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Alice Club, CERN TH, May 14, 2007. Non-linear evolution in QCD and hadron multiplicity predictions for the LHC. D. Kharzeev Nuclear Theory Group @ BNL. Based on work with E. Levin, M. Nardi, K. Tuchin. Two questions:. What is the mechanism of multi-particle production
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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
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
Strings vs partons in high energy QCD string picture: color string = longitudinal color fields parton picture: “Weizsacker-Williams” gluons = transverse color fields
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
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!
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”
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
Renormalization group Emitted partons become a part of the classical field for slower partons; “slow” and “fast” are relative
Parton production in the background field Parton propagator in the background field
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
Equivalent form: where is the BFKL splitting kernel; initial conditions are provided e.g. by MV model: Is this evolution equation unique?
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
Why static? The lifetime of a field configuration is (y is the rapidity distance from the beam); The ratio is for BFKL, >>1
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
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
Integrated spectrum: Average transverse momentum (saturation scale): Saturation momentum is a measure of the field strength
Towards the evolution equation the energy density of the field grows with rapidity: this is just the energy conservation!
The evolution equation Sudakov-type factor needed to avoid double counting (no gluons produced between Y and Y’) DK, E. Levin, to appear
Equation for the saturation momentum(differential form) where
The solution Initial condition RHIC phenomenology (KLN):
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!
Phenomenology central Au-Au collisions: GeV2
Energy dependence of multiplicity power growth new evolution equation logarithmic fit
Predictions for the LHC KLN, hep-ph/0408050 pp: little change; Pb-Pb: decrease by ~ 30%
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