QCD Phenomenology and Heavy Ion Physics

1. QCD Phenomenology and Heavy Ion Physics Yuri Kovchegov The Ohio State University

2. Outline We’ll describe application of Saturation/Color Glass Condensate physics to Heavy Ion Collisions, concentrating on: • Multiplicity vs. Centrality and vs. Energy, dN/dη vs. rapidity η • Hadron production in p(d)A collisions: going from mid- to forward rapidity at RHIC, transition from Cronin enhancement to suppression. • Two-particle correlations, back-to-back jets.

3. Multiplicity

4. Particle Multiplicity In Saturation/Color Glass Physics one has • only one scalein the problem – the saturation scale QS . • the leading fields are classical: The resulting gluon multiplicity is given by such that since d2b ~ S ~ p R2 , with R the nuclear radius.

5. Particle Multiplicity vs. Centrality Since and we get : which is not a constant due to running of the coupling: Thus

6. Particle Multiplicity vs. Centrality This simple reasoning allowed D. Kharzeev and E. Levin to fit multiplicity as a function of centrality. (from nucl-th/0108006)

7. Particle Multiplicity vs. Energy Let’s try to use the same simple formula to check the energy dependence of multiplicity. Start with From saturation models of HERA DIS data we know that with Therefore we write obtaining Kharzeev, Levin ‘01

8. Particle Multiplicity vs. Energy Using the known multiplicity at 130 GeV Kharzeev and Levin predicted multiplicity at 200 GeV using the above model: The result agreed nicely with the data: (PHOBOS) • Energy dependence works too!

9. dN/dη To understand the rapidity dependence one has to make a few more steps. Starting with factorization assumption inspired by the production diagram, and assuming a saturation/CGC form of the unintegrated gluon distribution f:

10. dN/dη Kharzeev and Levin obtained a successfull fit of the pseudo-rapidity distribution of charged particles in AA: The value of the saturation scale turned out to be (see also Kharzeev & Nardi ’00, Kharzeev, Levin, Nardi ’01)

11. dN/dη in dAu The same approach works for pseudo-rapidity distribution of total charged multiplicity in dAu collisions: (from Kharzeev, Levin, Nardi, hep-ph/0212316)

12. Thermalization: Bottom-Up Scenario Baier, Mueller, Schiff, Son ‘00 • Includes 2 → 3 and 3 → 2 rescattering processes with the LPM effect due to interactions with CGC medium. • Does not introduce any new scale, one still has QS only, with • Can fit the multiplicity data assuming that less particles were produced initially (smaller QS) but their numbers increased during thermalization. Baier, Mueller, Schiff, Son ‘02

13. Bottom-Up Scenario: Questions • Instabilities!!! Evolution of the system may develop instabilities. (Mrowczynski, Arnold, Lenaghan, Moore, Romatschke, Strickland, Yaffe) However, it is not clear whether instabilities would speed up the thermalization process and how to interpret them diagrammatically . • Another problem is that since and Stronger than classical field? Stronger than any QCD gluon field? It appears that

14. Hadron Spectra Let’s consider gluon production, it will have all the essential features, and quark production could be done by analogy.

15. Gluon Production in Proton-Nucleus Collisions (pA): Classical Field To find the gluon production cross section in pA one has to solve the same classical Yang-Mills equations for two sources – proton and nucleus. This classical field has been found by Yu. K., A.H. Mueller in ‘98

16. Gluon Production in pA: McLerran-Venugopalan model The diagrams one has to resum are shown here: they resum powers of Yu. K., A.H. Mueller, hep-ph/9802440

17. Gluon Production in pA: McLerran-Venugopalan model Classical gluon production: we need to resum only the multiple rescatterings of the gluon on nucleons. Here’s one of the graphs considered. Yu. K., A.H. Mueller, hep-ph/9802440 Resulting inclusive gluon production cross section is given by With the gluon-gluon dipole-nucleus forward scattering amplitude

18. McLerran-Venugopalan model: Cronin Effect To understand how the gluon production in pA is different from independent superposition of A proton-proton (pp) collisions one constructs the quantity Enhancement (Cronin Effect) We can plot it for the quasi-classical cross section calculated before (Y.K., A. M. ‘98): Kharzeev Yu. K. Tuchin ‘03 Classical gluon production leads to Cronin effect! Nucleus pushes gluons to higher transverse momentum! (see also Kopeliovich et al, ’02; Baier et al, ’03; Accardi and Gyulassy, ‘03)

19. Proof of Cronin Effect • Plotting a curve is not a proof of Cronin effect: one has to trust the plotting routine. • To prove that Cronin effect actually does take place one has to study the behavior of RpA at large kT (cf. Dumitru, Gelis, Jalilian-Marian, quark production, ’02-’03): Note the sign! RpA approaches 1 from above at high pT  there is an enhancement!

20. Cronin Effect • The height and position of the Cronin maximum are increasing functions of centrality (A)! The position of the Cronin maximum is given by kT ~ QS~ A1/6 as QS2 ~ A1/3. Using the formula above we see that the height of the Cronin peak is RpA (kT=QS) ~ ln QS ~ ln A.

21. Including Quantum Evolution To understand the energy dependence of particle production in pA one needs to include quantum evolution resumming graphs like this one. This resums powers of a ln 1/x = a Y. This has been done in Yu. K., K. Tuchin, hep-ph/0111362. The rules accomplishing the inclusion of quantum corrections are Proton’s LO wave function Proton’s BFKL wave function  and where the dipole-nucleus amplitude N is to be found from (Balitsky, Yu. K.)

22. Including Quantum Evolution Amazingly enough, gluon production cross section reduces to kT –factorization expression (Yu. K., Tuchin, ‘01): with the proton and nucleus “unintegrated distributions” defined by with NGp,A the amplitude of a GG dipole on a p or A.

23. Our Prediction Toy Model! RpA Our analysis shows that as energy/rapidity increases the height of the Cronin peak decreases. Cronin maximum gets progressively lower and eventually disappears. • Corresponding RpA levels off at roughly at energy / rapidity increases (Kharzeev, Levin, McLerran, ’02) k / QS D. Kharzeev, Yu. K., K. Tuchin, hep-ph/0307037; (see also numerical simulations by Albacete, Armesto, Kovner, Salgado, Wiedemann, hep-ph/0307179 and Baier, Kovner, Wiedemann hep-ph/0305265 v2.) • At high energy / rapidity RpAat the Cronin peak becomes a decreasing function of both energy and centrality.

24. 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

25. RdAu at different rapidities RdAu RCP – central to peripheral ratio Most recent data from BRAHMS Collaboration nucl-ex/0403005 Our prediction of suppression was confirmed!

26. Our Model RdAu pT RCP pT from D. Kharzeev, Yu. K., K. Tuchin, hep-ph/0405045, where we construct a model based on above physics + add valence quark contribution

27. Our Model We can even make a prediction for LHC: Dashed line is for mid-rapidity pA run at LHC, the solid line is for h=3.2 dAu at RHIC. Rd(p)Au pT from D. Kharzeev, Yu. K., K. Tuchin, hep-ph/0405045

28. Two-Particle Correlations

29. 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 Yu.K., Tuchin ’02) : which leads to suppression of B2B jets at mid-rapidity dAu (vs pp):

30. 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 Yu.K., ’04.

31. 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

32. 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)

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

34. Back-to-back Correlations • However, KLM calculations are just a model. An exact calculation of two-particle inclusive cross section in p(d)+A (or DIS) has been performed in J. Jalilian-Marian and Yu.K., ’04. • The resulting expression for the cross section is so horrible that no sane person would show it in a talk. It won’t fit in the PowerPoint format anyway.  Nevertheless it exists and can be used to make numerical predictions, though after a lot of work. (One has to solve 6 integral equations to get the answer.)

35. Conclusions • Particle multiplicity in AuAu and dAu collisions varies as a function of energy, centrality and rapidity in apparent agreement with saturation/CGC predictions. • New RHIC dAu data at forward rapidity seem to confirm expectations of Saturation / CGC physics: at mid-rapidity we see Cronin enhancement, while at forward rapidity we see suppression arising from the small-x evolution. • Back-to-back correlations seem to disappear in a certain transverse momentum region in dAu, in agreement with preliminary CGC expectations. • Implications for AA collisions need to be understood.

36. Backup Slides

37. Extended Geometric Scaling A general solution to BFKL equation can be written as where It turns out that the full solution of nonlinear evolution equation N(z,y) is a function of a single variable, N=N(z QS(y)), with (geometric scaling): • Inside the saturation region, , where nonlinear • evolution dominates (Levin, Tuchin ‘99 ) (ii) In the extended geometric scaling region, where g≈1/2: (Iancu, Itakura, McLerran ‘02)

38. Geometric Scaling in DIS Geometric scaling has been observed in DIS data by Stasto, Golec-Biernat, Kwiecinski in ’00. Here they plot the total DIS cross section, which is a function of 2 variables - Q2 and x, as a function of just one variable:

39. “Phase Diagram” of High Energy QCD III II I High Energy or Rapidity kgeom = QS2 / QS0 QS Moderate Energy or Rapidity QS  pT2 Cronin effect and low-pT suppression

40. Region I: Double Logarithmic Approximation At very high momenta, pT >> kgeom, the gluon production is given by the double logarithmic approximation, resumming powers of Resulting produced particle multiplicity scales as with where y=ln(1/x) is rapidity and QS0 ~ A1/6 is the saturation scale of McLerran-Venugopalan model. For pp collisions QS0 is replaced by L leading to as QS0 >> L. Kharzeev Yu. K. Tuchin ‘03 RpA < 1 in Region I  There is suppression in DLA region!

41. Region II: Anomalous Dimension At somewhat lower but still large momenta, QS < kT < kgeom, the BFKL evolution introduces anomalous dimension for gluon distributions: Kharzeev, Levin, McLerran, hep-ph/0210332 with BFKL g=1/2 (DLA g=1) The resulting gluon production cross section scales as (we loose one power of QS) such that For large enough nucleus RpA << 1 – high pT suppression! How does energy dependence come into the game?

42. Region II: Anomalous Dimension A more detailed analysis gives the following ratio in the extended geometric scaling region – our region II: RpA is also a decreasing function of energy, leveling off to a constant RpA ~ A-1/6 at very high energy. • RpAis a decreasing function of both energy and centrality at high energy / rapidity. (D. Kharzeev, Yu. K., K. Tuchin, hep-ph/0307037)

43. Region III: What Happens to Cronin Peak? • The position of Cronin peak is given by saturation scale QS , such that the • height of the peak is given by RpA (kT = QS (y), y). • It appears that to find out what happens to Cronin maximum we need to know the gluon distribution function of the nucleus at the saturation scale – fA (kT = QS, y). For that we would have to solve nonlinear BK evolution equation – a very difficult task. • Instead we can use the scaling property of the solution of BK equation which leads to Levin, Tuchin ’99 Iancu, Itakura, McLerran, ‘02 • We do not need to know fA to determine how Cronin peak scales with • energy and centrality! (The constant carries no dynamical information.)