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

Light-like mesons and deep inelastic scattering in finite-temperature AdS/CFT with flavor

We use the holographic dual of a finite-temperature, strongly-coupled, gauge theory with a small number of flavors of massive fundamental quarks to study meson excitations and deep inelastic scattering (DIS) in the low-temperature phase, where the mesons are stable. We show that a high-energy flavor current with nearly light-like kinematics disappears into the plasma by resonantly producing mesons in highly excited states. This mechanism generates the same DIS structure functions as in the high temperature phase, where mesons are unstable and the current disappears through medium-induced parton branching. To establish this picture, we derive analytic results for the meson spectrum, which are exact in the case of light-like mesons and which corroborate and complete previous, mostly numerical, studies in the literature. We find that the meson levels are very finely spaced near the light-cone, so that the current can always decay, without a fine-tuning of its kinematics.Comment: 43 pages, 6 figure

Jet evolution from weak to strong coupling

Recent studies, using the AdS/CFT correspondence, of the radiation produced by a decaying system or by an accelerated charge in the N=4 supersymmetric Yang-Mills theory, led to a striking result: the 'supergravity backreaction', which is supposed to describe the energy density at infinitely strong coupling, yields exactly the same result as at zero coupling, that is, it shows no trace of quantum broadening. We argue that this is not a real property of the radiation at strong coupling, but an artifact of the backreaction calculation, which is unable to faithfully capture the space-time distribution of the radiation. This becomes obvious in the case of a decaying system ('virtual photon'), for which the backreaction is tantamount to computing a three-point function in the conformal gauge theory, which is independent of the coupling since protected by symmetries. Whereas this non-renormalization property is specific to the conformal N=4 SYM theory, we argue that the failure of the three-point function to provide a local measurement is in fact generic: it holds in any field theory with non-trivial interactions. To properly study a localized distribution, one should rather compute a four-point function, as standard in deep inelastic scattering. We substantiate these considerations with studies of the radiation produced by the decay of a time-like photon at both weak and strong coupling. We show that by computing four-point functions, in perturbation theory at weak coupling and, respectively, from Witten diagrams at strong coupling, one can follow the quantum evolution and thus demonstrate the broadening of the energy distribution. This broadening is slow when the coupling is weak but it proceeds as fast as possible in the limit of a strong coupling.Comment: 49 pages, 6 figure

Violation of kT factorization in quark production from the Color Glass Condensate

We examine the violation of the kT factorization approximation for quark production in high energy proton-nucleus collisions. We comment on its implications for the open charm and quarkonium production in collider experiments.Comment: 4 pages, 6 figures, contribution to proceedings of Quark Matter 2005, Budapest, Aug 4-

Determination of nuclear parton distribution functions and their uncertainties at next-to-leading order

Nuclear parton distribution functions (NPDFs) are determined by global analyses of experimental data on structure-function ratios F_2^A/F_2^{A'} and Drell-Yan cross-section ratios \sigma_{DY}^A/\sigma_{DY}^{A'}. The analyses are done in the leading order (LO) and next-to-leading order (NLO) of running coupling constant \alpha_s. Uncertainties of the NPDFs are estimated in both LO and NLO for finding possible NLO improvement. Valence-quark distributions are well determined, and antiquark distributions are also determined at x<0.1. However, the antiquark distributions have large uncertainties at x>0.2. Gluon modifications cannot be fixed at this stage. Although the advantage of the NLO analysis, in comparison with the LO one, is generally the sensitivity to the gluon distributions, gluon uncertainties are almost the same in the LO and NLO. It is because current scaling-violation data are not accurate enough to determine precise nuclear gluon distributions. Modifications of the PDFs in the deuteron are also discussed by including data on the proton-deuteron ratio F_2^D/F_2^p in the analysis. A code is provided for calculating the NPDFs and their uncertainties at given x and Q^2 in the LO and NLO.Comment: 15 pages, LaTeX, 22 eps files, to appear in PRC. A code for calculating our nuclear parton distribution functions and their uncertainties can be obtained from http://research.kek.jp/people/kumanos/nuclp.htm

Random walks of partons in SU(N_c) and classical representations of color charges in QCD at small x

The effective action for wee partons in large nuclei includes a sum over static color sources distributed in a wide range of representations of the SU(N_c) color group. The problem can be formulated as a random walk of partons in the N_c-1 dimensional space spanned by the Casimirs of SU(N_c). For a large number of sources, k >> 1, we show explicitly that the most likely representation is a classical representation of order O(\sqrt{k}). The quantum sum over representations is well approximated by a path integral over classical sources with an exponential weight whose argument is the quadratic Casimir operator of the group. The contributions of the higher N_c-2 Casimir operators are suppressed by powers of k. Other applications of the techniques developed here are discussed briefly.Comment: 51 pages, includes 3 eps file

Resumming large higher-order corrections in non-linear QCD evolution

Linear and non-linear QCD evolutions at high energy suffer from severe issues related to convergence, due to higher order corrections enhanced by large double and single transverse logarithms. We resum double logarithms to all orders by taking into account successive soft gluon emissions strongly ordered in lifetime. We further resum single logarithms generated by the first non-singular part of the splitting functions and by the one-loop running of the coupling. The resulting collinearly improved BK equation admits stable solutions, which are used to successfully fit the HERA data at small-x for physically acceptable initial conditions and reasonable values of the fit parameters.Comment: 4 pages, 4 figures, based on talk given at Hard Probes 2015, 29 June - 3 July 2015, Montreal, Canad

Resummation of Large Logarithms in the Rapidity Evolution of Color Dipoles

Perturbative corrections beyond leading-log accuracy to BFKL and BK equations, describing the rapidity evolution of QCD scattering amplitudes at high energy, exhibit strong convergence problems due to radiative corrections enhanced by large single and double transverse logs. We identify explicitly the physical origin of double transverse logs and resum them directly in coordinate space as appropriate for BK equation, in terms of an improved local-in-rapidity evolution kernel. Numerical results show the crucial role of double-logarithmic resummation for BK evolution, which is stabilized and slowed down by roughly a factor of two.Comment: 6 pages, 4 figures; Proceedings of the XXIII International Workshop on Deep-Inelastic Scattering (27 April-May 1 2015, Dallas (USA)

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.Comment: v2: 45 pages, 4 figures, various corrections, section 4.4 updated, to appear in JHE

Pomeron loops in zero transverse dimensions

We analyze a toy model which has a structure similar to that of the recently found QCD evolution equations, but without transverse dimensions. We develop two different but equivalent methods in order to compute the leading-order and next-to-leading order Pomeron loop diagrams. In addition to the leading-order result which has been derived from Mueller's toy model~\cite% {Mueller:1994gb}, we can also calculate the next-to-leading order contribution which provides the $(\alpha_{s}^{2}\alpha Y)$ correction. We interpret this result and discuss its possible implications for the four-dimensional QCD evolution.Comment: 11 pages, 4 figure