arXiv subjects

D. N. Triantafyllopoulos

Publications and source records attributed to D. N. Triantafyllopoulos.

At least 55 records · Page 3Linked to original sources

arXiv2012

JIMWLK evolution in the Gaussian approximation

We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors Nc. This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it reproduces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite Nc. Any higher n-point function with n greater than or equal to 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.

hep-ph↗

arXiv2012

Higher-point correlations from the JIMWLK evolution

We develop a new approximation scheme aiming at extracting higher-point correlation functions from the JIMWLK evolution, in the limit where the number of colors is large. Namely, we show that by exploiting the structure of the 'virtual' terms in the Balitsky-JIMWLK equations, one can derive functional relations expressing arbitrary n-point functions of the Wilson lines in terms of the 2-point function (the scattering amplitude for a color dipole). These approximations are correct not only in the regime of strong scattering, where the evolution is indeed controlled by the 'virtual' terms, but also in the regime of weak scattering, where they reduce to the corresponding BFKL solutions. This last feature follows from the fact that the JIMWLK Hamiltonian is a linear combination of the pieces responsible for the 'real' and 'virtual' terms, respectively. We apply this scheme to two examples: the 'color quadrupole' (the 4-point function of the Wilson lines which enters the cross-section for the production of a pair of jets at forward rapidities) and the 'color sextupole' (the 6-point function). For particular configurations of the quadrupole, our general formula reduces to relatively simple expressions that have been previously proposed on the basis of the McLerran-Venugopalan model and which were recently shown to agree quite well with exact, numerical, solutions to the JIMWLK equation.

hep-ph↗

arXiv2011

Next-to-leading and resummed BFKL evolution with saturation boundary

We investigate the effects of the saturation boundary on small-x evolution at the next-to-leading order accuracy and beyond. We demonstrate that the instabilities of the next-to-leading order BFKL evolution are not cured by the presence of the nonlinear saturation effects, and a resummation of the higher order corrections is therefore needed for the nonlinear evolution. The renormalization group improved resummed equation in the presence of the saturation boundary is investigated, and the corresponding saturation scale is extracted. A significant reduction of the saturation scale is found, and we observe that the onset of the saturation corrections is delayed to higher rapidities. This seems to be related to the characteristic feature of the resummed splitting function which at moderately small values of x possesses a minimum.

hep-ph↗

arXiv2011

Forward and Mueller-Navelet Jets

We discuss the production of forward jets in high energy processes where one probes a dense hadronic wavefunction. In particular, and as a signature of parton saturation, we discuss the possibility of a strong momentum decorrelation in Mueller-Navelet jets which leads to a geometric scaling behavior.

hep-ph↗

arXiv2011

Radiation by a heavy quark in N=4 SYM at strong coupling

Using the AdS/CFT correspondence in the supergravity approximation, we compute the energy density radiated by a heavy quark undergoing some arbitrary motion in the vacuum of the strongly coupled N=4 supersymmetric Yang-Mills theory. We find that this energy is fully generated via backreaction from the near-boundary endpoint of the dual string attached to the heavy quark. Because of that, the energy distribution shows the same space-time localization as the classical radiation that would be produced by the heavy quark at weak coupling. We believe that this and some other unnatural features of our result (like its anisotropy and the presence of regions with negative energy density) are artifacts of the supergravity approximation, which will be corrected after including string fluctuations. For the case where the quark trajectory is bounded, we also compute the radiated power, by integrating the energy density over the surface of a sphere at infinity. For sufficiently large times, we find agreement with a previous calculation by Mikhailov [hep-th/0305196].

hep-th↗

arXiv2010

Aspects of the UV/IR correspondence : energy broadening and string fluctuations

We show that a source which radiates in the vacuum of the strongly coupled N=4 SYM theory produces an energy distribution which, in the supergravity approximation, has the same space-time pattern as the corresponding classical distribution: the radiation propagates at the speed of light without broadening. We illustrate this on the basis of several examples: a small perturbation propagating down a steady string, a massless particle falling into AdS_5, and the decay of a time-like wave-packet. A similar observation was made in Phys. Rev. D81 (2010) 126001 for the case of a rotating string. In all these cases, the absence of broadening is related to the fact that the energy backreaction on the boundary arises exclusively from the bulk perturbation at, or near, the boundary. This is so since bulk sources which propagate in AdS_5 at the speed of light do not generate any energy on the boundary. We interpret these features as an artifact of the supergravity approximation, which fails to encode quantum mechanical fluctuations that should be present even in the strong coupling limit. We argue that such fluctuations should enter the dual string theory as longitudinal string fluctuations, which are not suppressed at strong coupling. We heuristically estimate the effects of such fluctuations and argue that they restore the broadening of the radiation, in agreement with expectations from both quantum mechanics and the ultraviolet/infrared correspondence.

hep-th↗

arXiv2009

Shockwaves and deep inelastic scattering within the gauge/gravity duality

Within the gauge/gravity correspondence, we discuss the general formulation of the shockwave metric which is dual to a 'nucleus' described by the strongly-coupled N=4 SYM theory in the limit where the number of colors Nc is arbitrarily large. We emphasize that the 'nucleus' must possess Nc^2 degrees of freedom per unit volume, so like a finite-temperature plasma, in order for a supergravity description to exist. We critically reassess previous proposals for introducing transverse inhomogeneity in the shockwave and formulate a new proposal in that sense, which involves no external source but requires the introduction of an 'infrared' cutoff which mimics confinement. This cutoff however plays no role when the shockwave is probed by a highly virtual projectile, so like in deep inelastic scattering. We consider two such projectiles, the dilaton and the R-current, and compute the respective structure functions including unitarity corrections. We find that there are no leading-twist contributions to the structure functions at high virtuality, meaning that there are no point-like constituents in the strongly coupled 'nucleus'. In the black-disk regime at low virtuality, the structure functions are suggestive of parton saturation with occupation numbers of order one. The saturation momentum Qs grows with the energy like Qs^2 ~ 1/x (with x the Bjorken variable), which is the hallmark of graviton exchanges and is also necessary for the fulfillment of the energy-momentum sum rules.

hep-th↗

arXiv2008

Running Coupling Effects in Small-x QCD

We study effects of the running of the coupling in QCD at small Bjorken-x and in particular the ones related to gluon saturation. After introducing the steps taken to the derivation of the next to leading order nonlinear evolution equation, we discuss the infrared sensitivity of the Pomeron intercept, the energy dependence of the saturation momentum and the appearance of geometrical scaling, and the dominance of the running coupling effects over the ones introduced by loops of Pomerons.

hep-ph↗

arXiv2008

Geometric Scaling in Mueller-Navelet Jets

We argue that the production of Mueller-Navelet jets at the LHC represents a convenient environment to study gluon saturation and high energy scattering in the presence of unitarity corrections. We show that, in a suitable range of transverse momenta for the produced jets, the cross section for the partonic subprocess should exhibit geometric scaling. We point out that, in the presence of a running coupling, the cross section for producing hard jets cannot be fully computed in perturbation theory, not even after taking into account the saturation effects: the non-perturbative physics affects the overall normalization of the cross section, but not also its geometric scaling behavior.

hep-ph↗

arXiv2007

RpA ratio: total shadowing due to running coupling

We predict that the RpA ratio at the most forward rapidities to be measured at LHC should be strongly suppressed, close to "total shadowing'' (RpA = A^(-1/3)), as a consequence of running coupling effects in the nonlinear QCD evolution.

hep-ph↗

arXiv2007

Pomeron loop and running coupling effects in high energy QCD evolution

Within the framework of a (1+1)-dimensional model which mimics evolution and scattering in QCD at high energy, we study the influence of the running of the coupling on the high-energy dynamics with Pomeron loops. We find that the particle number fluctuations are strongly suppressed by the running of the coupling, by at least one order of magnitude as compared to the case of a fixed coupling, for all the rapidities that we have investigated, up to Y=200. This reflects the slowing down of the evolution by running coupling effects, in particular, the large rapidity evolution which is required for the formation of the saturation front via diffusion. We conclude that, for all energies of interest, processes like deep inelastic scattering or forward particle production can be reliably studied within the framework of a mean-field approximation (like the Balitsky-Kovchegov equation) which includes running coupling effects.

hep-ph↗

arXiv2006

One-dimensional model for QCD at high energy

We propose a stochastic particle model in (1+1)-dimensions, with one dimension corresponding to rapidity and the other one to the transverse size of a dipole in QCD, which mimics high-energy evolution and scattering in QCD in the presence of both saturation and particle-number fluctuations, and hence of Pomeron loops. The model evolves via non-linear particle splitting, with a non-local splitting rate which is constrained by boost-invariance and multiple scattering. The splitting rate saturates at high density, so like the gluon emission rate in the JIMWLK evolution. In the mean field approximation obtained by ignoring fluctuations, the model exhibits the hallmarks of the BK equation, namely a BFKL-like evolution at low density, the formation of a traveling wave, and geometric scaling. In the full evolution including fluctuations, the geometric scaling is washed out at high energy and replaced by diffusive scaling. It is likely that the model belongs to the universality class of the reaction-diffusion process. The analysis of the model sheds new light on the Pomeron loops equations in QCD and their possible improvements.

hep-ph↗

arXiv2006

A zero-dimensional model for high-energy scattering in QCD

We investigate a zero-dimensional toy model originally introduced by Mueller and Salam which mimics high-energy scattering in QCD in the presence of both gluon saturation and gluon number fluctuations, and hence of Pomeron loops. Unlike other toy models of the reaction-diffusion type, the model studied in this paper is consistent with boost invariance and, related to that, it exhibits a mechanism for particle saturation close to that of the JIMWLK equation in QCD, namely the saturation of the emission rate due to high-density effects. Within this model, we establish the dominant high-energy behaviour of the S-matrix element for the scattering between a target obtained by evolving one particle and a projectile made with exactly n particles. Remarkably, we find that all such matrix elements approach the black disk limit S=0 at high rapidity Y, with the same exponential law: ~ exp(-Y) for all values of n. This is so because the S-matrix is dominated by rare target configurations which involve only few particles. We also find that the bulk distribution for a saturated system is of the Poisson type.

hep-ph↗

arXiv2006

Diffusive scaling and the high-energy limit of deep inelastic scattering in QCD at large N_c

Within the limits of the large-N_c approximation (with N_c the number of colors), we establish the high-energy behaviour of the diffractive and inclusive cross-sections for deep inelastic scattering at fixed impact parameter. We demonstrate that for sufficiently high energies and up to very large values of Q^2, well above the proton average saturation momentum , the cross-sections are dominated by dense fluctuations in the target wavefunction, that is, by the relatively rare gluon configurations which are at saturation on the resolution scale Q^2 of the virtual photon. This has important physical consequences, like the emergence of a new, diffusive, scaling, which replaces the `geometric scaling' property characteristic of the mean field approximation. To establish this, we shall rely on a dipole version of the Good-Walker formula for diffraction (that we shall derive here in the context of DIS), together with the high-energy estimates for the dipole scattering amplitudes which follow from the recently established evolution equations with Pomeron loops and include the relevant fluctuations. We also find that, as a consequence of fluctuations, the diffractive cross-section at high energy is dominated by the elastic scattering of the quark-antiquark component of the virtual photon, up to relatively large virtualities Q^2 >> .

hep-ph↗

arXiv2005

Pomeron Loops in High Energy QCD

We discuss the QCD evolution equations governing the high energy behavior of scattering amplitudes at the leading logarithmic level. This hierarchy of equations accommodates normal BFKL dynamics, Pomeron mergings and Pomeron splittings. Pomeron loops are built in the course of evolution and the scattering amplitudes satisfy the unitarity bound.

hep-ph↗

arXiv2005

On the Probabilistic Interpretation of the Evolution Equations with Pomeron Loops in QCD

We study some structural aspects of the evolution equations with Pomeron loops recently derived in QCD at high energy and for a large number of colors, with the purpose of clarifying their probabilistic interpretation. We show that, in spite of their appealing dipolar structure and of the self-duality of the underlying Hamiltonian, these equations cannot be given a meaningful interpretation in terms of a system of dipoles which evolves through dissociation (one dipole splitting into two) and recombination (two dipoles merging into one). The problem comes from the saturation effects, which cannot be described as dipole recombination, not even effectively. We establish this by showing that a (probabilistically meaningful) dipolar evolution in either the target or the projectile wavefunction cannot reproduce the actual evolution equations in QCD.

hep-ph↗

arXiv2005

Effective Hamiltonian for QCD evolution at high energy

We construct the effective Hamiltonian which governs the renormalization group flow of the gluon distribution with increasing energy and in the leading logarithmic approximation. This Hamiltonian defines a two-dimensional field theory which involves two types of Wilson lines: longitudinal Wilson lines which describe gluon recombination (or merging) and temporal Wilson lines which account for gluon bremsstrahlung (or splitting). The Hamiltonian is self-dual, i.e., it is invariant under the exchange of the two types of Wilson lines. In the high density regime where one can neglect gluon number fluctuations, the general Hamiltonian reduces to that for the JIMWLK evolution. In the dilute regime where gluon recombination becomes unimportant, it reduces to the dual partner of the JIMWLK Hamiltonian, which describes bremsstrahlung.

hep-ph↗

arXiv2005

Duality and Pomeron effective theory for QCD at high energy and large N_c

We propose an effective theory which governs Pomeron dynamics in QCD at high energy, in the leading logarithmic approximation, and in the limit where N_c, the number of colors, is large. In spite of its remarkably simple structure, this effective theory generates precisely the evolution equations for scattering amplitudes that have been recently deduced from a more complete microscopic analysis. It accounts for the BFKL evolution of the Pomerons together with their interactions: dissociation (one Pomeron splitting into two) and recombination (two Pomerons merging into one). It is constructed by exploiting a duality principle relating the evolutions in the target and the projectile, more precisely, splitting and merging processes, or fluctuations in the dilute regime and saturation effects in the dense regime. The simplest Pomeron loop calculated with the effective theory is free of both ultraviolet or infrared singularities.

hep-ph↗