1. Quarkonia: theoretical overview Marzia Nardi INFN Torino III Convegno Nazionale sulla Fisica di ALICE Frascati, 12-14 Novembre 2007

2. CGC effects on J/  production in nuclear collisions p(d)-A : D. Kharzeev, K. Tuchin, hep-ph/0510358 (published) A-A : D. Kharzeev, E. Levin, M.N., K. Tuchin (in preparation)

3. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi Hadron scattering at high energy A new phenomenon is expected : parton saturation From HERA: At high energies hadrons appear dense.

4. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi Gluon density in hadrons McLerran, hep-ph/0311028

5. III Conv. Naz. ALICE, Frascati, 12-14 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 )

6. III Conv. Naz. ALICE, Frascati, 12-14 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.

7. III Conv. Naz. ALICE, Frascati, 12-14 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

8. III Conv. Naz. ALICE, Frascati, 12-14 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

9. III Conv. Naz. ALICE, Frascati, 12-14 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.

10. III Conv. Naz. ALICE, Frascati, 12-14 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

11. III Conv. Naz. ALICE, Frascati, 12-14 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

12. III Conv. Naz. ALICE, Frascati, 12-14 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

13. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi At y>1, at RHIC : t f > t p > t int J/  is formed outside the nucleus, no nuclear effects !

14. III Conv. Naz. ALICE, Frascati, 12-14 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

15. III Conv. Naz. ALICE, Frascati, 12-14 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.

16. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi J/  production cross-section

17. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi Probability of gluon radiation by a valence q: with J/  wave function (NR approximation)

18. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi The saturation properties are contained in the amplitude with

19. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi Total cross-section where  =mr. If M  >Q s : and If M  <Q s : and

20. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi Results for d-Au

21. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi

22. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi

23. III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007Marzia Nardi Results for Au-Au (RHIC)