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

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

Diffractive Excitation in DIS and pp Collisions

We have in earlier papers presented an extension of Mueller's dipole cascade model, which includes subleading effects from energy conservation and running coupling as well as colour suppressed effects from pomeron loops via a ``dipole swing''. The model was applied to describe the total cross sections in pp and gamma*p collisions. In this paper we present a number of improvements of the model, in particular related to the confinement mechanism. A consistent treatment of dipole evolution and dipole--dipole interactions is achieved by replacing the infinite range Coulomb potential by a screened potential, which further improves the frame-independence of the model. We then apply the model to elastic scattering and diffractive excitation, where we specifically study the effects of different sources for fluctuations. In our formalism we can take into account contributions from all different sources, from the dipole cascade evolution, the dipole--dipole scattering, from the impact-parameter dependence, and from the initial photon and proton wavefunctions. Good agreement is obtained with data from the Tevatron and from HERA, and we also present some predictions for the LHC.Comment: correction of titl

Small-x Dipole Evolution Beyond the Large-N_c Limit

We present a method to include colour-suppressed effects in the Mueller dipole picture. The model consistently includes saturation effects both in the evolution of dipoles and in the interactions of dipoles with a target in a frame-independent way. When implemented in a Monte Carlo simulation together with our previous model of energy--momentum conservation and a simple dipole description of initial state protons and virtual photons, the model is able to reproduce to a satisfactory degree both the gamma*-p cross sections as measured at HERA as well as the total p-p cross section all the way from ISR energies to the Tevatron and beyond

Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation

Nonlinear evolution equation at small x with impact parameter dependence is analyzed numerically. Saturation scales and the radius of expansion in impact parameter are extracted as functions of rapidity. Running coupling is included in this evolution, and it is found that the solution is sensitive to the infrared regularization. Kinematical effects beyond leading logarithmic approximation are taken partially into account by modifying the kernel which includes the rapidity dependent cuts. While the local nonlinear evolution is not very sensitive to these effects, the kinematical constraints cannot be neglected in the evolution with impact parameter.Comment: 22 pages, 37 figures, RevTe

Small x nonlinear evolution with impact parameter and the structure function data

The nonlinear Balitsky-Kovchegov equation at small x is solved numerically, incorporating impact parameter dependence. Confinement is modeled by including effective gluon mass in the dipole evolution kernel, which regulates the splitting of dipoles with large sizes. It is shown, that the solution is sensitive to different implementations of the mass in the kernel. In addition, running coupling effects are taken into account in this analysis. Finally, a comparison of the calculations using the dipole framework with the inclusive data from HERA on the structure functions F2 and FL is performed.Comment: 19 pages, 11 figures. Minor revision. One reference added, two figures update

Fluctuations, Saturation, and Diffractive Excitation in High Energy Collisions

Diffractive excitation is usually described by the Good--Walker formalism for low masses, and by the triple-Regge formalism for high masses. In the Good--Walker formalism the cross section is determined by the fluctuations in the interaction. In this paper we show that by taking the fluctuations in the BFKL ladder into account, it is possible to describe both low and high mass excitation by the Good--Walker mechanism. In high energy $pp$ collisions the fluctuations are strongly suppressed by saturation, which implies that pomeron exchange does not factorise between DIS and $pp$ collisions. The Dipole Cascade Model reproduces the expected triple-Regge form for the bare pomeron, and the triple-pomeron coupling is estimated.Comment: 20 pages, 12 figure

Elastic and quasi-elastic pppp and γ⋆p\gamma^\star p scattering in the Dipole Model

We have in earlier papers presented an extension of Mueller's dipole cascade model, which includes sub-leading effects from energy conservation and running coupling as well as colour suppressed saturation effects from pomeron loops via a ``dipole swing''. The model was applied to describe the total and diffractive cross sections in $pp$ and $\gamma^*p$ collisions, and also the elastic cross section in $pp$ scattering. In this paper we extend the model to describe the corresponding quasi-elastic cross sections in $\gamma^*p$, namely the exclusive production of vector mesons and deeply virtual compton scattering. Also for these reactions we find a good agrement with measured cross sections. In addition we obtain a reasonable description of the $t$-dependence of the elastic $pp$ and quasi-elastic $\gamma^\star p$ cross sections

Next-to-leading and resummed BFKL evolution with saturation boundary

We investigate the effects of the saturation boundary on small-x evolution at the next-to-leading order accuracy and beyond. We demonstrate that the instabilities of the next-to-leading order BFKL evolution are not cured by the presence of the nonlinear saturation effects, and a resummation of the higher order corrections is therefore needed for the nonlinear evolution. The renormalization group improved resummed equation in the presence of the saturation boundary is investigated, and the corresponding saturation scale is extracted. A significant reduction of the saturation scale is found, and we observe that the onset of the saturation corrections is delayed to higher rapidities. This seems to be related to the characteristic feature of the resummed splitting function which at moderately small values of x possesses a minimum.Comment: 34 page