In this note the leptonic contribution to the running of the electromagnetic coupling constant is discussed up to the three-loop level. Special emphasize is put on the evaluation of the double-bubble diagrams. The dominant correction to electroweak observables is provided by the running of the electromagnetic coupling constant from its value at vanishing momentum transfer to high energies. The ...

A bstract We describe a systematic approach for the evaluation of Witten diagrams multi-loop scattering amplitudes conformally coupled scalar ϕ 4 -theory in Euclidean AdS , by recasting as flat space Feynman integrals. derive closed form expressions anomalous dimensions all double-trace operators up to second order coupling constant. explain relation between unitarity methods and discontinuitie...

A recently proposed scheme for numerical evaluation of Feynman diagrams is extended to cover all two-loop two-point functions with arbitrary internal and external masses. The adopted algorithm is a modification of the one proposed by F. V. Tkachov and it is based on the so-called generalized Bernstein functional relation. On-shell derivatives of self-energies are also considered and their infra...

A FORM based package (ON-SHELL2) for the calculation of two loop self-energy diagrams with one nonzero mass in internal lines and the external momentum on the same mass shell is elaborated. The algorithm, based on recurrence relations obtained from the integration-by-parts method, allows us to reduce diagrams with arbitrary indices (powers of scalar propagators) to a set of master integrals. Th...

The interpretation of electroweak precision data in particle physics makes it necessary to compute higher-order quantum corrections in perturbation theory. The traditional manual treatment of the corresponding Feynman diagrams is limited by the large amount of their occurrence and the enormous complexity of the mathematical expressions. In the framework of our research project in quantum chromo...

fe49co33ni18 nanowire arrays (175 nm in diameter and lengths ranging from 5 to 32μm) were fabricated into nanopores of hard-anodized aluminum oxide templates using pulsed ac electrodeposition technique. hysteresis loop measurements indicated that increasing the length decreases coercivity and squareness values (from 274 oe and 0.58 to200 oe and 0.105, respectively), indicating the increase in m...

Topological string theory with twistor space as the target makes visible some otherwise difficult to see properties of perturbative Yang-Mills theory. But left-right symmetry, which is obvious in the standard formalism, is highly unclear from this point of view. Here we prove that tree diagrams computed from connected D-instanton configurations are paritysymmetric. The main point in the proof a...

A simple algorithm is presented for the tensorial reduction of oneloop diagrams with massless external momenta. At most rank one tensor integrals with the initial number of denominators appear, plus, eventually, higher rank integrals with less denominators. The number of Gram determinants in the tensorial decomposition is then reduced, giving a better numerical stability of the results. In some...