TY - JOUR

T1 - Solution for the BFKL pomeron calculus in zero transverse dimensions

AU - Kozlov, M.

AU - Levin, E.

N1 - Funding Information:
This research was supported in part by the Israel Science Foundation, founded by the Israeli Academy of Science and Humanities and by BSF grant # 20004019.

PY - 2006/11/27

Y1 - 2006/11/27

N2 - In this paper the exact analytical solution is found for the BFKL pomeron calculus in zero transverse dimensions, in which all pomeron loops have been included. The comparison with the approximate methods of the solution is given, and the kinematic regions are discussed where they describe the behaviour of the scattering amplitude quite well. In particular, the semi-classical approach is considered, which reproduces the main properties of the exact solution at large values of rapidity (Y ≥ 10). It is shown that the mean field approximation leads to a good description of the scattering amplitude only if the amplitude at low energy is rather large. However, even in this case, it does not lead to the correct asymptotic behaviour of the scattering amplitude at high energies.

AB - In this paper the exact analytical solution is found for the BFKL pomeron calculus in zero transverse dimensions, in which all pomeron loops have been included. The comparison with the approximate methods of the solution is given, and the kinematic regions are discussed where they describe the behaviour of the scattering amplitude quite well. In particular, the semi-classical approach is considered, which reproduces the main properties of the exact solution at large values of rapidity (Y ≥ 10). It is shown that the mean field approximation leads to a good description of the scattering amplitude only if the amplitude at low energy is rather large. However, even in this case, it does not lead to the correct asymptotic behaviour of the scattering amplitude at high energies.

KW - BFKL pomeron

KW - Exact solution

KW - Generating functional

KW - Semi-classical solution

KW - Sturm-Liouville problem

UR - http://www.scopus.com/inward/record.url?scp=33750147752&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysa.2006.08.011

DO - 10.1016/j.nuclphysa.2006.08.011

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AN - SCOPUS:33750147752

SN - 0375-9474

VL - 779

SP - 142

EP - 176

JO - Nuclear Physics A

JF - Nuclear Physics A

ER -