Andrey Grozin

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We evaluate all the primitive divergences contributing to the 7–loop β–function of φ4 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 10124,(More)
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)
I discuss methods of calculation of propagator diagrams (massless, those of Heavy Quark Effective Theory, and massive on-shell diagrams) up to 3 loops. Integrationby-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)
We compute the four-loop nf contribution proportional to the quartic Casimir of the QCD cusp anomalous dimension as an expansion for small cusp angle φ. This piece is gauge invariant, violates Casimir scaling, and first appears at four loops. It requires the evaluation of genuine non-planar four-loop Feynman integrals. We present results up to O(φ4). One(More)
In this lecture, the early history of asymptotic freedom is discussed. The first completely correct derivation of β0 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 chromomagnetic properties of vacuum(More)
Effective field theories are very useful for describing physics at low energies ≪ M , or large distances ≫ 1/M , where M is a high energy scale where some new particles or interactions become important. Effective Lagrangians are constructed as series in 1/M . Coefficients in them are obtained by matching scattering amplitudes in the full theory and in the(More)
The large-β0 limit of QCD is discussed, with the emphasize on simple technical methods of calculating various quantities at the order 1/β0. Many examples, mainly from heavy quark physics, are considered. Some QCD results based on renormalization group (and not restricted to the large-β0 limit) are also discussed. 1 Large-β0 Limit It is well known that(More)
Methods of calculation of loop diagrams in Heavy Quark Effective Theory (HQET) are presented. 1 Hadrons with a Heavy Quark B meson is the hydrogen atom of Quantum Chromodynamics (QCD), its simplest nontrivial object. In the leading approximation, the b quark in it just seats at rest at the origin and creates chromoelectric field. Light constituents (gluons,(More)