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In the Color Glass Condensate, the inclusive spectrum of produced quarks in a heavy ion collision is obtained as the Fourier transform of a $2$-fermion correlation function. Due to its non-locality, the two points of this function must be linked by a Wilson line in order to have a gauge invariant result, but when the quark spectrum is evaluated in a background that has a non-zero chromo-magnetic field, this procedure suffers from an ambiguity related to the choice of the contour defining the Wilson line. In this paper, we use an analytically tractable toy model of the background field in order to study this contour dependence. We show that for a straight contour, unphysical contributions to the spectrum in $p_\perp^{-2}$ and $p_\perp^{-3}$ cancel, leading to a spectrum with a tail in $p_\perp^{-4}$. If the contour defining the Wilson line deviates from a straight line, the path dependence is at most of order $p_\perp^{-5}$ if its curvature is bounded, and of order $p_\perp^{-4}$ otherwise. When the contour is forced to go through a fixed point, the path dependence is even larger, of order $p_\perp^{-2}$., Comment: 28 pages, 9 figures

We use an expansion in angular mode functions in order to solve the Boltzmann equation for a gluon plasma undergoing longitudinal expansion. By comparing with the exact solution obtained numerically by other means we show that the expansion in mode functions converges rapidly for all cases of practical interest, and represents a substantial gain in numerical effort as compared to more standard methods. We contrast the cases of a non expanding plasma and of longitudinally expanding plasmas, and follow in both cases the evolutions towards thermalization. In the latter case, we observe that, although the spherical mode function appears to be well reproduced after some time by a local equilibrium distribution function depending on slowly varying temperature and chemical potential, thereby suggesting thermalization of the system, the longitudinal and transverse pressures take more time to equilibrate. This is because the expansion hinders the relaxation of the first angular mode function. This feature was also observed in a simpler context where the Boltzmann equation is solved in terms of special moments within the relaxation time approximation, and attributed there to the particular coupling between the first two moments of the distribution function. The present analysis confirms this observation in a more realistic setting., 23 pages, 16 figures, version published in Nuclear Physics A

We present recent results on in-medium spectral functions of vector and axial-vector mesons, the electromagnetic (EM) spectral function and dilepton rates using the Functional Renormalization Group (FRG) approach. Our method is based on an analytic continuation procedure that allows us to calculate real-time quantities like spectral functions at finite temperature and chemical potential. As an effective low-energy model for Quantum Chromodynamics (QCD) we use an extended linear-sigma model including quarks where (axial-)vector mesons as well as the photon are introduced as gauge bosons. In particular, it is shown how the $\rho$ and the $a_1$ spectral function become degenerate at high temperatures or chemical potentials due to the restoration of chiral symmetry. Preliminary results for the EM spectral function and the dilepton production rate are discussed with a focus on the possibility to identify signatures of the chiral crossover and the critical endpoint (CEP) in the QCD phase diagram., Comment: Quark Matter 2018 proceedings

We present a parametric estimate of photon production at early times in heavy-ion collisions based on a consistent weak coupling thermalization scenario. We quantify the contribution of the off-equilibrium Glasma phase relative to that of a thermalized Quark-Gluon Plasma. Taking into account the constraints from charged hadron multiplicity data, the Glasma contribution is found to be significant especially for large values of the saturation scale., 4 pages, 4 figures, proceedings for Quark Matter 2017

We report on a numerical study of the Boltzmann equation including $2\leftrightarrow 2$ scatterings of gluons and quarks in an overoccupied Glasma undergoing longitudinal expansion. We find that when a cascade of gluon number to the infrared occurs, corresponding to an infrared enhancement analogous to a transient Bose-Einstein condensate, gluon distributions qualitatively reproduce the results of classical-statistical simulations for the expanding Glasma. These include key features of the distributions that are not anticipated in the "bottom-up" thermalization scenario. We also find that quark distributions, like those of gluons, satisfy self-similar scaling distributions in the overoccupied Glasma. We discuss the implications of these results for a deeper understanding of the self-similarity and universality of parton distributions in the Glasma., 34 pages, 21 figures; version accepted in PRD

Recent classical-statistical numerical simulations have established the "bottom-up" thermalization scenario of Baier et al. as the correct weak coupling effective theory for thermalization in ultrarelativistic heavy-ion collisions. We perform a parametric study of photon production in the various stages of this bottom-up framework to ascertain the relative contribution of the off-equilibrium "Glasma" relative to that of a thermalized Quark-Gluon Plasma. Taking into account the constraints imposed by the measured charged hadron multiplicities at RHIC and the LHC, we find that Glasma contributions are important especially for large values of the saturation scale at both energies. These non-equilibrium effects should therefore be taken into account in studies where weak coupling methods are employed to compute photon yields., 33 pages, 9 figures; version accepted in PRC, title changed

We investigate axial charge production in two-color QCD out of equilibrium. We compute the real-time evolution starting with spatially homogeneous strong gauge fields, while the fermions are in vacuum. The idealized class of initial conditions is motivated by glasma flux tubes in the context of heavy-ion collisions. We focus on axial charge production at early times, where important aspects of the anomalous dynamics can be derived analytically. This is compared to real-time lattice simulations. Quark production at early times leading to anomalous charge generation is investigated using Wilson fermions. Our results indicate that coherent gauge fields can transiently produce significant amounts of axial charge density, while part of the induced charges persist to be present even well beyond characteristic decoherence times. The comparisons to analytic results provide stringent tests of real-time representations of the axial anomaly on the lattice., 12 pages, 10 figures; To appear in Phys. Rev. D

In this article, we review recent theoretical works on the Schwingermechanism of particle production in external electrical fields. Although the non-perturbative Schwinger mechanism is at the center of this discussion, many of the approaches that we discuss can cope with general time and space dependent fields, and therefore also capture the perturbative contributions to particle production., Review for Progress in Particle and Nuclear Physics. 76 pages, 36 figures

We revisit the problem of quark production in high energy heavy ion collisions, at leading order in $\alpha_s$ in the color glass condensate framework. In this first paper, we setup the formalism and express the quark spectrum in terms of a set of mode functions of the Dirac equation. We determine analytically their initial value in the Fock-Schwinger gauge on a proper time surface $Q_s\tau_0\ll 1$, in a basis which makes manifest the boost invariance properties of this problem. We also describe a statistical algorithm to perform the sampling of the mode functions., Comment: 40 pages, 3 figures, alternate derivation in the new appendix B

In this paper, we show how classical statistical field theory techniques can be used to efficiently perform the numerical evaluation of the non-perturbative Schwinger mechanism of particle production by quantum tunneling. In some approximation, we also consider the back-reaction of the produced particles on the external field, as well as the self-interactions of the produced particles., 28 pages, 28 pdf figures; title changed, to appear in Phys.Rev.D