Medium-induced gluon radiation in hard forward parton scattering in the saturation formalism

We derive the medium-induced, coherent gluon radiation spectrum associated with the hard forward scattering of an energetic parton off a nucleus, in the saturation formalism and within the Gaussian approximation for the relevant correlators of Wilson lines. The calculation reproduces the simple expression for the spectrum previously obtained in the opacity expansion formalism, and rigorously specifies its validity range. The connection between the calculations in the opacity expansion and saturation formalisms is made apparent. This study may serve as a first step in order to implement consistently induced coherent energy loss and gluon shadowing in `saturation-based models' of hadron nuclear suppression in proton-nucleus collisions.Comment: 25 pages, 2 figure

Distribution of the number of particles in the final state of hadron-nucleus collisions

Recently, Liou, Mueller and Munier have argued that proton-nucleus collisions at the LHC may give access to the full statistics of the event-by-event fluctuations of the gluon density in the proton. Indeed, the number of particles produced in an event in rapidity slices in the fragmentation region of the proton may, under some well-defined assumptions, be directly related to the number of gluons which have a transverse momentum larger than the nuclear saturation scale present in the proton at the time of the interaction with the nucleus. A first calculation of the probability distribution of the number of gluons in a hadron was performed, using the color dipole model. In this talk, we review this proposal, and present preliminary numerical calculations which support the analytical results obtained so far.Comment: 6 pages, 2 figures. Talk presented at DIS 201

Probabilistic picture for particle number densities in stretched tips of the branching Brownian motion

In the framework of a stochastic picture for the one-dimensional branching Brownian motion, we compute the probability density of the number of particles near the rightmost one at a time $T$, that we take very large, when this extreme particle is conditioned to arrive at a predefined position $x_T$ chosen far ahead of its expected position $m_T$. We recover the previously-conjectured fact that the typical number density of particles a distance $\Delta$ to the left of the lead particle, when both $\Delta$ and $x_T-\Delta-m_T$ are large, is smaller than the mean number density by a factor proportional to $e^{-\zeta\Delta^{2/3}}$, where $\zeta$ is a constant that was so far undetermined. Our picture leads to an expression for the probability density of the particle number, from which a value for $\zeta$ may be inferred.Comment: 6 pages, 1 figur

Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections

We review the factorization of the $S$-matrix elements in the context of particle scattering off an external field, which can serve as a model for the field of a large nucleus. The factorization takes the form of a convolution of light cone wave functions describing the physical incoming and outgoing states in terms of bare partons, and products of Wilson lines. The latter represent the interaction between the bare partons and the external field. Specializing to elastic scattering amplitudes of onia at very high energies, we introduce the color dipole model, which formulates the calculation of the modulus-squared of the wave functions in quantum chromodynamics with the help of a branching random walk, and the scattering amplitudes as observables on this classical stochastic process. Methods developed for general branching processes produce analytical formulas for the asymptotics of such observables, and thus enable one to derive exact large-rapidity expressions for onium-nucleus cross sections, from which electron-nucleus cross sections may be inferred.Comment: 97 pages, 24 figures. Lecture notes of the QCD Master Class, Saint-Jacut-de-la-Mer, September 202

On the small-x evolution of the color quadrupole and the Weizsäcker–Williams gluon distribution

AbstractColor quadrupoles have been found to be important in the proper description of observables sensitive to the small-x regime in nuclei as well as in the operator definition of the Weizsäcker–Williams gluon distribution. In this Letter, we derive the small-x evolution equation of the quadrupole and the Weizsäcker–Williams gluon distribution without taking the large Nc limit and study the properties of the equation in both dilute and saturation regime. We find that the quadrupole evolution follows the BFKL evolution in the dilute regime and then saturates in the dense region due to nonlinear terms. This leads us to conclude that the Weizsäcker–Williams gluon distribution should obey the same geometrical behavior as the dipole gluon distribution as found in the inclusive DIS measurement

A Quantization of 2+1-Gravity Related to High-Energy Yang-Mills Theory

We point out that canonical quantization of the two-body problem in 2+1-Gravity is related to the high-energy equation in Yang-Mills theory by a proper ordering of the relevant operators. This feature arises from expanding the Hamiltonian around its conformal limit - or treating running coupling effects in the Yang-Mills case - and yields a peculiar short distance behaviour of the wave functions.Comment: 11 page

Diffractive photon dissociation in the saturation regime from the Good and Walker picture

Combining the QCD dipole model with the Good and Walker picture, we formulate diffractive dissociation of a photon of virtuality Q^2 off a hadronic target, in the kinematical regime in which Q is close to the saturation scale and much smaller than the invariant mass of the diffracted system. We show how the obtained formula compares to the HERA data and discuss what can be learnt from such a phenomenology. In particular, we argue that diffractive observables in these kinematics provide useful pieces of information on the saturation regime of QCD.Comment: 17 pages, 7 figures, revte

Geometric Scaling in a Symmetric Saturation Model

We illustrate geometric scaling for the photon-proton cross section with a very simple saturation model. We describe the proton structure function F2 at small x in a wide kinematical range with an elementary functional form and a small number of free parameters. We speculate that the symmetry between low and high Q2 recently discovered in the data could be related to a well-known symmetry of the two-gluon- exchange dipole-dipole cross section.Comment: 15 pages, 4 figure

Diffractive patterns in deep-inelastic scattering and parton genealogy

International audienceWe report on our recent observation that the occurrence of diffractive patterns in the scattering of electrons off nuclei obeys the same law as the fluctuations of the height of genealogical trees in branching diffusion processes

Contributions à l'étude de la chromodynamique quantique perturbative appliquée à la diffusion profondément inélastique à petit x

Les premiers chapitres résument la dérivation du modèle des dipôles de Mueller à partir du lagrangien de la QCD.The proton is a composite object, consisting of a collection of partons, quarks and gluons, which interact according to the laws of Quantum Chromodynamics (QCD). In this work, we consider a Hamiltonian formulation of this theory in a light-cone frame.In this context, we derive the parton evolution equations in transverse momentum (DGLAP equation) as well as in longitudinal momentum (BFKL equation) on the same footing. The latter is obtained as the colour-dipole model. We traduce in this Hamiltonian formalism the complete set of calculations that are needed to present our personal contributions, which mainly consist in new developments and applications of the colour-dipole model.The latter is successfully fitted to the HERA data for the inclusive structure functions, which are related to the electron-proton cross-sections. The contribution of the production of charmed particules is predicted, and exhibits a fair agreement with the experimental data. On the other hand, we show the phenomenological relevance of some subleading components of the BFKL equation (classified according to their conformal spin), which appear as solutions of the evolution equations: we compare their effect to the one of Donnachie and Landshoff's soft Pomeron.Studying some particular observables, we show the equivalence between the Hamiltonian formulation of QCD and a covariant formulation. We apply it to the derivation of the effective primordial dipole density at the origin of a forward jet which sometimes appears in the final state of either a deep-inelastic scattering process or a proton diffusion.Finally, hard diffraction is studied in the BFKL approach. On the phenomenological side, we compare the HERA experimental data to the dipole model. On the theoretical side, we compute the higher-conformal spin components of the BFKL equation for diffractive photon production.Le proton est un objet composite, constitué d'une collection de partons, quarks et gluons, qui interagissent selon les lois de la chromodynamique quantique (QCD). Dans cette thèse, on expose une formulation hamiltonienne de cette théorie dans le repère du cône de lumière.On retrouve dans ce cadre les équations d'évolution des partons en impulsion transverse (équation DGLAP), et longitudinale (équation BFKL). Cette dernière se présente ici sous la forme du modèle des dipôles de couleur. On transpose dans ce formalisme l'ensemble des calculs nécessaires à nos recherches personnelles, portant sur le développement et les applications du modèle des dipôles.Ce modèle est ajusté aux données expérimentales d'HERA pour les fonctions de structure inclusives, qui sont reliées aux sections efficaces d'interaction électron-proton. La contribution à celles-ci de la production de particules charmées est prédite, en bon accord avec l'expérience. D'autre part, l'importance phénoménologique de certaines composantes sous-dominantes de l'équation BFKL (de spin conforme non nul), qui apparaissent comme solutions des équations d'évolution, est démontrée: on compare leur effet à celui du poméron mou de Donnachie-Landshoff.On montre sur des observables particulières l'équivalence entre la formulation hamiltonienne et une formulation covariante de la QCD, et on l'applique à la détermination de la densité effective de dipôles primordiaux à l'origine d'un jet vers l'avant qui se matérialise quelquefois dans l'état final d'une réaction de diffusion profondément inélastique ou d'une diffusion de protons.Enfin, le processus de diffraction dure, plus exclusif, est considéré dans l'approche BFKL. Sur le plan phénoménologique, une étude des données des expériences d'HERA dans le cadre du modèle des dipôles est présentée. Sur le plan théorique, le calcul des composantes de spin conforme non nul de l'équation BFKL pour la production diffractive de photons est effectué