Quarkonia: theoretical overview Marzia Nardi INFN Torino III Convegno Nazionale sulla Fisica di ALICE Frascati, Novembre 2007

CGC effects on J/  production in nuclear collisions p(d)-A : D. Kharzeev, K. Tuchin, hep-ph/ (published) A-A : D. Kharzeev, E. Levin, M.N., K. Tuchin (in preparation)

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi Hadron scattering at high energy A new phenomenon is expected : parton saturation From HERA: At high energies hadrons appear dense.

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi Gluon density in hadrons McLerran, hep-ph/

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi Saturation scale in nuclei [D.Kharzeev, E.Levin, M.Nardi] [D.Kharzeev, E.Levin, M.Nardi] Consider a nucleus or hadron interacting with an external probe, exchanging Q Transverse area of a parton ~ 1/Q 2 Cross section parton-probe :  ~  s /Q 2 If many partons interact : S~N parton  In a nucleus : N A =N parton A [ N parton = xG(x,Q 2 ) ] The parton density saturates when S~  R A 2 Saturation scale : Q s 2 ~  s (Q s 2 )N A /  R A 2 ~A 1/3 At saturation N A is proportional to 1/  s Q s 2 is proportional to the (transverse) density of participating nucleons n A =N A /  R A 2 ; larger for heavy nuclei. N A ~ Q s 2 /  s (Q s 2 )

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi Color Glass Condensate Classical effective theory : high density limit of QCD color : partons are colored glass : they evolve slowly compared to their natural time-scale condensate : their density is proportional to the inverse of the coupling constant, typical of a Bose condensate.

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi Hadron production from the CGC Hadron multiplicities can be described in a parton saturation model, based on the Color Glass Condensate theory. In particular : Au-Au and d-Au collisions at RHIC, √s NN =20÷200 GeV Pb-Pb and p-Pb collisions at LHC, √s NN = 5500 GeV – total multiplicity – centrality dependence – rapidity dependence

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi J/  production The production mechanism of J/  in nuclear collisions at RHIC energies is different from that in pp collisions, because of gluon saturation in the nucleus. In p-A: at forward y more suppression at backward y weak enhancement

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi m c >  QCD  perturbative QCD, but non-perturbative effects are not negligible In A-A collisions: J/  suppression is a signature of QGP formation  it is important to understand the production mechanism. At RHIC : experimental data on hadron multiplicity can be explained by CGC, parton (gluon) saturation in the nuclear wave function. Q s 2 (x 2 ) >>  QCD. For heavy quarks : Q s < m : Q production is incoherent, pQCD Q s > m : Q production is coherent, the projectile interacts with the whole nucleus.

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi Time scales in p-A collisions t p = c-cbar production time –in the pair rest frame t p 0 = 1/2m c. –in the nucleus rest frame (  =E g /2m c ) : t p =E g /(2m c ) 2 E g = x 1 E p s=(x 1 p p +x 2 p t ) 2 =2x 1 x 2 E p M=2x 2 E g M s=(2m c ) 2 t p =1/(2x 2 M) x 2 =m c e -y /sqrt(s) at RHIC : x 2 =6.5x10 -3 e -y  t p =15 e y fm

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi t int = interaction time = R A /c at high energies t p > t int or l c =t p c > R A t p =15 e y fm : at forward y t p is very large – the projectile interacts with the whole nucleus – eikonal approximation for the calculation of scattering amplitude

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi t f = J/  formation time – in the pair rest frame t f 0 = 2/(m  ’- m  ) – in the nucleus rest frame (  =E g /M  ) : t f = 2E g /(m  ’- m  ) M  – t f 0 =0.45 fm  t f RHIC =41 e y fm

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi At y>1, at RHIC : t f > t p > t int J/  is formed outside the nucleus, no nuclear effects !

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi At -1<y<0 the production time at RHIC becomes smaller than he nuclear size : the c-cbar pair is produced in the interaction with a few nucleons: enhancement of J/  production. Correction for nuclear absorption. A-A :  s 6 A 2/3 p-A :  s 5 A 1/3 For large A, diagram (a) dominates

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi At y<-2 the coherence is lost. The production of J/  in p-A is similar to the one in pp collisions J/  can be formed inside the nucleus. c-cbar and J/  interact with nuclear matter.

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi J/  production cross-section

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi Probability of gluon radiation by a valence q: with J/  wave function (NR approximation)

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi The saturation properties are contained in the amplitude with

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi Total cross-section where  =mr. If M  >Q s : and If M  <Q s : and

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi Results for d-Au

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi

III Conv. Naz. ALICE, Frascati, Nov. 2007Marzia Nardi Results for Au-Au (RHIC)