Dipole-dipole scattering at high energy in the Pomeron field theory with Braun Hamiltonian and beyond
Abstract
In this paper we find that the scattering matrix for dipole-dipole interaction in the saturation region has the form: cal Sdd xrightarrowz ≫ 1 expLb − Cdd z2Rb ∝ Lb cal SBKRb4 = expLb − 4 CBK z2Rb, where z = bas κY + lnLb r2/r'2Rb for interaction of a dipole r at rapidity Y with dipole r' at rest. SBK is the S-matrix for the Balitsky-Kovchegov amplitude. All constants are determined in the text. The proof is given in the same theoretical framework for both cases (cal Sdd and cal SBK): the Pomeron interaction which takes into account the Pomeron vertices in the leading 1/Nc approximation (Nc is the number of colours). This result is in striking contradiction with 'rare' fluctuation approach as well as with summing the large Pomeron loops. These lead to cal Sdd ∝ √(cal SBK) at large z. In the paper we collect arguments supporting the idea that the sum of large Pomeron loops can be trusted in a wide region of energy: Y ≤ 1/as4. In addition we discuss the influence of the structure of the Hamiltonian on the asymptotic behaviour of the scattering amplitudes using the exactly solvable one dimensional model as our theoretical ground.
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BibTeX
@misc{levin2026dipoledipole,
title = {{Dipole-dipole scattering at high energy in the Pomeron field theory with Braun Hamiltonian and beyond}},
author = {Eugene Levin},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.00506},
eprint = {2608.00506},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.00506},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dipole-dipole scattering at high energy in the Pomeron field theory with Braun Hamiltonian and beyond
AU - Eugene Levin
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.00506
UR - https://arxiv.org/abs/2608.00506
AB - In this paper we find that the scattering matrix for dipole-dipole interaction in the saturation region has the form: cal S^d_d xrightarrowz ≫ 1 expLb − C^d_d z^2Rb ∝ Lb cal S_BKRb^4 = expLb − 4 C_BK z^2Rb, where z = bas κY + lnLb r^2/r'^2Rb for interaction of a dipole r at rapidity Y with dipole r' at rest. S_BK is the S-matrix for the Balitsky-Kovchegov amplitude. All constants are determined in the text. The proof is given in the same theoretical framework for both cases (cal S^d_d and cal S_BK): the Pomeron interaction which takes into account the Pomeron vertices in the leading 1/N_c approximation (N_c is the number of colours). This result is in striking contradiction with 'rare' fluctuation approach as well as with summing the large Pomeron loops. These lead to cal S^d_d ∝ √(cal S_BK) at large z. In the paper we collect arguments supporting the idea that the sum of large Pomeron loops can be trusted in a wide region of energy: Y ≤ 1/as^4. In addition we discuss the influence of the structure of the Hamiltonian on the asymptotic behaviour of the scattering amplitudes using the exactly solvable one dimensional model as our theoretical ground.
ER -