Heavy quark diffusion in an overoccupied gluon plasma

We extract the heavy-quark diffusion coefficient kappa and the resulting momentum broadening in a far-from-equilibrium non-Abelian plasma. We find several features in the time dependence of the momentum broadening: a short initial rapid growth of , followed by linear growth with time due to Langevin-type dynamics and damped oscillations around this growth at the plasmon frequency. We show that these novel oscillations are not easily explained using perturbative techniques but result from an excess of gluons at low momenta. These oscillation are therefore a gauge invariant confirmation of the infrared enhancement we had previously observed in gauge-fixed correlation functions. We argue that the kinetic theory description of such systems becomes less reliable in the presence of this IR enhancement.Peer reviewe

Conserved energy-momentum tensor for real-time lattice simulations

We derive an expression for the energy-momentum tensor in the discrete lattice formulation of pure glue QCD. The resulting expression satisfies the continuity equation for energy conservation up to numerical errors with a symmetric procedure for the time discretization. In the case of the momentum conservation equation, we obtain an expression that is of higher accuracy in lattice spacing ($\mathcal{O}(a^2)$) than the naive discretization where fields in the continuum expressions are replaced by discretized counterparts. The improvements are verified by performing numerical tests on the derived expressions using classical real-time lattice gauge theory simulations. We demonstrate substantial reductions in relative error of one to several orders of magnitude compared to a naive discretization for both energy and momentum conservation equations. We expect our formulation to have applications in the area of pre-equilibrium dynamics in ultrarelativistic heavy ion collisions, in particular for the extraction of transport coefficients such as shear viscosity.Comment: 19 pages, 7 figure

Non-Abelian Electric Field Correlator at NLO for Dark Matter Relic Abundance and Quarkonium Transport

We perform a complete next-to-leading order calculation of the non-Abelian electric field correlator in a SU($N_c$) plasma, which encodes properties of the plasma relevant for heavy particle bound state formation and dissociation. The calculation is carried out in the real-time formalism of thermal field theory and includes both vacuum and finite temperature contributions. By working in the $R_\xi$ gauge, we explicitly show the results are gauge independent, infrared and collinear safe. The previous results on the renormalization of the electric field correlator are also confirmed. Our next-to-leading order calculation can be directly applied to any dipole singlet-adjoint transition of heavy particle pairs. For example, it can be used to describe dissociation and (re)generation of heavy quarkonia inside the quark-gluon plasma well below the melting temperature, as well as heavy dark matter pairs (or charged co-annihilating partners) in the early universe.Comment: 77 pages, 13 figure

The art of simulating the early Universe -- Part I

We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of $O(dt^2)$ accuracy like $staggered~leapfrog$ and $Verlet$ integration, to $Runge-Kutta$ methods up to $O(dt^4)$ accuracy, and the $Yoshida$ and $Gauss-Legendre$ higher-order integrators, accurate up to $O(dt^{10})$. We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in $3+1$ dimensions, including the case of `self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: $i)$ Interacting scalar fields, $ii)$ Abelian $U(1)$ gauge theories, and $iii)$ Non-Abelian $SU(2)$ gauge theories. In all three cases we provide symplectic integrators, with accuracy ranging from $O(dt^2)$ up to $O(dt^{10})$. For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. Remarkably, all our algorithms for gauge theories respect the Gauss constraint to machine precision, including when `self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under $SU(2)\times U(1)$. The present manuscript is meant as part of the theoretical basis for $CosmoLattice$, a modern C++ MPI-based package for simulating the non-linear dynamics of scalar-gauge field theories in an expanding universe, publicly available at www.cosmolattice.netComment: Minor corrections to match published version, and one more algorithm added. Still 79 pages, 8 figures, 1 appendix, and many algorithm

Heavy quark diffusion in an overoccupied gluon plasma

We extract the heavy quark diffusion coefficient k and the resulting momentum broadening h p2i of a heavy quark embedded in a far-from-equilibrium gluon plasma using classical-statistical lattice simulations. We find several features in the time dependence of the momentum broadening: a short initial rapid growth of h p2i, followed by linear growth with time due to Langevin-type dynamics and damped oscillations around this growth at the plasmon frequency. We show that these novel oscillations are not easily explained using perturbative techniques but result from an excess of gluons at low momenta. These oscillation are therefore a gauge invariant confirmation of the infrared enhancement we had previously observed in gauge-fixed correlation functions. We argue that the kinetic theory description of such systems becomes less reliable in the presence of this IR enhancement