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Effective Hamiltonian for QCD evolution at high energy

Effective Hamiltonian for QCD evolution at high energy. Yoshitaka Hatta (RIKEN BNL). In collaboration with E.Iancu, L.McLerran, A.Stasto, D. Triantafyllopoulos hep-ph/0504182,0505235 (NPA, in press). QCD in the high energy limit.

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Effective Hamiltonian for QCD evolution at high energy

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  1. Effective Hamiltonian for QCD evolution at high energy Yoshitaka Hatta (RIKEN BNL) In collaboration with E.Iancu, L.McLerran, A.Stasto, D. Triantafyllopoulos hep-ph/0504182,0505235 (NPA, in press)

  2. QCD in the high energy limit What is the asymptotic behavior of cross section? BFKL equation (Leading Log Approximation) predicts indefinite growth of the gluon number. Must be tamed (How?) NLLA, BKP, Nonlinear evolution equations Mutual interaction of partons leads to the formation of Color Glass Condensate.

  3. QCD evolution equations at small-x BFKL, BKP equation Reggeized gluon (“reggeon”) ~ Free propagator

  4. Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner Balitsky-JIMWLK equation ~1 dressed propagator Wilson line Intended for dense-dilute (asymmetric) scatterings. Saturation at fixed impact parameter.

  5. Beyond the B-JIMWLK equation An evolution equation with all possible reggeon number changing vertices describes both the gluon recombination and the gluon multiplication.

  6. Evolution equation with Pomeron Loops The new kernel must be symmetric under

  7. Construction of the symmetric kernel Calculate the effective action in the presence of two background fields in the CGC framework. The total gauge field classical semi-hard soft

  8. High density regime: JIMWLK Hamiltonian Start with in the background Coulombgauge, integration ( )

  9. Low density regime: BREM Hamiltonian Start with in the background light cone gauge, integration dual to JIMWLK c.f. Kovner & Lublinsky

  10. The symmetric effective action Start again with in the background light cone gauge,

  11. Two-dimensional effective theory of Wilson lines zero curvature

  12. Summary • B-JIMWLK equation misses Pomeron loops. Necessity to construct a symmetric kernel. • We constructed the “leading” contribution to the complete kernel by combining the CGC and the effective action approaches. c.f. Balitsky ‘99, ‘05, Kovner&Lublinsky ‘05 • There are other diagrams still to be calculated to obtain the complete kernel.

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