An influence functional for ultrasoft QCD

A real-time path integral for ultrasoft QCD is formulated. It exhibits a Feynman's influence functional. The statistical properties of the theory and the gauge symmetry are explicit. The correspondence is established with the alternative version, where a noise term enters a transport equation.Comment: 6 pages, no figure Strong Electroweak Matter (SEWM 2002), Heidelberg, 2-5 october 200

Theory Summary: Quark Matter 2006

I report on recent theoretical developments at Quark Matter 2006

Anomalous Gluon Production and Condensation in Glasma

The collinear color electric and magnetic fields have been discussed to be produced immediately after high energy heavy ion collisions. We discuss anomalous gluon production under the background gauge fields. The gluons are Nielsen-Olesen unstable modes. The production rate of the modes by Schwinger mechanism has recently been found to be anomalously larger than the rate of quarks or other stable gluons. Analyzing classical evolutions of the modes with initial conditions given by vacuum fluctuations, we find that their production makes the color electric field decay very rapidly. The life time of the field is approximately given by the inverse of saturation momentum in the collisions. We also show that the mode with zero momentum form a Bose condensate and its gluon number density grows up to be of the order of $1/\alpha_g$. After the saturation of the gluon number density, the condensate melts into quark gluon plasma owing to nonlinear interactions in QCD.Comment: 9 pages, 2figures To be published in Phys. Rev.

Non-linear QCD evolution with improved triple-pomeron vertices

In a previous publication, we have constructed a set of non-linear evolution equations for dipole scattering amplitudes in QCD at high energy, which extends the Balitsky-JIMWLK hierarchy by including the effects of fluctuations in the gluon number in the target wavefunction. In doing so, we have relied on the color dipole picture, valid in the limit where the number of colors is large, and we have made some further approximations on the relation between scattering amplitudes and dipole densities, which amount to neglecting the non-locality of the two-gluon exchanges. In this Letter, we relax the latter approximations, and thus restore the correct structure of the `triple-pomeron vertex' which describes the splitting of one BFKL pomeron into two within the terms responsible for fluctuations. The ensuing triple-pomeron vertex coincides with the one previously derived by Braun and Vacca within perturbative QCD. The evolution equations can be recast in a Langevin form, but with a multivariable noise term with off-diagonal correlations. Our equations are shown to be equivalent with the modified version of the JIMWLK equation recently proposed by Mueller, Shoshi, and Wong.Comment: 15 page

A lattice test of strong coupling behaviour in QCD at finite temperature

We propose a set of lattice measurements which could test whether the deconfined, quark-gluon plasma, phase of QCD shows strong coupling aspects at temperatures a few times the critical temperature for deconfinement, in the region where the conformal anomaly becomes unimportant. The measurements refer to twist-two operators which are not protected by symmetries and which in a strong-coupling scenario would develop large, negative, anomalous dimensions, resulting in a strong suppression of the respective lattice expectation values in the continuum limit. Special emphasis is put on the respective operator with lowest spin (the spin-2 operator orthogonal to the energy-momentum tensor within the renormalization flow) and on the case of quenched QCD, where this operator is known for arbitrary values of the coupling: this is the quark energy-momentum tensor. The proposed lattice measurements could also test whether the plasma constituents are pointlike (as expected at weak coupling), or not.Comment: 16 page

JIMWLK evolution: from color charges to rapidity correlations

We study multi-particle production with rapidity correlations in high-energy p+A collisions. In the context of the Color Glass Condensate, the evolution for such correlations is governed by a generalization of the JIMWLK equation which evolves the strong nuclear fields both in the amplitude and in the complex conjugate one. We give the equivalent Langevin formulation, whose main ingredient is the color charge density linked to a projectile parton (a Wilson line).Comment: 4 pages, 2 figures, based on talk given at Hard Probes 2013, 4 - 8 Nov 2013, Cape Town, South Afric

JIMWLK evolution for multi-particle production with rapidity correlations

We study multi-particle production with rapidity correlations in proton-nucleus collisions at high energy in the Color Glass Condensate framework. The high-energy evolution responsible for such correlations is governed by a generalization of the JIMWLK equation describing the simultaneous evolution of the strong nuclear color fields in the direct amplitude and the complex conjugate amplitude. This functional equation can be used to derive ordinary evolution equations for the cross-sections for particle production, but the ensuing equations appear to be too complicated to be useful in practice, including in the limit of a large number of colors Nc. We propose an alternative formulation based on a Langevin process, which is valid for generic Nc and is better suited for numerical implementations. For illustration, we present the stochastic equations which govern two gluon production with arbitrary rapidity separation.Comment: 8 pages, 6 figures, based on talk given at IS 2013, 8 - 14 Sep 2013, Illa da Toxa, Spai

Running coupling effects in the evolution of jet quenching

We study the consequences of including the running of the QCD coupling in the equation describing the evolution of the jet quenching parameter $\hat q$ in the double logarithmic approximation. To start with, we revisit the case of a fixed coupling, for which we obtain exact solutions valid for generic values of the transverse momentum (above the medium saturation scale) and corresponding to various initial conditions. In the case of a running coupling, we construct approximate solutions in the form of truncated series obtained via successive iterations, whose convergence is well under control. We thus deduce the dominant asymptotic behavior of the renormalized $\hat q$ in the limit of a large evolution time $Y\equiv\ln(L/\lambda)$, with $L$ the size of the medium and $\lambda$ the typical wavelength of a medium constituent. We show that the asymptotic expansion is universal with respect to the choice of the initial condition at $Y=0$ and, moreover, it is remarkably similar to the corresponding expansion for the saturation momentum of a shockwave (a large nucleus). As expected, the running of the coupling significantly slows down the increase of $\hat q$ with $Y$ in the asymptotic regime at $Y\gg 1$. For the phenomenologically interesting value $Y\simeq 3$, we find an enhancement factor close to 3, independently of the initial condition and for both fixed and running coupling.Comment: 25 pages, 5 figure