Variational techniques in non-perturbative QCD

We review attempts to apply the variational principle to understand the vacuum of non-abelian gauge theories. In particular, we focus on the method explored by Ian Kogan and collaborators, which imposes exact gauge invariance on the trial Gaussian wave functional prior to the minimization of energy. We describe the application of the method to a toy model -- confining compact QED in 2+1 dimensions -- where it works wonderfully and reproduces all known non-trivial results. We then follow its applications to pure Yang-Mills theory in 3+1 dimensions at zero and finite temperature. Among the results of the variational calculation are dynamical mass generation and the analytic description of the deconfinement phase transition.Comment: 71 pages, 1 figure. To be published in the memorial volume "From Fields to Strings: Cirvumnavigating Theoretical Physics", World Scientific, 2004. Dedicated to the memory of Ian Koga

Forward-Backward rapidity correlations at all rapidities

We discuss forward-bacward rapidity correlations in the general situation of asymmetrical collisions, asymmetric rapidity windows, higher rapidities and higher energy. We give predictions for RHIC and LHC.Comment: 6 pages, 3 figure

Variational analysis of the deconfinement phase transition

We study the deconfining phase transition in 3+1 dimensional pure SU(N) Yang-Mills theory using a gauge invariant variational calculation. We generalize the variational ansatz of Phys. Rev. D52, 3719 (1995) to mixed states (density matrices) and minimize the free energy. For N > 3 we find a first order phase transition with the transition temperature of T_C = 450 Mev. Below the critical temperature the Polyakov loop has vanishing expectation value, while above T_C, its average value is nonzero. According to the standard lore this corresponds to the deconfining transition. Within the accuracy of our approximation the entropy of the system in the low temperature phase vanishes. The latent heat is not small but, rather, is of the order of the nonperturbative vacuum energy.Comment: 15 pages, correction of minor typos only, submitted to JHE

Testing collinear factorization and nuclear parton distributions with pA collisions at the LHC

Global perturbative QCD analyses, based on large data sets from electron-proton and hadron collider experiments, provide tight constraints on the parton distribution function (PDF) in the proton. The extension of these analyses to nuclear parton distributions (nPDF) has attracted much interest in recent years. nPDFs are needed as benchmarks for the characterization of hot QCD matter in nucleus-nucleus collisions, and attract further interest since they may show novel signatures of non- linear density-dependent QCD evolution. However, it is not known from first principles whether the factorization of long-range phenomena into process-independent parton distribution, which underlies global PDF extractions for the proton, extends to nuclear effects. As a consequence, assessing the reliability of nPDFs for benchmark calculations goes beyond testing the numerical accuracy of their extraction and requires phenomenological tests of the factorization assumption. Here we argue that a proton-nucleus collision program at the LHC would provide a set of measurements allowing for unprecedented tests of the factorization assumption underlying global nPDF fits.Comment: 4 pages, 5 figure

Vector potential versus colour charge density in low-x evolution

We reconsider the evolution equations for multigluon correlators derived in hep-ph/9709432. We show how to derive these equations directly in terms of vector potentials (or colour field strength) avoiding the introduction of the concept of colour charge density in the intermediate steps. The two step procedure of deriving the evolution of the charge density correlators followed by the solution of classical equations for the vector potentials is shown to be consistent with direct derivation of evolution for vector potentials. In the process we correct some computational errors of hep-ph/9709432 and present the corrected evolution equations which have a somewhat simpler appearance.Comment: 15 pages, 1 figure, changes made referee report, to be published in Phys. Rev

Jet Quenching via Jet Collimation

The ATLAS Collaboration recently reported strong modifications of dijet properties in heavy ion collisions. In this work, we discuss to what extent these first data constrain already the microscopic mechanism underlying jet quenching. Simple kinematic arguments lead us to identify a frequency collimation mechanism via which the medium efficiently trims away the soft components of the jet parton shower. Through this mechanism, the observed dijet asymmetry can be accomodated with values of $\hat{q}\, L$ that lie in the expected order of magnitude.Comment: 6 pages, 4 figure

The contribution of medium-modified color flow to jet quenching

Multiple interactions between parton showers and the surrounding QCD matter are expected to underlie the strong medium-modifications of jet observables in ultra-relativistic heavy ion collisions at RHIC and at the LHC. Here, we note that such jet-medium interactions alter generically and characteristically the color correlations in the parton shower. We characterize these effects in a color-differential calculation of the medium-induced gluon radiation spectrum to first and second order in opacity. By interfacing simple branching histories of medium-modified color flow with the Lund hadronization model, we analyze how the medium modification of color correlations can affect the distribution of hadronic fragments in jets. Importantly, we observe that jet-medium interactions give rise to the medium-induced color decoherence of gluons from the parton shower. Since hadronization respects color flow and since each color singlet in a parton shower is hadronized separately, this medium-induced color decoherence leaves characteristic signatures in the jet fragmentation pattern. In particular, it can contribute to the quenching of leading hadron spectra. Moreover, it can increase strongly the yield of soft hadronic fragments from a jet, while the distribution of more energetic hadrons follows naturally the shape of a vacuum-like fragmentation pattern of lower total energy