Summary of theoretical aspects of pA physics

1. Summary of theoretical aspects of pA physics Kirill Tuchin eA+pA Workshop, May 8, 2005, BNL

2. QCD at small x: review  • Life-time of a dipole is • Total cross section is a forward scattering amplitude • Quasi-classical regime: (McLerran,Venugopalan,94)

3. Linear evolution • High energy linear evolution regime (Fadin,Kuraev,Lipatov,Balitsky,75,78) • Evolution equation:

4. Evolution in a dense system • Evolution in a Color Glass Condensate:  (Balitski,Kovchegov,96,00) • Effective theory: color glass condensate, JIMWLK equations…

5. CGC vs shadowing models It’s all about parameters: Is there a quantum evolution? Is x small enough to induce coherence? How close is RHIC to CGC? Is the color field strong? • Shadowing models: take into account some of the above • effects and match well with pQCD at large x. • CGC takes them all into account but cannot be easily • matched with the conventional pQCD at moderate x.

6. Geometric scaling in nuclei p Armesto et al 

7. D-Au multiplicities Data from BRAHMS and PHOBOS Collaborations Kharzeev,Levin, Nardi

8. D-Au multiplicities PHOBOS nucl-ex/0311009 Conventional shadowing works well too!

9. Pseudo-rapidity asymmetry By Kharzeev, K.T. STAR Collaboration; nucl-ex/0408016

10. Shadowing Ratio Defining the shadowing ratio for the unintegrated gluon distributions Enhancement (anti-shadowing), most glue are here we plot it for the distribution in quasi-classical approximation Shadowing! (small k, small x)  Gluons are redistributed from low to high pT.

11. What Happens to Gluon Distributions? With the onset of evolution, as energy/rapidity increases, the shadowing ratio starts to decrease: Anti-shadowing Suppression! A new phenomenon. Shadowing (Toy model picture)

12. What Happens to Gluon Distributions? At very high energy “anti-shadowing” disappears: Suppression everywhere! (Toy model picture)

13. Why Suppression? In general one can write: Without quantum evolution =1 and there is no suppression: Kharzeev, Levin, McLerran, hep-ph/0210332 Quantum evolution leads to =1/2, such that leading to

14. Onset of saturation in pA

15. Particle spectra in dA   Evolution leads to suppression of RdA as a function of rapidity and centrality!  =3.2 Valence quarks are taken into account Kovchegov, K.T (2001); Kharzeev, Kovchegov, K.T. (2003,2004)

16. Other Predictions Color Glass Condensate / Saturation physics predictions are in sharp contrast with other models. The prediction presented here uses a Glauber-like model for dipole amplitude with energy dependence in the exponent. figure from I. Vitev, nucl-th/0302002, see also a review by M. Gyulassy, I. Vitev, X.-N. Wang, B.-W. Zhang, nucl-th/0302077

17. Fragmentation effect? • Fragmentation effect • due to large x1 does not • depend on energy, • while the saturation effect • does • Increase or decrease • DAu energy to verify. Kopeliovich et al. • Measure eA.

18. Particle production at LHC • Suppression at • y=3.2 at RHIC is the same as at LHC at rapidity y=0. • No Kopeliovich effect.

19. Particle production in DIS A very interesting 3-scale problem: a lot of information about “pdf”s (Kovchegov, K.T.,01)

20. Nuclear Modification in DIS

21. Heavy quark production • All quarks with m<Qs are produced in the same way. • At RHIC Qs=1.4e0.15GeV (at b=0),while mc=1.3 GeV • Thus, we expect suppression of charm in pA and AA • relative to pp at ~2-3. AA dA     Kharzeev, K.T., 2003;K.T. 2004.

22. Open Charm Spectrum The effect of saturation on spectrum at y=0: coherent incoherent Kharzeev, K.T., 2003; K.T. 2004. Experimental fit: ~(1+pT/p0)-n with p0=1.32 GeV/c ~Qs

23. Energy Loss in Nuclear Medium kT, Quenching factor qT,E Kharzeev, K.T. Cold Hot Gluon radiation into the “dead cone”  is suppressed Heavy quarks loose less energy then light ones.

24. J/ in pA: enhancement and suppression pA=App Kharzeev, K.T. What about polarization? y=0 y=1.8

25. Back-to-back Correlations Saturation and small-x evolution effects may also deplete back-to-back correlations of jets. Kharzeev, Levin and McLerran came up with the model shown below (see also Kovchegov, K.T. ’02) : which leads to suppression of B2B jets at mid-rapidity dAu (vs pp):

26. Back-to-back Correlations and at forward rapidity: from Kharzeev, Levin, McLerran, hep-ph/0403271 Warning: only a model, for exact analytical calculations see J. Jalilian-Marian and Kovchegov, ’04.

27. Back-to-back Correlations An interesting process to look at is when one jet is at forward rapidity, while the other one is at mid-rapidity: The evolution between the jets makes the correlations disappear: from Kharzeev, Levin, McLerran, hep-ph/0403271

28. Back-to-back Correlations • Disappearance of back-to-back correlations in dAu collisions predicted by KLM seems to be observed in preliminary STAR data. (from the contribution of Ogawa to DIS2004 proceedings)

29. Back-to-back Correlations • The observed data shows much less correlations for dAu than predicted by models like HIJING:

30. AuAu (flow + non-flow) dAu (“some flow”) At high pt in central collisions, azimuthal correlation in AuAu could be dominated by nonflow. pp (nonflow) In VERY peripheral collisions, azimuthal correlation in AuAu could be dominated by nonflow. Azimuthal correlation in AuAu, dAu and pp collisions: by A.Tang (STAR) v2·Mult. STAR Preliminary

31. Di-lepton Production • To calculate hadron production one always needs to convolute quark and gluon production cross sections with the • fragmentation functions which are poorly known. • Di-lepton production involves no fragmentation functions. It is, therefore, a much cleaner probe of the collision dynamics. • Theoretical calculation for di-lepton production in dAu is pretty straightforward.

32. Di-lepton Production from J. Jalilian-Marian, hep-ph/0402014 M2 is the photon’s invariant mass, kT and qT are total and relative transverse momenta of the lepton pair. • The photon does not interact (while everything else is just like for gluons): theoretical calculations are simpler! They were first performed by Kopeliovich, Schafer, and Tarasov in ’98.

33. Di-lepton Production Again one should get suppression at forward rapidities at RHIC. Here we plot Rp(d)A integrated over kT and qT , for both pA and dA, for y=2.2 as a function of M. from J. Jalilian-Marian, hep-ph/0402014

34. Di-lepton Production The suppression at forward rapidities at RHIC can also be seen as a function of kT: RpA as a function of kT for M=2GeV for y=1.5 (short-dashed) and y=3 (dashed), as well as for M=4GeV and y=3 (lower solid line). from Baier, Mueller, Schiff, hep-ph/0403201

35. Di-lepton Production and as a function of centrality: RpA as a function of A for kT=5 GeV, M=2GeV and y=3 for the saturation model (solid curve) and for analytical estimate RpA ~ A-0.124. from Baier, Mueller, Schiff, hep-ph/0403201

36. Summary • In high energy pA, eA collisions we study strong field • regime of QCD: • perturbative : CGC; • non-perturbative: Schwinger pair production by “Gluon Lasers”. • Observables to look at: • inclusive hadrons; • open and hidden charm; • correlations; • di-leptons. • Theoretically, eA is much better then pA for most of • observables. In addition one can measure • structure functions; • diffraction.