D. Kharzeev Nuclear Theory Group @ BNL

1. Alice Club, CERN TH, May 14, 2007 Non-linear evolution in QCDand hadron multiplicity predictions for the LHC D. Kharzeev Nuclear Theory Group @ BNL Based on work with E. Levin, M. Nardi, K. Tuchin

2. Two questions: What is the mechanism of multi-particle production at high energies in QCD? What are the implications for high-energy evolution and for the energy dependence? A possible answer: strong semi-classical color fields

3. Strings vs partons in high energy QCD string picture: color string = longitudinal color fields parton picture: “Weizsacker-Williams” gluons = transverse color fields

4. What is the structure of the classical fields?warm-up: electrodynamics • Lienard-Weichert potential of a moving charge • Electro-magnetic fields: ≈Ez transverse a longitudinal v R E

5. The space-time picture of high-energy interactions in QCD 1. Fast (large y) partons live for a long time; 2. Parton splitting probability is ~ as y - not small!

6. The origin of classical background field static field sources Gluons with large rapidity and large occupation number act as a background field for the production of slower gluons “Color Glass Condensate”

7. What is the dynamics of non-linear evolution in QCD? Parton splitting in the background of the color field? (generalization of the linear QCD evolution equations - BFKL, DGLAP) GLR, MQ, JIMWLK, BK equations

8. Renormalization group Emitted partons become a part of the classical field for slower partons; “slow” and “fast” are relative

9. Parton production in the background field Parton propagator in the background field

10. Mean field approach: BK equation Let us compute an imaginary part of the gluon propagator in the background field: where the S-matrix is related to the imaginary scattering amplitude

11. The equation

12. Equivalent form: where is the BFKL splitting kernel; initial conditions are provided e.g. by MV model: Is this evolution equation unique?

13. What are the properties of the color field at high energies? The field created by faster moving partons is seen by the slower produced partons as: • Static • Constant in space

14. Why static? The lifetime of a field configuration is (y is the rapidity distance from the beam); The ratio is for BFKL, >>1

15. Why constant in space? at rapidity y, the field is constant at distances up to gluon production occurs at y-Dy, at distances The ratio is “large”: BFKL yields R ~ 10

16. What is the mechanism of gluon production in strong, constant, static color field at weak coupling? Schwinger-like gluon pair production: where SU(3): G.Nayak, P.Nieuwenhuizen, hep-ph/0504070

17. Integrated spectrum: Average transverse momentum (saturation scale): Saturation momentum is a measure of the field strength

18. Towards the evolution equation the energy density of the field grows with rapidity: this is just the energy conservation!

19. The evolution equation Sudakov-type factor needed to avoid double counting (no gluons produced between Y and Y’) DK, E. Levin, to appear

20. Equation for the saturation momentum(differential form) where

21. The solution Initial condition RHIC phenomenology (KLN):

22. Properties of the solution for moderate energies, power growth with the intercept (for as ~ 0.3) ~ 0.25; at very high energies, a universal limit!

23. Phenomenology central Au-Au collisions: GeV2

25. Energy dependence of multiplicity power growth new evolution equation logarithmic fit

26. Predictions for the LHC KLN, hep-ph/0408050 pp: little change; Pb-Pb: decrease by ~ 30%

27. Summary The hadron multiplicity measurements at the LHC will enable us to understand the nature of multiparticle production and the origin of parton evolution at high energies