Random walks of partons in SU(N_c) and classical representations of color charges in QCD at small x

Details Random walks of partons in SU(N_c) and classical representations of color charges in QCD at small x Random walks of partons in SU(N_c) and classical representations of color charges in QCD at small x

2004-06-15

arxiv.org/abs/hep-ph/0406169v2

Phys.Rev. D70 (2004) 105012

Physics

High Energy Physics

High Energy Physics - Phenomenology

51 pages, includes 3 eps files

Scientific paper

10.1103/PhysRevD.70.105012

The effective action for wee partons in large nuclei includes a sum over static color sources distributed in a wide range of representations of the SU(N_c) color group. The problem can be formulated as a random walk of partons in the N_c-1 dimensional space spanned by the Casimirs of SU(N_c). For a large number of sources, k >> 1, we show explicitly that the most likely representation is a classical representation of order O(\sqrt{k}). The quantum sum over representations is well approximated by a path integral over classical sources with an exponential weight whose argument is the quadratic Casimir operator of the group. The contributions of the higher N_c-2 Casimir operators are suppressed by powers of k. Other applications of the techniques developed here are discussed briefly.

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