and N.Sakai, Phys. Lett. B 93 (1980), 451 The intrinsic charm contribution consist of a five-quark state , originates from fluctuations, and has nonperturbative nature since scales as We however will not consider the intrinsic charm in this report. Our proposals for intrinsic charm measurement are given in: 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

Charm density in the proton - a bit of history: 2. The perturbative charm was introduced about 15 years ago in J.C.Collins, Phys. Rev. D 58 (1998) , 094002 M.A.G.Aivazis, J.C.Collins, F.I.Olness, and W.-K.Tung, Phys. Rev. D 50 (1994) , 3102 The perturbative charm contribution is defined in the VFNS : FFNS : p → (u, d, s, g) VFNS : p → (u, d, s, g) + (c, b, t) originates from process, has perturbative nature and obeys usual DGLAP evolution

Charm density in the proton - a bit of history: Order master equation for charm production within VFNS: The only constraint on the subtraction term:

Our approach is based on following observations: The ratios R= FL/ FT and A=2xFA/ F2 in heavy-quark leptoproduction are perturbatively stable within the FFNS. The quantities FL/ FT and 2xFA/ F2 are sensitive to resummation of the mass logarithms of the type αs ln(Q2 / m2) within the VFNS. These facts together imply that (future) high-Q2 data on the ratios R= FL/ FT and A=2xFA/ F2 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. Remember that, within the VFNS, the heavy-quark content of the proton is due to resummation of the mass logarithms of the type αs ln(Q2 / m2) and, for this reason, closely related to behavior of asymptotic perturbative series for high Q2.

Brief description of the idea: Within the FFNS, the leading mechanism is which contributes to F2, FL and FA. Within the VFNS, there is also the diagram which contributes only to F2, but not to FL and FA! This is because FL and FA do not contain mass logarithms αs ln(Q2 / m2) So, the mass logarithms resummation (or heavy-quark densities) should reduce the pQCD predictions for R= FL/ FT and A=2xFA/ F2 .

pQCD Predictions for F2 and R Resummation for F2 For F2 the NLO and resummation contributions are very close CTEQ6M PDFs are used for estimates Check with Iv and CW, add pi from D distributions. ACOT – CTEQ collaboration factorization cheme. M.A.G. Aivazis , John C. Collins , Fredrick I. Olness , Wu-Ki Tung, hep-ph/9312319 Resummation for R= FL/ FT

pQCD Predictions for F2 and R Resummation for F2 For F2 the NLO and resummation contributions are very close CTEQ6M PDFs are used for estimates Check with Iv and CW, add pi from D distributions. ACOT – CTEQ collaboration factorization cheme. M.A.G. Aivazis , John C. Collins , Fredrick I. Olness , Wu-Ki Tung, hep-ph/9312319 Resummation for R= FL/ FT

pQCD Predictions for A Resummation for A= 2xFA/F2

How to test the pQCD applicability? 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 Corresponding cross section is: where is the degree of linear polarization of the photon, and is the centre of mass energy of the reaction. is the angle between the photon polarization and quark ┴ momentum

We observe the following remarkable properties: 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.

Perturbative instability of the cross sections Check with Iv and CW, add pi from D distributions. ACOT – CTEQ collaboration factorization cheme. M.A.G. Aivazis , John C. Collins , Fredrick I. Olness , Wu-Ki Tung, hep-ph/9312319

Perturbative stability of the asymmetry Check with Iv and CW, add pi from D distributions. ACOT – CTEQ collaboration factorization cheme. M.A.G. Aivazis , John C. Collins , Fredrick I. Olness , Wu-Ki Tung, hep-ph/9312319

3. A Remark on the Gluon Contribution to the Proton Spin Bruell,Ent Projected data on Dg/g with an EIC, via g + p  D0 + X K- + p+ assuming vertex separation of 100 mm. Measure 90% of DG (@ Q2 = 10 GeV2) Check with Iv and CW, add pi from D distributions. ACOT – CTEQ collaboration factorization cheme. M.A.G. Aivazis , John C. Collins , Fredrick I. Olness , Wu-Ki Tung, hep-ph/9312319 RHIC-Spin Open theoretical problem: At high Q2 one should resum the mass logarithms in g 1 . Since the signs of c(x, Q2) and Δc(x, Q2) are opposite, resummation can affect essentially predicted value ΔG/G ~ g 1 / F2 . RHIC-Spin N.Ya. Ivanov e.a., in preparation

Conclusion 1. High-Q2 data on the ratios R= FL/ FT and A=2xFA/ F2 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. 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. 3. The mass logarithms contributions to c(x, Q2) and Δc(x, Q2) have opposite signs, and their resummation can affect essentially predicted values of ΔG/G ~ g 1 / F2 .