High-precision e-expansions of massive four-loop vacuum bubbles

In this paper we calculate at high-precision the expansions in e=(4-D)/2 of the master integrals of 4-loop vacuum bubble diagrams with equal masses, using a method based on the solution of systems of difference equations. We also show that the analytical expression of a related on-shell 3-loop self-mass master integral contains new transcendental constants made up of complete elliptic integrals of first and second kind.Comment: 7 pages, 2 figures, LaTex, to be published in Physics Letters

Renormalization Group Flows in Sigma--Models Coupled to Two--Dimensional Dynamical Gravity

We consider a bosonic \s--model coupled to two--dimensional gravity. In the semiclassical limit, $c\rightarrow -\infty$, we compute the gravity dressing of the \b--functions at two--loop order in the matter fields. We find that the corrections due to the presence of dynamical gravity are {\em not} expressible simply in terms of a multiplicative factor as previously obtained at the one--loop level. Our result indicates that the critical points of the theory are nontrivially influenced and modified by the induced gravity.Comment: Latex file, 18 pages plus 7 figure

Theoretical uncertainties for measurements of alpha_s from electroweak observables

One of the most precise measurements of the strong coupling constant alpha_s(MZ) is obtained in the context of global analyses of precision electroweak data. This article reviews the sensitivity of different electroweak observables to alpha_s and describes the perturbative uncertainties related to missing higher orders. The complete renormalisation scale dependence for the relevant observables is calculated at next-to-next-to-leading order and a new method is presented to determine the corresponding perturbative uncertainty for measurements of alpha_s based on these observables.Comment: v4: Revised version with new tables and figure

Matching QCD and HQET heavy-light currents at three loops

We consider the currents formed by a heavy and a light quark within Quantum Chromodynamics and compute the matching to Heavy Quark Effective Theory to three-loop accuracy. As an application we obtain the third-order perturbative corrections to ratios of B-meson decay constants.Comment: 23 pages, full results are available as Mathematica files at http://www-ttp.particle.uni-karlsruhe.de/Progdata/ttp09/ttp09-41/ ; v2: an error in comparison with Ref. [8] fixed ; v3: Journal versio

Gravitational Dressing of N=2 Sigma-Models Beyond Leading Order

We study the beta-function of the N=2 sigma-model coupled to N=2 induced supergravity. We compute corrections to first order in the semiclassical limit, $c \to -\infty$, beyond one-loop in the matter fields. As compared to the corresponding bosonic, metric sigma-model calculation, we find new types of contributions arising from the dilaton coupling automatically accounted for, once the K\"ahler potential is coupled to N=2 supergravity.Comment: latex, 16 pages, 8 figure

Transcendental numbers and the topology of three-loop bubbles

We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.Comment: 4 pages in REVTeX, 1 PostScript figure included, submitted to Phys. Rev. Let

Mass Corrections to the Tau Decay Rate

In this note radiative corrections to the total hadronic decay rate of the $\tau$-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate ration $R_{\tau}$ to the order ${\cal O}(\alpha_s^2 m^2)$ and find that they contribute appreciably to the Cabbibo supressed decay modes of the $\tau$-lepton. We also discuss corrections of mass dimension D=4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.Comment: 13 pages, LaTeX, no figures. This version fixes a typo in eq. (25) of the original paper (Z. Phys. C59 (1993) 525) and an errror in a numerical integration procedure which has resulted to a significant increase of the O(\alpha_s^2) coefficient in eq. (27). As a consequence also some tables in Section 4 have been modifie

Higgs Decay to Top Quarks at O(\alpha_s^2)

Three-loop corrections to the scalar and pseudo-scalar current correlator are calculated. By applying the large momentum expansion mass terms up to order (m^2/q^2)^4 are evaluated analytically. As an application O(\alpha_s^2) corrections to the decay of a scalar and pseudo-scalar Higgs boson into top quarks are considered. It is shown that for a Higgs mass not far above the $t\bar{t}$ threshold these higher order mass corrections are necessary to get reliable results.Comment: Latex, 20 pages, 14 ps-figures. The complete paper, including figures, is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

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

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases of their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD.Comment: 100 pages, 16 eps-figures include