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

3. Introduction. Heavy ion collisions at high energies – Heavy ion collisions at high energies – a tool to study hadronic matter at extreme conditions: high density quark a tool to study hadronic matter at extreme conditions: high density quark -gluon systems in deconfined phase. -gluon systems in deconfined phase. What are relevant degrees of freedom? What are relevant degrees of freedom? What are characteristic signals of a new phase (QGP)?. What are characteristic signals of a new phase (QGP)?. Charmonium suppression due to Debye screening in QGP. Long history of theoretical and experimental investigations. 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. J/ψ-suppression is observed in hA- collisions. Usually considered as an absorption in nuclear medium. “Anomalous suppression” was observed in “Anomalous suppression” was observed in Pb-Pb collisions Pb-Pb collisions at CERN at CERN

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

6. Space-time picture of high-energy interactions Large coherence length (time) of Large coherence length (time) of hadronic fluctuations at high energies Δt ~ 2p/(M²-m²) Δt ~ 2p/(M²-m²) At high energies hadronic (nuclear) At high energies hadronic (nuclear) fluctuations are “prepared” long before an interaction. fluctuations are “prepared” long before an interaction. What are Fock state vectors of hadrons (nuclei) in the infinite momentum frame? 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 E c when l coh ~ Δt ~ R A. For typical interactions The space-time picture of hA (AB) – interaction changes at energies E c when l coh ~ Δt ~ R A. For typical interactions E c ~ m N ²R A. At E < E c an elastic hA – scattering amplitude can be considered as successive rescatterings of an initial hadron on nucleons of a nucleus E c ~ m N ²R A. At E < E c an elastic hA – scattering amplitude can be considered as successive rescatterings of an initial hadron on nucleons of a nucleus (Glauber model) (Glauber model)

8. Space-time picture of high-energy interactions For E > E c there is a coherent interaction of constituents of a hadron with nucleons of a nucleus. For E > E c there is a coherent interaction of constituents of a hadron with nucleons of a nucleus. However hA elastic amplitude can be However hA elastic amplitude can be calculated as in the Glauber model, but with account of inelastic intermediate states ( M² << s )- Gribov approach. 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 Partons of a fast nucleus with small relative momenta x < 1/m N R A 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 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 Calculations of interactions of soft partons in QCD perturbation theory has been performed by many authors 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 (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 border of the saturation region Q s (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 in the Glauber-Gribov approach

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

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

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

18. Distributions of quarks and gluons in the pomeron 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. 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 Fit B is preferable at present from data on present from data on diffractive jets and charm. diffractive jets and charm.

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

20. Dependence on Q² Weak dependence on Q ² - 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 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 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 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. 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 ”Color glass condensate” approach in PQCD

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

32. Calculation of nuclear suppression Simplest partonic kinematics suggests Note that these effects are important in the small-x region: x << 1/m N R A. So they are absent for large p T 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 and RHIC data. Decrease of particle densities in comparison with Glauber model agrees with RHIC data. Decrease of particle densities in comparison with Glauber model agrees with RHIC data. Dependence on b Dependence on b (N part ) is also reproduced. (N part ) is also reproduced. Glauber With account With account of shado- wing of shado- wing Experi- ment √s= 130 GeV 1200 ± 100 100 630± 120 120 555± 12±35 622±1 ±41

35. J/ψ-production at RHIC. Interesting result of PHENIX collaboration 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 : at RHIC is smaller than at SPS : σ a = 1÷2 mb at √s =200 GeV σ a = 1÷2 mb at √s =200 GeV ( σ a = 4÷ 5 mb at √s ~ 20 GeV ). This was not expected by most of theoretical models. This was not expected by most of theoretical models.

36. Effects of gluon shadowing and J/ψ -production. For J/psi production at x F =0 in NA collisions the critical energy E c is in the RHIC region and the “ low energy” formulas are not valid. For J/psi production at x F =0 in NA collisions the critical energy E c is in the RHIC region and the “ low energy” formulas are not valid. The Glauber-type rescatterings are very 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. 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 for J/ψ- production in NA-collisions. Parameterization of inclusive cross section 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 Main theoretical ingredients for heavy quarkonia production and description of fixed targets data were given in K.Boreskov, A.Capella, were given in K.Boreskov, A.Capella, A.Kaidalov, J.Tran Thanh Van (1993) A.Kaidalov, J.Tran Thanh Van (1993) Important role of energy-momentum conservation effects for x F ~ 1. Important role of energy-momentum conservation effects for x F ~ 1.

39. 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 This is drastically different from statistical models

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

50. Conclusions. Data on D-Au collisions at RHIC are 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. 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.

51. Conclusions. Combined effects of nuclear shadowing, comovers dissociation and recombination are consistent with Au-Au and Cu-Cu data at RHIC. Combined effects of nuclear shadowing, comovers dissociation and recombination are consistent with Au-Au and Cu-Cu data at RHIC. Rapidity dependence is reproduced. Rapidity dependence is reproduced. Predictions for charmonia production at LHC are given. Predictions for charmonia production at LHC are given.