arXiv subjects
Publications and source records attributed to G. P. Salam.
This talks examines the effect of angular ordering on the small-x evolution of the unintegrated gluon distribution, and discusses the characteristic function for the CCFM equation, as well as some preliminary results on final-state properties.
This talks examines the effect of angular ordering on the small-x evolution of the unintegrated gluon distribution, and discusses the characteristic function for the CCFM equation.
We compute the gluon distribution in deep inelastic scattering at small x by solving numerically the angular ordering evolution equation. The leading order contribution, obtained by neglecting angular ordering, satisfies the BFKL equation. Our aim is the analysis of the subleading corrections. Although not complete - the exact next-to-leading contribution is not yet available - these corrections are important since they come from the physical property of coherence of QCD radiation. In particular we discuss the subleading correction to the BFKL characteristic function and the gluon distribution's dependence on the maximum available angle. Conformal invariance of the BFKL equation is lost, however this is not enough to bring the small-x gluon distribution into the perturbative regime: although large momentum regions are enhanced by angular ordering, the small momentum regions are not fully suppressed. As a consequence, the gluon anomalous dimension is finite and tends to the BFKL value $γ=1/2$ for $α_S \to 0$. The main physical differences with respect to the BFKL case are that angular ordering leads to 1) a larger gluon anomalous dimension, 2) less singular behaviour for $x \to 0$ and 3) reduced diffusion in transverse momentum.
This talk reviews briefly some of the main results of the small-x dipole formulation with regards to unitarity corrections. It illustrates the correspondence between unitarity and saturation corrections in the dipole approach and multiple t-channel pomeron exchange in the traditional BFKL view, and discusses how one can estimate and understand the effects of saturation.
The QCD dipole picture of BFKL dynamics provides an attractive theoretical approach to the study of the QCD (resummed) perturbative expansion of small-x physics and more generally to hard high-energy processes. We discuss applications to the phenomenology of proton structure functions in the HERA range and to the longstanding problem of unitarity corrections, and outline some specific predictions of the dipole picture.
This paper studies two related questions in high energy onium-onium scattering: the probability of producing an unusually large number of particles in a collision, where it is found that the cross section for producing a central multiplicity proportional to $k$ should decrease exponentially in $\sqrt{k}$. Secondly, the nature of gluon (dipole) evolution when dipole densities become so high that saturation effects due to dipole-dipole interactions become important: measures of saturation are developed to help understand when saturation becomes important, and further information is obtained by exploiting changes of frame, which interchange unitarity and saturation corrections.
A Monte Carlo simulation program is presented which can be used to determine the small-$x$ evolution of a heavy onium using Mueller's colour dipole formulation, giving the full distribution of dipoles in rapidity and impact parameter. Routines are also provided which calculate onium-onium scattering amplitudes between individual pairs of onium configurations, making it possible to establish the contribution of multiple pomeron exchange terms to onium-onium scattering (the unitarisation corrections).
Mueller's dipole formulation of onium-onium scattering is used to study unitarity corrections to the BFKL power growth at high energies. After a short discussion of the spatial distribution of colour dipoles in a heavy quarkonium and the associated fluctuations, results are presented showing that the one and two-pomeron contributions to the total cross section are the same at a rapidity $Y \simeq 14$. Above this rapidity the large fluctuations in the onium wave function cause the multiple pomeron series to diverge. Resumming the series allows one to show that unitarity corrections set in gradually for the total cross section, which is dominated by rare, large, configurations of the onia. The elastic cross section comes mostly from much smaller impact parameters and has significant unitarity corrections starting at a rapidity $Y\simeq 8$.
The colour dipole multiplicity distribution is analysed for the wave function of a heavy onium state at small $x$. Numerical results for the average multiplicity and the effect of cutoffs on its power growth are presented. Then, the full multiplicity distribution is analysed: the second multiplicity moment is derived and the tail of the distribution is shown to behave as $\exp(-\log^2 n)$. These results are confirmed by a Monte Carlo simulation which also gives the fluctuations in the spatial density of dipoles.