Energy loss in unstable QGP - problem of the upper cut-off

The energy loss of a highly energetic parton in a weakly coupled quark-gluon plasma is studied as an initial value problem. An extremely prolate plasma, where the momentum distribution is infinitely elongated along one direction, is considered. The energy loss is strongly time and direction dependent and its magnitude can much exceed the equilibrium value. It is logarithmically ultraviolet divergent. We argue that a good approximation to the energy loss can be obtained if this divergence is cut off with the parton energy.Comment: 6 pages, presented by St. Mrowczynski at International Conference on New Frontiers in Physics, Kolymbari, Crete, Greece, August 28 - September 5, 201

The energy-momentum tensor at the earliest stage of relativistic heavy ion collisions -- formalism

Nuclear collisions at high energies produce a gluon field that can be described using the Colour Glass Condensate (CGC) effective theory at proper times $\tau \lesssim 1$ fm/c. The theory can be used to calculate the gluon energy-momentum tensor, which provides information about the early time evolution of the chromo-electric and chromo-magnetic fields, energy density, longitudinal and transverse pressures, and other quantities. We obtain an analytic expression for the energy-momentum tensor using an expansion in the proper time, and working to sixth order. The calculation is technically difficult, in part because the number of terms involved grows rapidly with the order of the $\tau$ expansion, but also because of several subtle issues related to the definition of event-averaged correlators, the method chosen to regulate these correlators, and the dependence of results on the parameters introduced by the regularization and nuclear density profile functions. All of these issues are crucially related to the important question of the extent to which we expect a CGC approach to be able to accurately describe the early stages of a heavy ion collision. We present some results for the evolution of the energy density and the longitudinal and transverse pressures. We show that our calculation gives physically meaningful results up to values of the proper time which are close to the regime at which hydrodynamic simulations are initialized. In a companion paper we will present a detailed analysis of several other experimentally relevant quantities that can be calculated from the energy-momentum tensor.Comment: 41 pages, 5 figure

Transport of hard probes through glasma

We calculate the transverse momentum broadening $\hat q$ and collisional energy loss $dE/dx$ of hard probes traversing an evolving glasma during the earliest phase of a relativistic heavy-ion collision. We use a Fokker-Planck equation and apply a proper time expansion to describe the temporal evolution of the glasma. The correlators of the chromodynamic fields that determine the Fokker-Planck collision terms, which in turn provide $\hat q$ and $dE/dx$, are computed to fifth order. Both transport coefficients are strongly dependent on time. The maximum values they acquire before the proper time expansion breaks down are large: $\hat q$ is of the order of a few ${\rm GeV^2/fm}$ and $dE/dx \sim 1~{\rm GeV/fm}$. Their precise values depend on the probe's velocity ${\bf v}$, the saturation momentum $Q_s$, and an IR regulator $m$ that is related to the confinement scale. We study the dependence of our results on these quantities. Different regularization procedures are analysed and shown to produce similar results. We also discuss the validity of the proper time expansion and the compatibility of the approximations that are inherent in the derivation of the Fokker-Planck equation. We show that hard probes lose a comparable amount of energy when they propagate through the short-lived glasma phase, and the long-lasting hydrodynamic phase. The conclusion is that the glasma plays an important role in jet quenching.Comment: 41 pages, 18 figures, a few comments added, accepted for publication in Phys. Rev.

The HTL Lagrangian at NLO: The photon case

We calculate the two loop hard correction to the photon self-energy in an electron-positron plasma (EPP) for arbitrary soft momenta. This provides the only missing ingredient to obtain the Hard Thermal Loop (HTL) effective Lagrangian at next-to-leading order (NLO), and the full photon propagator at the same order. This result can be easily extended to obtain the soft photon propagator in a quark gluon plasma. We use the Keldysh representation of the real time formalism in the massless fermion limit, and dimensional regularization (DR) to regulate any ultraviolet (UV), infrared (IR) or collinear divergences that appear in the intermediate steps of the calculation. In the limit of soft photon momenta, our result is finite. It not only provides an correction to the Debye mass, but also a new non-local structure. A consistent regularization of radial and angular integrals is crucial to get this new structure. As an application we calculate the plasmon dispersion relations at NLO