Initial and final state effects in charmonium production at RHIC and LHC.

1. Initial and final state effects in charmonium production at RHIC and LHC. A.B.Kaidalov ITEP, Moscow Based on papers with L.Bravina, K.Tywoniuk, E.Zabrodin (Oslo U.), A. Capella, E.Ferreiro (Orsay, Saintiago U.)

2. Contents: • Introduction. • Nuclear shadowing for quarks and gluons. • Shadowing effects in heavy ion collisions. • Charmonium production in NA-interactions. • Charmonium production in heavy ion collisions. • Conclusions.

3. Introduction. • Heavy ion collisions at high energies – a tool to study hadronic matter at extreme conditions: high density quark -gluon systems in deconfined phase. • What are relevant degrees of freedom? • What are characteristic signals of a new phase (QGP)?. • Charmonium suppression due to Debye screening in QGP . Long history of theoretical and experimental investigations.

4. J/ψ-suppression history. • J/ψ-suppression is observed in hA- collisions. Usually considered as an absorption in nuclear medium. • “Anomalous suppression” was observed in Pb-Pb collisions at CERN

5. J/ψ-suppression history. • Different theoretical models for description of anomalous suppression : with QGP and without QGP (comovers model).

6. Space-time picture of high-energy interactions • Large coherence length (time) of hadronic fluctuations at high energies Δt ~ 2p/(M²-m²) • At high energies hadronic (nuclear) fluctuations are “prepared” long before an interaction. What are Fock state vectors of hadrons(nuclei) in the infinite momentum frame?

7. Space-time picture of high-energy interactions • The space-time picture of hA (AB) –interaction changes at energies Ecwhen lcoh ~ Δt~ RA . For typical interactions Ec ~ mN²RA . At E < Ec an elastic hA –scattering amplitude can be considered as successive rescatterings of an initial hadron on nucleons of a nucleus (Glauber model)

8. Space-time picture of high-energy interactions • For E > Ec there is a coherent interaction of constituents of a hadron with nucleons of a nucleus. However hA elastic amplitude can be calculated as in the Glauber model, but with account of inelastic intermediate states ( M² << s )- Gribov approach.

9. Shadowing of soft partons • Partons of a fast nucleus with small relative momenta x < 1/mN RA overlap in longitudinal space and can interact. For example two chains from different nucleons can fuse into a single chain (corresponds to PPP-interaction). Large masses of intermediate states in Gribov approach. Couplings can be determined from diffractive production processes and turned out to be small.

10. Shadowing of soft partons. • Calculations of interactions of soft partons in QCD perturbation theory has been performed by many authors (starting from GLR). Saturation of parton densities for x 0. For nuclei the state of saturated gluons :”Color glass condensate” (CGC) L.McLerran et al

11. Saturation effects for x 0. • The border of the saturation region Qs(х) depends on A.

12. Calculation of nuclear shadowing. The total cross section of a virtual photon (γ*) – nucleus cross section in the Glauber-Gribov approach

13. Contribution of the second rescattering where The longitudinal part of nuclear form-factor takes into account the coherence condition: x<< 1/mN RA

14. Higher order corrections Higher order corrections are model dependent. Two models have been used in papers by A.Capella et al(1997), N.Armesto et al (2003), K.Tywoniuk et al(2006): a) Schwimmer model where

15. Higher order corrections b) Eikonal-type model The ratio of cross sections per nucleon for different nuclei In the Schwimmer model

16. Diffractive production in γ*p-collisions To calculate nuclear shadowing in this approach it is necessary to know diffractive dissociation of a virtual photon on a nucleon. In paper by A.Capella et al parametrization of HERA data (with account of QCD evolution) was used to describe nuclear structure functions in the small-x region (shadowing for quarks).

17. In the paper by N.Armesto et al the unitary model for γ*p-collisions valid in a broad region of Q was used. K.Tywoniuk et al used recent fits of H1 to calculate shadowing for gluons Diffractive production in γ*p-collisions

18. Distributions of quarks in the pomeron are known reasonably well. There are still uncertainties in distributions of gluons at β > 0.5. Fits A and B of H1 were used. Fit B is preferable at present from data on diffractive jets and charm. Distributions of quarks and gluons in the pomeron

19. From A.Capella et al Comparison with experiment (NMC)

20. Dependence on Q² Weak dependence on Q²- leading twist effect.

21. Comparison with experiment (E665) From N.Armesto et al

22. Comparison with other theoretical determinations of shadowing From N.Armesto et al

23. Predictions for higher energies (smaller x)

24. Shadowing for gluons Red curves –fit A, blue ones –fit B

25. Q² -dependence

26. Comparison with other models

27. Impact parameter dependence

28. Shadowing effects in heavy ion collisions. • Inclusive spectra and particle densities For Glauber-type rescatterings AGK – cancellation takes place in the central rapidity region at s ∞ where

29. Particle densities in nucleus-nucleus collisions For particle densities we have where is the number of collisions in the Glauber model.

30. Shadowing for soft partons At very high energies soft partons of different nucleons overlap and can interact. This leads to shadowing effects for these partons (”saturation” for x 0). They are related to the shadowing for quarks and gluons in nuclei discussed above. ”Color glass condensate” approach in PQCD

31. In the Schwimmer model the suppression for inclusive spectra is described by a simple formula Calculation of suppression

32. Calculation of nuclear suppression Simplest partonic kinematics suggests Note that these effects are important in the small-x region: x << 1/mN RA. So they are absent for large pT particle production at RHIC. Suppression in this region is due to final state interactions.

33. Energy and impact parameter dependence of suppression Predictions of N.Armesto et al.

34. Nuclear shadowing andRHIC data. • Decrease of particle densities in comparison withGlauber model agrees withRHIC data. Dependenceon b (Npart) is also reproduced.

35. J/ψ-production at RHIC. • Interesting result of PHENIX collaboration at RHIC: J/ψ –suppression in the central rapidity region for D-Au collisions at RHIC is smaller than at SPS : σa =1÷2 mb at √s =200 GeV (σa= 4÷5 mb at√s ~ 20 GeV ). This was not expected by most of theoretical models.

36. Effects of gluon shadowing and J/ψ -production. For J/psi production at xF=0 in NA collisions the critical energy Ec is in the RHIC region and the “ low energy” formulas are not valid. The Glauber-type rescatterings are very small at central rapidities in this energy region (due to AGK cancellations) and the main mechanism of suppression is the gluon shadowing.

37. Nuclear effects forJ/ψ- production in NA-collisions. • Parameterization of inclusive cross section

38. Glauber-Gribov approach for charmonia production in hA-collisions. • Main theoretical ingredients for heavy quarkonia production and description of fixed targets data were given in K.Boreskov, A.Capella, A.Kaidalov, J.Tran Thanh Van (1993) Important role of energy-momentum conservation effects for xF ~ 1.

39. Glauber-Gribov approach for charmonia production in hA-collisions.

40. Glauber-Gribov approach for charmonia production in hA-collisions.

42. J/ψ-production in AA at RHIC.

48. This is drastically different from statistical models

49. Conclusions. • Unitarity effects are important for high energy interactions of hadrons and nuclei. • Shadowing for nuclear structure functions can be calculated using Gribov`s formalism and is related to diffractive processes. • Interactions of soft partons play an important role at RHIC and especially at LHC.

50. Conclusions. • Data on D-Au collisions at RHIC are consistent with gluon shadowing and indicate to a change of the space-time picture of charmonia production with energy. Strong shadowing effects are predicted for heavy onia production at LHC in p-Pb collisions and are important as an initial condition for Pb-Pb.