On the dipole swing and the search for frame independence in the dipole model

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.

Small-xnonlinear evolution with impact parameter and the structure function data

“…The knowledge of the parton density distribution in impact parameter is essential not only in the context of heavy ion collisions but also for hadronic collisions (for example in the problem of the underlying event) and in particular for diffractive processes. For example, in exclusive diffractive production of vector mesons in DIS the momentum transfer dependence crucially depends on the impact parameter profile of the dipole scattering amplitude [43][44][45] The impact parameter dependence has been taken into account in Monte Carlo simulations based on dipole evolution and scattering [46][47][48][49][50][51] as well as in numerical solutions to the BK evolution equation, see [52,53] and [54]. It has been also discussed in the context of the conformal properties of the equation [55].…”

Exclusive vector meson production and small-x evolution

“…The increase of the t slope, B D , with the energy W should be directly coupled with the increase of the transverse interaction area caused by the diffusion of the dipoles in coordinate space. This diffusion in transverse coordinate space is present in the dipole branching Monte-Carlo [21][22][23][24] as well as the Balitsky-Kovchegov equation when the impact parameter dependence is taken into account [25,26]. The main goal of the present work is to use the numerical solution to the BK equation, which includes the full impact parameter dependence, and verify its compatibility with the experimental data on the exclusive vector meson production in deep inelastic lepton-proton scattering.…”

“…The wave function of the vector meson is parametrized as in [15,17]. In this model, the radial part of the wave function φ(r, z) satisfies the following normalization condition for the transversely polarized part 24) and for the longitudinally polarized part…”

Dipole evolution: perspectives for collectivity and γ*A collisions

“…An approach for going beyond leading colour in the cascade, which is also suited for Monte Carlo implementation, is the so-called "swing" mechanism, introduced by Avsar et al [43,61]. This can be understood as an extension of the identification of multiple interactions in the collision frame with Pomeron loops, as presented in the previous section.…”

“…Worth mentioning already here, is the treatment of sub-leading N c (number of colours) effects in the evolution, leading to saturation in the cascade. In Dipsy, this is addressed through so-called swing mechanisms [42,43], which suppresses the contribution from large dipoles in dense environments by replacing them with small dipoles. In this paper we consider only sub-leading N c effects in the collision frame, by including multiple interactions in a way consistent with unitarity.…”