Robert B. Peschanski

Moments of rapidity distributions as a measure of short-range fluctuations in high-energy collisions

Abstract It is proposed to study the dependence of factorial moments of the rapidity distribution on the size δy of the resolution. It is shown that if the fluctuations are purely statistical no variation of moments δy is expected, and thus observation of such a variation indicates the presence of genuine fluctuations of physical origin. The region in which the change occurs corresponds to the size (in rapidity) of the observed fluctuations. Intermittency, i.e. fluctuations of many different sizes, would show up as a power-law behaviour of moments on δy . A good experimental resolution can be obtained from the rapidity distribution of high multiplicity events.

Intermittency in multiparticle production at high energy

Abstract We present predictions of random cascading models for multiparticle production at high energy. Standard and correlated factorial moments in rapidity are shown to provide stringent tests of the intermittency patterns characteristic of random cascades. Using the central limit theorem we show how to test directly for the existence of a cascading process. Finally, we discuss how to take into account statistical corrections.

Minimal surfaces and Reggeization in the AdS / CFT correspondence

Abstract We address the problem of computing scattering amplitudes related to the correlation function of two Wilson lines and/or loops elongated along light-cone directions in strongly coupled gauge theories. Using the AdS/CFT correspondence in the classical approximation, the amplitudes are shown to be related to minimal surfaces generalizing the helicoid in various AdS 5 backgrounds. Infra-red divergences appearing for Wilson lines can be factorized out or can be cured by considering the IR finite case of correlation functions of two Wilson loops. In non-conformal cases related to confining theories, reggeized amplitudes with linear trajectories and unit intercept are obtained and shown to come from the approximately flat metrics near the horizon, which sets the scale for the Regge slope. In the conformal case the absence of confinement leads to a different solution. A transition between both regimes appears, in a confining theory, when varying impact parameter.

On the existence of a non-thermal phase transition in multi-particle production

Abstract One derives a statistical mechanical formulation of multi-particle production considered as a random cascading process. It leads to a prescription for the existence of a phase transition using factorial intermittency moments characteristic of event-per-event fluctuations. This prescription is discussed in various cases, including second order phase transitions and cascading models without phase transition. We discuss existing data on intermittency and the nature of the new phase which is of non-thermal type for random cascading models.

CONFORMAL INVARIANCE AND THE EXACT SOLUTION OF BFKL EQUATIONS

Abstract The conformal invariance properties of the QCD Pomeron in the transverse plane allow us to give an explicit analytical expression for the solution of the BFKL equations both in the transverse coordinate and momentum spaces. This result is obtained from the solution of the conformal eigenvectors in the mixed representation in terms of two conformal blocks, each block being the product of a holomorphic times an antiholomorphic function. This property is used to give an exact expression for the QCD dipole multiplicities and dipole-dipole cross-sections in the whole parameter space, proving the identity between the BFKL and dipole amplitudes of the QCD Pomeron.

Reggeon exchange from AdS/CFT

Abstract Using the AdS/CFT correspondence in a confining background and the worldline formalism of gauge field theories, we compute scattering amplitudes with an exchange of quark and antiquark in the t-channel corresponding to reggeon exchange. It requires going beyond the eikonal approximation, which was used when studying pomeron exchange. The wordline path integral is evaluated through the determination of minimal surfaces and their boundaries by the saddle-point method at large gauge coupling g2Nc. We find a Regge behaviour with linear Regge trajectories. The slope is related to the q q static potential and is four times the pomeron slope obtained in the same framework. A contribution to the intercept, related to the Luscher term, comes from the fluctuations around the minimal surface.

Multifractal analysis of intermittency and phase transitions in multiparticle dynamics

Abstract Multifractal properties of intermittency-like fluctuations as observed in multiparticle collisions are demonstrated, using their description in terms of random cascading models. The f(α) singularity spectrum of these models is explicitly derived and reveals the existence of a spin-glass type transition which can correspond to the physical transient phase produced in such reactions. One finds four classes, with a combination of two different phase transitions. One is analogous to a transition at positive temperature and characterized as a “transition of peaks”. The other one with negative temperature is reanalyzed as a “transition of holes”. The phase transition diagram depends heavily on the tree structure of the model. The applications of this multifractal scheme to particle multiproduction lead to a practical criterion for the existence and the nature of the new phases one is looking for in particle physics in relation with quantum chromodynamics.

Angular intermittency in QCD jets

Using two methods, via fluctuations and correlations, an analytical formula is derived for the factorial multiplicity moments in a QCD jet at the Double Leading Logarithm accuracy. The resulting self-similar dependence on the solid-angle cell size is characteristic of an intermittency behaviour in angular variables. The intermittency indices depend on the diffusion angle through the running of αS. Physical features of jet fluctuations such as collimation at large angles and saturation at small angles are well described in the perturbative framework. A parameter-free prediction of angular intermittency is proposed for Z0 decays into hadrons, assuming hadronparton duality.

Hard diffraction at HERA in the dipole model of BFKL dynamics

Using the QCD dipole picture of the hard BFKL pomeron, we derive the general expressions of the elastic and inelastic components of the proton diffractive structure functions. We obtain a good seven-parameter fit (including a secondary reggeon contribution) to data taken at HERA by the H1 and ZEUS Collaborations. The main characteristic features of the model in reproducing the data are discussed, namely the effective pomeron intercept, the scaling violations and the β-dependence. A difference obtained in the separate H1 and ZEUS fits leads us to analyze directly the differences between both measurements. Predictions on R, the ratio of longitudinal to transverse photon cross sections are performed and lead to very large values at high beta and large virtuality Q which may lead to a discrimination between models.

QCD dipole model and K(t) factorization

Abstract It is shown that the colour dipole approach to hard scattering at high energy is fully compatible with k T factorization at the leading logarithm approximation (in − log x Bj ). The relations between the dipole amplitudes and unintegrated diagonal and non-diagonal gluon distributions are given. It is also shown that including the exact gluon kinematics in the k T factorization formula destroys the conservation of transverse position vectors and thus is incompatible with the dipole model for both elastic and diffractive amplitudes.