arXiv subjects

A. H. Mueller

Publications and source records attributed to A. H. Mueller.

At least 73 records · Page 4Linked to original sources

arXiv2008

Separating hard and soft scales in hard processes in a QCD plasma

We present a picture of hard processes in a hot plasma in terms of the hard scale part of the process, where perturbative QCD should be applicable, and the soft scale part of the process, where we look to the AdS/CFT correspondence for guidance to possible strong effective coupling phenomena. In particular we estimate $\hat{q}$, the transport coefficient, supposing that at soft scales partons in the plasma all cascade to small-$x$-values as indicated by strong coupling SYM theory.

hep-ph↗

arXiv2008

Jet evolution in the N=4 SYM plasma at strong coupling

Within the framework of the AdS/CFT correspondence, we study the time evolution of an energetic R-current propagating through a finite temperature, strongly coupled, N=4 SYM plasma and propose a physical picture for our results. In this picture, the current splits into a pair of massless partons, which then evolve via successive branchings, in such a way that energy is quasi-democratically divided among the products of a branching. We point out a duality between the transverse size of the partonic system produced through branching and the radial distance traveled by the dual Maxwell wave in the AdS geometry. For a time-like current, the branching occurs already in the vacuum, where it gives rise to a system of low-momentum partons isotropically distributed in the transverse plane. But at finite temperature, the branching mechanism is modified by the medium, in that the rate for parton splitting is enhanced by the transfer of transverse momentum from the partons to the plasma. This mechanism, which controls the parton energy loss, is sensitive to the energy density in the plasma, but not to the details of the thermal state. We compute the lifetime of the current for various kinematical regimes and provide physical interpretations for other, related, quantities, so like the meson screening length, the drag force, or the trailing string, that were previously computed via AdS/CFT techniques.

hep-th↗

arXiv2008

Deep inelastic scattering at strong coupling from gauge/string duality : the saturation line

For gauge theories which admit a dual string description, we analyze deep inelastic scattering at strong 't Hooft coupling and high energy, in the vicinity of the unitarity limit. We discuss the onset of unitarity corrections and determine the saturation line which separates weak scattering from strong scattering in the parameter space of rapidity and photon virtuality. We discover that the approach towards unitarity proceeds through two different mechanisms, depending upon the photon virtuality Q^2 : single Pomeron exchange at relatively low Q^2 and, respectively, multiple graviton exchanges at higher Q^2. This implies that the total cross-section at high energy and large Q^2 is dominated by diffractive processes. This is furthermore suggestive of a partonic description where all the partons have transverse momenta below the saturation momentum and occupation numbers of order one.

hep-th↗

arXiv2008

Deep inelastic scattering off a N=4 SYM plasma at strong coupling

By using the AdS/CFT correspondence we study the deep inelastic scattering of an R-current off a N=4 supersymmetric Yang-Mills (SYM) plasma at finite temperature and strong coupling. Within the supergravity approximation valid when the number of colors is large, we compute the structure functions by solving Maxwell equations in the space-time geometry of the AdS_5 black three-brane. We find a rather sharp transition between a low energy regime where the scattering is weak and quasi-elastic, and a high-energy regime where the current is completely absorbed. The critical energy for this transition determines the plasma saturation momentum in terms of its temperature T and the Bjorken x variable: Q_s=T/x. These results suggest a partonic picture for the plasma where all the partons have transverse momenta below the saturation momentum and occupation numbers of order one.

hep-th↗

arXiv2007

Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization

We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model, that we shall call the exponential model, the properties of the traveling wave front can be calculated exactly, as well as the statistics of the genealogy of the population. One striking result is that, for this particular model, the genealogical trees have the same statistics as the trees of replicas in the Parisi mean-field theory of spin glasses. We also find that in the exponential model, the coalescence times along these trees grow like the logarithm of the population size. A phenomenological picture of the propagation of wave fronts that we introduced in a previous work, as well as our numerical data, suggest that these statistics remain valid for a larger class of models, while the coalescence times grow like the cube of the logarithm of the population size.

cond-mat.dis-nn↗

arXiv2007

Correlation of small-x gluons in impact parameter space

In the framework of the QCD dipole model at high energy, we present an analytic evaluation of the dipole pair density in two limits in which the parent dipole is much larger/smaller than the distance between the two child dipoles. Due to conformal symmetry, the two limits give an identical result. The power-law correlation between dipoles explicitly breaks the factorization of target-averaged scattering amplitudes.

hep-ph↗

arXiv2007

How does transverse (hydrodynamic) flow affect jet-broadening and jet-quenching ?

We give the modification of formulas for $p_{\perp}$-broadening and energy loss which are necessary to calculate parton interactions in a medium with flow. Arguments are presented leading to the conclusion that for large $p_{\perp}$-spectra observed in heavy ion collisions at RHIC, the influence of transverse flow on the determination of the "quenching power" of the produced medium is small. This leaves open the question of the interpretation of data in a consistent perturbative framework.

nucl-th↗

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↗

arXiv2006

On the equivalence of Reggeon field theory in zero transverse dimensions and reaction-diffusion processes

The Reggeon field theory in zero transverse dimensions is investigated. Two versions of the theory are considered: one that allows at most triple pomeron interactions and the other that embodies an additional 2-->2 quartic Reggeon coupling. The behavior of the scattering amplitude at asymptotic rapidities is obtained in both cases. In an s-channel picture of the high energy scattering both models can be viewed as reaction-diffusion processes. We derive known results in Reggeon field theory rather easily using the reaction-diffusion formalism. We find that some results which are surprising from the Reggeon field theory point of view turn out to have a simple interpretation from the reaction-diffusion point of view.

hep-ph↗

arXiv2006

On Kolmogorov Wave Turbulence in QCD

We investigate Kolmogorov wave turbulence in QCD or, in other words, we calculate the spectrum of gluons as a function of time, f_k(t), in the presence of a source which feeds in energy density in the infrared region at a constant rate. We find an early, an intermediate and a late time form for the gluon spectrum. Wave turbulence in QCD turns out to be somewhat different than the turbulence in the case of ϕ^4-type theories studied by Zakharov, L'vov and Falkovich. The hope is that a good understanding of QCD wave turbulence might lead to a better understanding of the instability problem in the early stages of the evolution after a heavy ion collision.

hep-ph↗

arXiv2005

A Modified "Bottom-up" Thermalization in Heavy Ion Collisions

In the initial stage of the bottom-up picture of thermalization in heavy ion collisions, the gluon distribution is highly anisotropic which can give rise to plasma instability. This has not been taken account in the original paper. It is shown that in the presence of instability there are scaling solutions, which depend on one parameter, that match smoothly onto the late stage of bottom-up when thermalization takes place.

hep-ph↗

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

A Possible Modified "bottom-up" Thermalization in Heavy Ion Collisions

We present a possible scaling solution to pre-equilibrium evolution which interpolates between the instability present in the dense gluon system produced immediately after a heavy ion collision and the final equilibration which occurs later. Our solution depends on a single parameter $δ$. Depending on the value of $δ$, our proposed solution matches onto the bottom-up picture either at an intermediate stage or toward the end of the evolution given by bottom-up. We discuss in detail the reasons why we believe our solution is self-consistent, and we also point out why it is difficult to actually prove consistency.

hep-ph↗

arXiv2005

On the Projectile-Target Duality of the Color Glass Condensate in the Dipole Picture

Recently Kovner and Lublinsky proposed a set of equations which can be viewed as dual to JIMWLK evolution. We show that these dual equations have a natural dipole-like structure, as conjectured by Kovner and Lublinsky. In the high energy large N_c limit these evolution equations reduce to equations previously derived in the dipole model. We also show that the dual evolution kernel is scheme dependent, although its action on the weight functional describing a high energy state gives a unique result.

hep-ph↗

arXiv2005

Extension of the JIMWLK Equation in the Low Gluon Density Region

It has recently been realized that the Balitsky-JIMWLK equations have serious shortcomings as equations to be used in small-x evolution near the unitarity limit. A recent generalization of the Balitsky equations has been given which corrects these shortcomings. In this paper we present an equivalent discussion, but in terms of the JIMWLK equation where we show that a new (fourth order functional derivative) term should be included. We also present a stochastic version of the new equation which, however, has some unusual mathematical aspects which are not as yet well understood.

hep-ph↗

arXiv2005

Saturation and High Density QCD

Recent progress in understanding general properties of high energy scattering near the unitarity limit, where high density gluon components of the wavefunction are dominant, is reviewed. The similarity of the QCD problem and that of reaction-diffusion processes in statistical physics is emphasized. The energy dependence of the saturation momentum and the status of geometric scaling are discussed.

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

Saturation and shadowing in high-energy proton-nucleus dilepton production

We discuss the inclusive dilepton cross section for proton (quark)-nucleus collisions at high energies in the very forward rapidity region. Starting from the calculation in the quasi-classical approximation, we include low-x evolution effects in the nucleus and predict leading twist shadowing together with anomalous scaling behaviour.

hep-ph↗