Initial and final state effects Initial and final state effects in charmonium production in charmonium production

at RHIC and LHC.at RHIC and LHC.

A.B.Kaidalov A.B.Kaidalov

ITEP, MoscowITEP, MoscowBased on papers withBased on papers with

L.Bravina, K.Tywoniuk, E.Zabrodin (Oslo U.),L.Bravina, K.Tywoniuk, E.Zabrodin (Oslo U.),

A. Capella, E.Ferreiro (Orsay, Saintiago U.)A. Capella, E.Ferreiro (Orsay, Saintiago U.)

Contents:Contents: Introduction.Introduction. Nuclear shadowing for quarks and Nuclear shadowing for quarks and

gluons.gluons. Shadowing effects in heavy ion Shadowing effects in heavy ion

collisions.collisions. Charmonium production in NA-Charmonium production in NA-

interactions.interactions. Charmonium production in heavy ion Charmonium production in heavy ion

collisions.collisions. Conclusions.Conclusions.

Introduction.Introduction.

Heavy ion collisions at high energies –Heavy ion collisions at high energies –

a tool to study hadronic matter at extreme a tool to study hadronic matter at extreme conditions: high density quarkconditions: 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 What are characteristic signals of a new phase

(QGP)?.(QGP)?. Charmonium suppression due to Debye Charmonium suppression due to Debye

screening in QGP . Long history of theoretical screening in QGP . Long history of theoretical and experimental investigations.and experimental investigations.

J/J/ψψ-suppression history.-suppression history.

J/J/ψψ-suppression is observed in hA- -suppression is observed in hA- collisions. Usually considered as an collisions. Usually considered as an absorption in nuclear medium.absorption in nuclear medium.

““Anomalous suppression” was Anomalous suppression” was observed in observed in

Pb-Pb collisionsPb-Pb collisions

at CERNat CERN

J/J/ψψ-suppression history.-suppression history.

Different theoretical models forDifferent theoretical models for

description of anomalous description of anomalous suppression : with QGP and without suppression : with QGP and without QGP (comovers model).QGP (comovers model).

Space-time picture of high-energy Space-time picture of high-energy interactionsinteractions

Large coherence length (time) ofLarge coherence length (time) of

hadronic fluctuations at high energieshadronic fluctuations at high energies

ΔΔt ~ 2p/(M²-m²)t ~ 2p/(M²-m²)

At high energies hadronic (nuclear)At high energies hadronic (nuclear)

fluctuations are “prepared” long before an fluctuations are “prepared” long before an interaction.interaction.

What are Fock state vectors of hadronsWhat are Fock state vectors of hadrons (nuclei) in the infinite momentum frame?(nuclei) in the infinite momentum frame?

Space-time picture of high-energy Space-time picture of high-energy interactionsinteractions

The space-time picture of hA (AB) –The space-time picture of hA (AB) –interaction changes at energies Einteraction changes at energies Ecc when when

llcoh coh ~ ~ ΔΔtt ~ R~ RA . A . For typical interactions For typical interactions

EEc c ~ m~ mNN²R²RA . A . At E < EAt E < Ec c an elastic hA –an elastic hA –scattering amplitude can be considered scattering amplitude can be considered as as successivesuccessive rescatterings of an initial rescatterings of an initial hadron on nucleons of a nucleushadron on nucleons of a nucleus

(Glauber model)(Glauber model)

Space-time picture of high-energy Space-time picture of high-energy interactionsinteractions

For E > EFor E > Ec c there is a coherent interaction there is a coherent interaction of constituents of a hadron with nucleons of constituents of a hadron with nucleons of a nucleus.of a nucleus.

However hA elastic amplitude can beHowever hA elastic amplitude can be calculated as in the Glauber model, but calculated as in the Glauber model, but

with account of inelastic intermediate with account of inelastic intermediate states ( M² << s )- Gribov approach.states ( M² << s )- Gribov approach.

Shadowing of soft partonsShadowing of soft partons Partons of a fast nucleus with smallPartons of a fast nucleus with smallrelative momenta x < 1/mrelative momenta x < 1/mNN R RA A overlap in overlap in

longitudinal space and can interact.longitudinal space and can interact.For example two chains from different For example two chains from different

nucleons can fuse into a single chain nucleons can fuse into a single chain (corresponds to PPP-interaction).(corresponds to PPP-interaction).

Large masses of intermediate states inLarge masses of intermediate states in Gribov approach. Couplings can beGribov approach. Couplings can bedetermined from diffractive productiondetermined from diffractive productionprocesses and turned out to be small.processes and turned out to be small.

Shadowing of soft partons.Shadowing of soft partons.

Calculations of interactions of soft Calculations of interactions of soft partons in QCD perturbation theorypartons in QCD perturbation theory

has been performed by many authorshas been performed by many authors

(starting from GLR). Saturation of (starting from GLR). Saturation of parton densities for xparton densities for x 0. For nuclei 0. For nuclei the state of saturated gluons :the state of saturated gluons :”Color ”Color glass condensate” (CGC) glass condensate” (CGC) L.McLerran L.McLerran et alet al

Saturation effects for xSaturation effects for x 0. 0.

The border ofThe border of

the saturationthe saturation

region Qregion Qss(х)(х)

depends on A. depends on A.

1/3sQ A

Calculation of nuclear shadowing. Calculation of nuclear shadowing.

The total cross section of a virtual The total cross section of a virtual photon (photon (γγ*) – nucleus cross section*) – nucleus cross section

in the Glauber-Gribov approachin the Glauber-Gribov approach

Contribution of the second Contribution of the second rescatteringrescattering

wherewhere

The longitudinal part of nuclear form-The longitudinal part of nuclear form-factorfactor

takes into account the coherence takes into account the coherence condition: x<< 1/mcondition: x<< 1/mNN R RA A

Higher order correctionsHigher order corrections

Higher order corrections are model Higher order corrections are model dependent. Two models have beendependent. Two models have been

used in papers by used in papers by A.Capella et alA.Capella et al (1997),(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

wherewhere

Higher order correctionsHigher order corrections

b) Eikonal-type modelb) Eikonal-type model

The ratio of cross sections per nucleon The ratio of cross sections per nucleon for different nucleifor different nuclei

In the Schwimmer modelIn the Schwimmer model

Diffractive production in Diffractive production in γγ*p-*p-collisionscollisions

To calculate nuclear shadowing in this To calculate nuclear shadowing in this approach it is necessary to know approach it is necessary to know diffractive dissociation of a virtual diffractive dissociation of a virtual photon on a nucleon.photon on a nucleon.

In paper by In paper by A.Capella et al A.Capella et al parametrization parametrization of HERA data (with account of QCD of HERA data (with account of QCD evolution) was used to describe nuclear evolution) was used to describe nuclear structure functions in the small-x region structure functions in the small-x region (shadowing for quarks).(shadowing for quarks).

Diffractive production in Diffractive production in γγ*p-*p-collisionscollisions

In the paper by In the paper by N.Armesto et al N.Armesto et al

the unitary model for the unitary model for γγ*p-collisions valid in *p-collisions valid in a broad region of Q a broad region of Q was used.was used.

K.Tywoniuk et al K.Tywoniuk et al used used recent fits of H1 to recent fits of H1 to calculate shadowing calculate shadowing for gluonsfor gluons

Distributions of quarks and gluons Distributions of quarks and gluons in the pomeronin the pomeron

Distributions of quarks Distributions of quarks in the pomeron are in the pomeron are known reasonably well. known reasonably well. There are still There are still uncertainties in uncertainties in distributions of gluons distributions of gluons at at ββ > 0.5. Fits A and B > 0.5. Fits A and B of H1 were used.of H1 were used.

Fit B is preferable atFit B is preferable at

present from data onpresent from data on

diffractive jets and diffractive jets and charm.charm.

Comparison with experiment Comparison with experiment (NMC)(NMC)

From From A.Capella et alA.Capella et al

Dependence on QDependence on Q²²

Weak dependence on Weak dependence on QQ² ² - leading twist - leading twist effect.effect.

Comparison with experiment Comparison with experiment (E665)(E665)

From From N.Armesto et alN.Armesto et al

Comparison with other theoretical Comparison with other theoretical determinations of shadowingdeterminations of shadowing

From From N.Armesto et alN.Armesto et al

Predictions for higher energies Predictions for higher energies (smaller x)(smaller x)

Shadowing for gluonsShadowing for gluons

Red curves –fit A, blue ones –fit BRed curves –fit A, blue ones –fit B

QQ² -dependence² -dependence

Comparison with other modelsComparison with other models

Impact parameter dependenceImpact parameter dependence

Shadowing effects in heavy ion Shadowing effects in heavy ion collisions.collisions.

Inclusive spectra and particle Inclusive spectra and particle densitiesdensities

For Glauber-type rescatterings AGK – For Glauber-type rescatterings AGK – cancellation takes place in the cancellation takes place in the central rapidity region at scentral rapidity region at s ∞ ∞

where where

Particle densities in nucleus-Particle densities in nucleus-nucleus collisionsnucleus collisions

For particle densities we haveFor particle densities we have

where is thewhere is the

number of collisions in the Glauber number of collisions in the Glauber model.model.

Shadowing for soft partonsShadowing for soft partons

At very high energies soft partons ofAt very high energies soft partons of different nucleons overlap and can different nucleons overlap and can

interact. This leads to shadowing interact. This leads to shadowing effects for these partons (”saturation” effects for these partons (”saturation” for xfor x 0). They are related to the 0). They are related to the shadowing for quarks and gluons in shadowing for quarks and gluons in nuclei discussed above.nuclei discussed above.

” ”Color glass condensate” approach in Color glass condensate” approach in PQCDPQCD

Calculation of suppressionCalculation of suppression

In the Schwimmer In the Schwimmer model the model the suppression for suppression for inclusive spectra is inclusive spectra is described by a described by a simple formulasimple formula

Calculation of nuclear suppressionCalculation of nuclear suppression

Simplest partonic kinematics suggestsSimplest partonic kinematics suggests

Note that these effects are important Note that these effects are important in the small-x region: in the small-x region: x << 1/mx << 1/mNN R RA.A.

So they are absent for large pSo they are absent for large pT T particle particle production at RHIC.production at RHIC.

Suppression in this region is due to Suppression in this region is due to final state interactions.final state interactions.

Energy and impact parameter Energy and impact parameter dependence of suppressiondependence of suppression

Predictions of N.Armesto et al.Predictions of N.Armesto et al.

Nuclear shadowing andNuclear shadowing and RHIC dataRHIC data..

Decrease of particle Decrease of particle densities in densities in comparison withcomparison with Glauber model Glauber model agrees withagrees with RHIC RHIC datadata..

DependenceDependence on bon b

(N(Npartpart) is also ) is also reproducedreproduced..

GlauberGlauber

With With accountaccount

of of shado-shado-wingwing

Experi-Experi-mentment

√√s=s=130 GeV130 GeV

12001200

±±

100100

630630±±

120120

555555±±

1212±±3535

622622±±11

±±4141

J/J/ψψ-production at RHIC.-production at RHIC. Interesting result of PHENIX collaboration Interesting result of PHENIX collaboration

at RHIC:at RHIC:

J/J/ψψ –suppression in the central rapidity –suppression in the central rapidity region for D-Au collisionsregion for D-Au collisions

at RHIC is smaller than at SPS :at RHIC is smaller than at SPS :

σσa a == 1÷2 mb at √s =200 GeV 1÷2 mb at √s =200 GeV

((σσaa = 4÷= 4÷ 5 mb at5 mb at √s √s ~ 20 ~ 20 GeVGeV ) ).. This was not expected by most of This was not expected by most of

theoretical models.theoretical models.

Effects of gluon shadowing and Effects of gluon shadowing and J/J/ψψ -production.-production.

For J/psi production at xFor J/psi production at xFF=0 in NA =0 in NA collisions the critical energy Ecollisions the critical energy Ec c is in the is in the RHIC region and the “ low energy” RHIC region and the “ low energy” formulas are not valid. formulas are not valid.

The The Glauber-type rescatterings are veryGlauber-type rescatterings are very small at central rapidities in this energy small at central rapidities in this energy

region (due to AGK cancellations) and the region (due to AGK cancellations) and the main mechanism of suppression is the main mechanism of suppression is the gluon shadowing.gluon shadowing.

Nuclear effects forNuclear effects for J/J/ψψ- - production production in NA-collisions.in NA-collisions.

Parameterization of inclusive cross Parameterization of inclusive cross section section

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

Main theoretical ingredients for Main theoretical ingredients for heavy quarkonia production and heavy quarkonia production and description of fixed targets datadescription of fixed targets data

were given in were given in K.Boreskov, A.Capella,K.Boreskov, A.Capella,

A.Kaidalov, J.Tran Thanh Van (1993)A.Kaidalov, J.Tran Thanh Van (1993)

Important role of energy-momentum Important role of energy-momentum conservation effects for xconservation effects for xF F ~ 1.~ 1.

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

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

J/J/ψψ-production in AA at RHIC.-production in AA at RHIC.

This is drastically This is drastically different from different from statistical modelsstatistical models

Conclusions.Conclusions.

Unitarity effects are important for high Unitarity effects are important for high energy interactions of hadrons and energy interactions of hadrons and nuclei.nuclei.

Shadowing for nuclear structure Shadowing for nuclear structure functions can be calculated usingfunctions can be calculated using

Gribov`s formalism and is related toGribov`s formalism and is related to

diffractive processes.diffractive processes. Interactions of soft partons play an Interactions of soft partons play an

important role at RHIC and especially at important role at RHIC and especially at LHC.LHC.

Conclusions.Conclusions.

Data on D-Au collisions at RHIC areData on D-Au collisions at RHIC areconsistent with gluon shadowing andconsistent with gluon shadowing andindicate to a change of the space-time indicate to a change of the space-time

picture of charmonia production with picture of charmonia production with energy.energy.

Strong shadowing effects are Strong shadowing effects are predicted for heavy onia production predicted for heavy onia production at LHC in p-Pb collisions and are at LHC in p-Pb collisions and are important as an initial condition for important as an initial condition for Pb-Pb.Pb-Pb.

Conclusions.Conclusions.

Combined effects of nuclear Combined effects of nuclear shadowing, comovers dissociation shadowing, comovers dissociation and recombination are consistent and recombination are consistent with Au-Au and Cu-Cu data at RHIC.with Au-Au and Cu-Cu data at RHIC.

Rapidity dependence is reproduced.Rapidity dependence is reproduced.

Predictions for charmonia production Predictions for charmonia production at LHC are given.at LHC are given.