Large multiplicity fluctuations and saturation effects in onium collisions

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.Comment: 30 pages LaTeX2e, 11 figures included using epsfig. Compressed postscript of whole paper also available at http://www.hep.phy.cam.ac.uk/theory/papers

High energy scattering in QCD as a statistical process

The scattering of two hadronic objects at high energy is similar to a reaction-diffusion process described by the stochastic Fisher-Kolmogorov equation. This basic observation enables us to derive universal properties of the scattering amplitudes in a straightforward way, by borrowing some general results from statistical physics.Comment: 4 pages, 2 figures; talk presented at Baryons 2004, Palaiseau, France, October 200

From Color Glass to Color Dipoles in high-energy onium--onium scattering

Within the Color Glass formalism, we construct the wavefunction of a high energy onium in the BFKL and large-N_c approximations, and demonstrate the equivalence with the corresponding result in the Color Dipole picture. We propose a simple factorization formula for the elastic scattering between two non-saturated ``color glasses'' in the center-of-mass frame. This is valid up to energies which are high enough to allow for a study of the onset of unitarization via multiple pomeron exchanges. When applied to the high energy onium-onium scattering, this formula reduces to the Glauber-like scattering between two systems of dipoles, in complete agreement with the dipole picture.Comment: 35 pages, 2 figure

The DLLA limit of BFKL in the Dipole Picture

In this work we obtain the DLLA limit of BFKL in the dipole picture and compare it with HERA data. We demonstrate that in leading-logarithmic- approximation, where $\alpha_s$ is fixed, a transition between the BFKL dynamics and the DLLA limit can be obtained in the region of $Q^2 \approx 150 GeV^2$. We compare this result with the DLLA predictions obtained with $\alpha_s$ running. In this case a transition is obtained at low $Q^2$ $(\le 5 GeV^2)$. This demonstrates the importance of the next-to-leading order corrections to the BFKL dynamics. Our conclusion is that the $F_2$ structure function is not the best observable for the determination of the dynamics, since there is great freedom in the choice of the parameters used in both BFKL and DLLA predictions.Comment: 14 pages, 2 figures, Accepted for publication in Phys. Lett.

A Simple Derivation of the JIMWLK Equation

A simple derivation of the Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (JIMWLK) equation for the evolution of small-x QCD wavefunctions is given. The derivation makes use of the equivalence between the evolution of a (in general complicated) small-x wavefunction with that of the evolution of the (simple) dipole probing the wavefunction in a high energy scattering.Comment: 11 pages, 3 figures, corrected typo in abstract titl

Stationary Algorithmic Probability

Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural approach to eliminate this machine-dependence. Our method is to assign algorithmic probabilities to the different computers themselves, based on the idea that "unnatural" computers should be hard to emulate. Therefore, we study the Markov process of universal computers randomly emulating each other. The corresponding stationary distribution, if it existed, would give a natural and machine-independent probability measure on the computers, and also on the binary strings. Unfortunately, we show that no stationary distribution exists on the set of all computers; thus, this method cannot eliminate machine-dependence. Moreover, we show that the reason for failure has a clear and interesting physical interpretation, suggesting that every other conceivable attempt to get rid of those additive constants must fail in principle, too. However, we show that restricting to some subclass of computers might help to get rid of some amount of machine-dependence in some situations, and the resulting stationary computer and string probabilities have beautiful properties.Comment: 13 pages, 5 figures. Added an example of a positive recurrent computer se