Combinatorics of $\mathbf{R}$-, ${\mathbf{R}}^{-1}$-, and ${\mathbf{R}}^{\ast }$-operations and asymptotic expansions of feynman integrals in the limit of large momenta and masses

Abstract

A generalization of the forest technique procedure --- the $R^{-1}$-operation---is elaborated and then employed to treat a variety of problems. First, it is employed to reveal the underlying simple structure of the Bogoliubov-Parasiuk renormalization prescription based on momentum subtractions. Second, we use this structure to derive a generalized Zimmermann identity connecting two different renormalized versions of a given Feynman integral. Third, the recursive procedure to minimally subtract the ultraviolet and infrared divergences from euclidean, dimensionally regularized Feynman integrals---the $R^{\ast }$-operation--- is simplified by reformulating it in terms of the R-operation alone. The new formulation is shown to lead immediately to a simple and regular algorithm for evaluating the overall ultraviolet divergences of arbitrary dimensionally regularized Feynman integrals, (including the ones appearing in two-dimensional field-theoretical models), the algorithm neatly reducing the problem to computing some massless propagator-type integrals. Finally, we construct a brief and concise proof of a general theorem which gives an explicitly finite large momenta and/or masses asymptotic expansion of an arbitrary (minimally subtracted) euclidean Feynman integral.

40 pages, this is an Archive copy of a preprint MPI-Ph/PTh 13/91 issued by the Max-Plank-Institute für Physik (Munich, Germany) in March of 1991. See the Comments Section in the very end. Some references are fixed

References in corpus (1)

• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory

Cited by in corpus (5)

• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• Critical behavior of isotropic systems with strong dipole-dipole interaction: three-loop study
• Top-quark loops and the muon anomalous magnetic moment
• The method of global R* and its applications
• Some examples of calculation of massless and massive Feynman integrals