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.
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.
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)
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.
The classical Lagrangian of chromodynamics, its quantization in the perturbation theory framework, and renormalization form the subject of these lectures. Symmetries of the theory are discussed. The dependence of the coupling constant α s on the renormalization scale µ is considered in detail.
In this lecture, the early history of asymptotic freedom is discussed. The first completely correct derivation of β 0 in non-abelian gauge theory (Khriplovich, 1969) was done in the Coulomb gauge; this derivation is reproduced (in modernized terms) in Sect. 2. A qualitative physical explanation of asymptotic freedom via chromomag-netic properties of vacuum… (More)