Screened perturbation theory for 3d Yang-Mills theory and the magnetic modes of hot QCD : International Workshop on QCD Green’s Functions, Confinement, and Phenomenology - QCD-TNT09, September 07 - 11 2009, ECT Trento, Italy

Perturbation theory for non-abelian gauge theories at finite temperature is plagued by infrared divergences which are caused by magnetic soft modes ~ g2T, corresponding to gluon fields of a 3d Yang-Mills theory. While the divergences can be regulated by a dynamically generated magnetic mass on that scale, the gauge coupling drops out of the effective expansion parameter requiring summation of all loop orders for the calculation of observables. Some gauge invariant possibilities to implement such infrared-safe resummations are reviewed. We use a scheme based on the non-linear sigma model to estimate some of the contributions ~ g6 of the soft magnetic modes to the QCD pressure through two loops. The NLO contribution amounts to ~ 10% of the LO, suggestive of a reasonable convergence of the series

Fun with higher-loop Feynman diagrams

We review recent progress that we have achieved in evaluating the class of fully massive vacuum integrals at five loops. After discussing topics that arise in classification, evaluation and algorithmic codification of this specific set of Feynman integrals, we present some selected new results for their expansions around 4 - 2ε dimensions

Recursion-free solution for two-loop vacuum integrals with "collinear" masses

We investigate the structure of a particular class of massive vacuum Feynman integrals at two loops. This class enjoys the linear relation $m_1+m_2=m_3$ between its three propagator masses, corresponding to zeros of the associated K\"all\'en function. Apart from having applications in thermal field theory, the integrals can be mapped onto one-loop three-point functions with collinear external momenta, suggesting the term "collinear" masses. We present a closed-form solution for these integrals, proving that they can always be factorized into products of one-loop cases, for all integer-valued propagator powers.Comment: 34 pages, 5 figures; v2: references adde

High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles

In this article we present a high-precision evaluation of the expansions in \e=(4-d)/2 of (up to) four-loop scalar vacuum master integrals, using the method of difference equations developed by S. Laporta. We cover the complete set of `QED-type' master integrals, i.e. those with a single mass scale only (i.e. $m_i\in\{0,m\}$) and an even number of massive lines at each vertex. Furthermore, we collect all that is known analytically about four-loop `QED-type' masters, as well as about {\em all} single-mass-scale vacuum integrals at one-, two- and three-loop order.Comment: 25 pages, uses axodraw.st

Four-Loop Decoupling Relations for the Strong Coupling

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 $\beta$ 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.Comment: 11 page

Towards the five-loop Beta function for a general gauge group.

We present analytical results for the N4 f and N3 f terms of the five-loop Beta function, for a general gauge group. While the former term agrees with results available from large-Nf studies, the latter is new and extends the value known for SU(3) from an independent calculation

Quark mass thresholds in QCD thermodynamics

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.Comment: 14 pages. v2: minor additions and clarifications; published versio

A new three-loop sum-integral of mass dimension two

We evaluate a new 3-loop sum-integral which contributes to the Debye screening mass in hot QCD. While we manage to derive all divergences analytically, its finite part is mapped onto simple integrals and evaluated numerically.Comment: 15 page

Do neurologists in Germany adhere to the national Parkinson’s disease guideline?

Implementation of guidelines can improve clinical practice. The aim in this study was to investigate whether neurologists in Germany adhered to the national Parkinson’s disease guideline. Data were obtained from a cross-sectional survey of 60 neurologists. Analyses were performed on 320 patients with idiopathic Parkinson’s disease with either low grades of functional impairment (Hoehn and Yahr stage I) or higher grades of functional impairment (stage II–V) but without motor complications. The sample was divided into four groups depending on age and grade of functional impairment. For each group, a biometric parameter on the use of dopamine agonists and L-dopa was defined based on the guideline. In patients aged <70 years, the recommendation to use dopamine agonists without L-dopa (parameter 1) was observed in 53% of patients with lower grades of functional impairment, whilst recommended use of dopamine agonists in more functionally impaired patients (parameter 2) was followed to a greater extent (84%). In patients aged ≥70 years, recommendations to use L-dopa without dopamine agonists were adhered to in only 50% of less functionally impaired (parameter 3) and 52% of more functionally impaired (parameter 4) patients. In conclusion, our results indicated there was moderate but not full adherence to the guideline

Debye screening mass of hot Yang-Mills theory to three-loop order

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