On the Dipole Swing and the Search for Frame Independence in the Dipole Model

TL;DR

This paper investigates how to incorporate saturation effects and boost invariance into Mueller's dipole model by introducing dipole swings, enhancing the model's ability to generate realistic color correlations.

Contribution

It demonstrates that combining dipole splitting with multiple simultaneous swings can produce all relevant color correlations in the dipole model.

Findings

Zero and one dimensional toy models exhibit saturation and boost invariance.

Dipole vertices can be generated by combining splitting with swings.

Maximum of N-1 swings needed for N dipoles to capture correlations.

Abstract

Small-x evolution in QCD is conveniently described by Mueller's dipole model which, however, does not include saturation effects in a way consistent with boost invariance. In this paper we first show that the recently studied zero and one dimensional toy models exhibiting saturation and explicit boost invariance can be interpreted in terms positive definite k-> k+1 dipole vertices. Such k-> k+1 vertices can in the full model be generated by combining the usual dipole splitting with k-1 simultaneous dipole swings. We show that, for a system consisting of N dipoles, one needs to combine the dipole splitting with at most N-1 simultaneous swings in order to generate all colour correlations induced by the multiple dipole interactions.