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We evaluate all the primitive divergences contributing to the 7–loop β–function of φ 4 theory, i.e. all 59 diagrams that are free of subdivergences and hence give scheme– independent contributions. Guided by the association of diagrams with knots, we obtain analytical results for 56 diagrams. The remaining three diagrams, associated with the knots 10 124 ,… (More)
After a brief introduction to Heavy Quark Effective Theory, we discuss α representation in HQET and methods of calculation of some kinds of HQET diagrams up to three loops.
I discuss methods of calculation of propagator diagrams (massless, those of Heavy Quark Effective Theory, and massive on-shell diagrams) up to 3 loops. Integration-by-parts recurrence relations are used to reduce them to linear combinations of basis integrals. Non-trivial basis integrals have to be calculated by some other method, e.g., using Gegenbauer… (More)
This is the first part of lectures about effective field theories. Decoupling of heavy-particle loops is considered (heavy leptons in QED, heavy quarks in QCD).
GNU TEXmacs is a free software for editing scientific documents, which can also be used as an interface for computer algebra systems. In this software demonstration we will briefly recall its main features and present some recent developments.
The large-β 0 limit of QCD is discussed, with the emphasize on simple technical methods of calculating various quantities at the order 1/β 0. Many examples, mainly from heavy quark physics, are considered. Some QCD results based on renormaliza-tion group (and not restricted to the large-β 0 limit) are also discussed. It is well known that perturbative… (More)
The lectures are a practical introduction to perturbative calculations in QED and QCD. I discuss methods of calculation of one-and two-loop diagrams in dimensional regularization, MS and on-shell renormalization schemes, decoupling of heavy-particle loops.
We present the full analytic result for the three loop angle-dependent cusp anomalous dimension in QCD. With this result, infrared divergences of planar scattering processes with massive particles can be predicted to that order. Moreover, we define a closely related quantity in terms of an effective coupling defined by the lightlike cusp anomalous… (More)
We compute the three-loop relation between the pole and the minimally subtracted quark mass allowing for virtual effects from a second massive quark. We also consider the analogue effects for the on-shell wave function renormalization constant.
This tutorial (based on the talk at the TeXmacs workshop in Faro, Portugal, February 26 - March 2, 2012) describes the new and improved Reduce plugin in GNU TeXmacs.