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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)

- Andrey Grozin, Johannes M Henn, Gregory P Korchemsky, Peter Marquard
- Physical review letters
- 2015

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)

- Andrey Grozin
- 2008

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.

- Andrey Grozin
- 2003

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)

- Andrey Grozin
- 2009

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).

- Joris van der Hoeven, Andrey Grozin, Massimiliano Gubinelli, Grégoire Lecerf, François Poulain, Denis Raux
- ACM Comm. Computer Algebra
- 2013

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.

- Andrey Grozin
- 2003

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)

- Andrey Grozin
- 2012

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.

- Andrey Grozin
- ArXiv
- 2012

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.

- Andrey Grozin
- 2005

B-meson light-cone distribution amplitudes are discussed in these lectures in the framework of HQET. The evolution equation for the leading-twist distribution amplitude is derived in one-loop approximation. QCD sum rules for distribution amplitudes are discussed.