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S. Munier

Publications and source records attributed to S. Munier.

At least 37 records · Page 2Linked to original sources
arXiv2007

Dense-dilute factorization for a class of stochastic processes and for high energy QCD

Stochastic processes described by evolution equations in the universality class of the FKPP equation may be approximately factorized into a linear stochastic part and a nonlinear deterministic part. We prove this factorization on a model with no spatial dimensions and we illustrate it numerically on a one-dimensional toy model that possesses some of the main features of high energy QCD evolution. We explain how this procedure may be applied to QCD amplitudes, by combining Salam's Monte-Carlo implementation of the dipole model and a numerical solution of the Balitsky-Kovchegov equation.

hep-ph↗
arXiv2006

Noisy traveling waves: effect of selection on genealogies

For a family of models of evolving population under selection, which can be described by noisy traveling wave equations, the coalescence times along the genealogical tree scale like $\log^αN$, where $N$ is the size of the population, in contrast with neutral models for which they scale like $N$. An argument relating this time scale to the diffusion constant of the noisy traveling wave leads to a prediction for $α$ which agrees with our simulations. An exactly soluble case gives trees with statistics identical to those predicted for mean-field spin glasses in Parisi's theory.

cond-mat.dis-nn↗
arXiv2005

A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts

We propose a phenomenological description for the effect of a weak noise on the position of a front described by the Fisher-Kolmogorov-Petrovsky-Piscounov equation or any other travelling wave equation in the same class. Our scenario is based on four hypotheses on the relevant mechanism for the diffusion of the front. Our parameter-free analytical predictions for the velocity of the front, its diffusion constant and higher cumulants of its position agree with numerical simulations.

cond-mat.dis-nn↗
arXiv2005

The high energy asymptotics of scattering processes in QCD

High energy scattering in the QCD parton model was recently shown to be a reaction-diffusion process, and thus to lie in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. We recall that the latter appears naturally in the context of the parton model. We provide a thorough numerical analysis of the mean field approximation, given in QCD by the Balitsky-Kovchegov equation. In the framework of a simple stochastic toy model that captures the relevant features of QCD, we discuss and illustrate the universal properties of such stochastic models. We investigate in particular the validity of the mean field approximation and how it is broken by fluctuations. We find that the mean field approximation is a good approximation in the initial stages of the evolution in rapidity.

hep-ph↗
arXiv2005

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.

hep-ph↗
arXiv2004

Universal behavior of QCD amplitudes at high energy from general tools of statistical physics

We show that high energy scattering is a statistical process essentially similar to reaction-diffusion in a system made of a finite number of particles. The Balitsky-JIMWLK equations correspond to the time evolution law for the particle density. The squared strong coupling constant plays the role of the minimum particle density. Discreteness is related to the finite number of partons one may observe in a given event and has a sizeable effect on physical observables. Using general tools developed recently in statistical physics, we derive the universal terms in the rapidity dependence of the saturation scale and the scaling form of the amplitude, which come as the leading terms in a large rapidity and small coupling expansion.

hep-ph↗
arXiv2004

Universality and tree structure of high energy QCD

Using non-trivial mathematical properties of a class of nonlinear evolution equations, we obtain the universal terms in the asymptotic expansion in rapidity of the saturation scale and of the unintegrated gluon density from the Balitsky-Kovchegov equation. These terms are independent of the initial conditions and of the details of the equation. The last subasymptotic terms are new results and complete the list of all possible universal contributions. Universality is interpreted in a general qualitative picture of high energy scattering, in which a scattering process corresponds to a tree structure probed by a given source.

hep-ph↗
arXiv2003

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.

hep-ph↗
arXiv2003

Traveling wave fronts and the transition to saturation

We propose a general method to study the solutions to nonlinear QCD evolution equations, based on a deep analogy with the physics of traveling waves. In particular, we show that the transition to the saturation regime of high energy QCD is identical to the formation of the front of a traveling wave. Within this physical picture, we provide the expressions for the saturation scale and the gluon density profile as a function of the total rapidity and the transverse momentum. The application to the Balitsky-Kovchegov equation for both fixed and running coupling constants confirms the effectiveness of this method.

hep-ph↗
arXiv2003

Saturation and BFKL dynamics in the HERA data at small x

We show that the HERA data for the inclusive structure function F_2(x,Q^2) for x < 0.01 and 0.045 < Q^2 < 45 GeV^2 can be well described within the color dipole picture, with a simple analytic expression for the dipole-proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q_s(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Q_s(x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x_0 of x at which the saturation scale Q_s equals 1GeV, and the logarithmic derivative of the saturation momentum λ. The value of λextracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism.

hep-ph↗
arXiv2003

Geometric scaling as traveling waves

We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky- Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale.

hep-ph↗
arXiv2003

Some remarks on geometric scaling

In order to explain a striking symmetry of the HERA data for virtual photon-proton cross section, I propose a simple model based on the elementary 2-gluon exchange dipole-dipole cross section, and which exhibits geometric scaling. I also suggest that geometric scaling should manifest itself in exclusive processes. A preliminary search for this property in the HERA data is presented.

hep-ph↗
arXiv2003

Geometric scaling in exclusive processes

We show that according to the present understanding of the energy evolution of the observables measured in deep-inelastic scattering, the photon-proton scattering amplitude has to exhibit geometric scaling at each impact parameter. We suggest a way to test it experimentally at HERA. A qualitative analysis based on published data is presented and discussed.

hep-ph↗
arXiv2002

Saturation and Vector Mesons

Through an analysis of diffractive vector meson production, we show that the proton appears quite dense to a small size probe at present HERA energies. This means that saturation effects are already important.

hep-ph↗
arXiv2002

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.

hep-ph↗
arXiv2002

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.

hep-ph↗
arXiv2001

Dipole-proton $S$-matrix derived from diffractive meson electroproduction

Through a determination of the $S$-matrix element for the scattering of a localized colour dipole on a proton, we show that saturation effects can already be sizable at HERA. The saturation scale is found to be around 1-1.5 $GeV^2$ for the highest available energies and for central collisions, and is a decreasing function of the impact parameter.

hep-ph↗