York Schröder

The Pressure of hot QCD up to g6 ln(1/g)

The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order g^5. We compute here the last contribution which can be determined perturbatively, g^6 ln(1/g), by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative g^6 ln(1/g) terms, once they are summed together with the so far unknown perturbative and non-perturbative g^6 terms, could potentially extend the applicability of the coupling constant series down to surprisingly low temperatures.

The Static potential in QCD to two loops

We evaluate the static QCD potential to two--loop order. Compared to a previous calculation a sizable reduction of the two--loop coefficient

Quark mass thresholds in QCD thermodynamics

a_2

Four-loop decoupling relations for the strong coupling

is found.We evaluate the static QCD potential to two–loop order. Compared to a previous calculation a sizable reduction of the two–loop coefficient a2 is found. ∗e–mail: York.Schroeder@desy.de

Two-loop QCD gauge coupling at high temperatures

We discuss radiative corrections to how quark mass thresholds are crossed, as a function of the temperature, in basic thermodynamic observables such as the pressure, the energy and entropy densities, and the heat capacity of high temperature QCD. The indication from leading order that the charm quark plays a visible role at surprisingly low temperatures, is confirmed. We also sketch a way to obtain phenomenological estimates relevant for generic expansion rate computations at temperatures between the QCD and electroweak scales, pointing out where improvements over the current knowledge are particularly welcome.

Four-loop singlet contribution to the electroweak ρ parameter

We compute the matching relation for the strong coupling constant within the framework of QCD up to four-loop order. This allows a consistent five-loop running (once the β function is available to this order) taking into account threshold effects. As a side product we obtain the effective coupling of a Higgs boson to gluons with five-loop accuracy.

The leading non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure

We determine the 2-loop effective gauge coupling of QCD at high temperatures, defined as a matching coefficient appearing in the dimensionally reduced effective field theory. The result allows to improve on one of the classic non-perturbative probes for the convergence of the weak-coupling expansion at high temperatures, the comparison of full and effective theory determinations of an observable called the spatial string tension. We find surprisingly good agreement almost down to the critical temperature of the deconfinement phase transition. We also determine one new contribution of order (g6T4) to the pressure of hot QCD.

Automatic reduction of four-loop bubbles

Abstract We compute the four-loop QCD contribution to the electroweak ρ parameter induced by the singlet diagrams of the Z -boson self-energy. The numerical impact on the weak mixing angle and the W -boson mass is small.

Plaquette expectation value and gluon condensate in three dimensions

Using Numerical Stochastic Perturbation Theory within three-dimensional pure SU(3) gauge theory, we estimate the last unknown renormalization constant that is needed for converting the vacuum energy density of this model from lattice regularization to the MS scheme. Making use of a previous non-perturbative lattice measurement of the plaquette expectation value in three dimensions, this allows us to approximate the first non-perturbative coefficient that appears in the weak-coupling expansion of hot QCD pressure.

Three-dimensional physics and the pressure of hot QCD

We give technical details about the computational strategy employed in a recently completed investigation of the four-loop QCD free energy. In particular, the reduction step from generic vacuum bubbles to master integrals is described from a practical viewpoint, for fully massive as well as QED-type integrals.Abstract We give technical details about the computational strategy employed in a recently completed investigation of the four-loop QCD free energy. In particular, the reduction step from generic vacuum bubbles to master integrals is described from a practical viewpoint, for fully massive as well as QED-type integrals.