Abstract:
The formalism of the $R^*$ operation [1] is developed; it generalizes the $R$ operation
and eliminates both ultraviolet and infrared divergences. By explicit formulation of
the concept of an infrared counterterm it is shown that the calculation of an arbitrary
$(\Re+1)$-loop ultraviolet or infrared eounterterm in the minimal subtraction scheme
can be reduced to the finding of the divergent and finite parts of certain massless
Feynman integrals that depend only on a single external momentum with number of
loops not exceeding $\Re$.
Citation:
V. A. Smirnov, K. G. Chetyrkin, “$R^*$ operation in the minimal subtraction scheme”, TMF, 63:2 (1985), 208–218; Theoret. and Math. Phys., 63:2 (1985), 462–469
This publication is cited in the following 28 articles:
Jae Goode, Franz Herzog, Sam Teale, “OPITeR: A program for tensor reduction of multi-loop Feynman Integrals”, Computer Physics Communications, 2025, 109606
Paul-Hermann Balduf, Springer Theses, Dyson–Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory, 2024, 81
J. A. Gracey, “Explicit no-
π2
renormalization schemes in QCD at five loops”, Phys. Rev. D, 109:3 (2024)
Jae Goode, Franz Herzog, Anthony Kennedy, Sam Teale, Jos Vermaseren, “Tensor reduction for Feynman integrals with Lorentz and spinor indices”, J. High Energ. Phys., 2024:11 (2024)
Weiguang Cao, Franz Herzog, Tom Melia, Jasper Roosmale Nepveu, “Non-linear non-renormalization theorems”, J. High Energ. Phys., 2023:8 (2023)
Anatoly V. Kotikov, “Effective Quantum Field Theory Methods for Calculating Feynman Integrals”, Symmetry, 16:1 (2023), 52
Giulio Falcioni, Franz Herzog, “Renormalization of gluonic leading-twist operators in covariant gauges”, J. High Energ. Phys., 2022:5 (2022)
Zeno Capatti, Valentin Hirschi, Ben Ruijl, “Local unitarity: cutting raised propagators and localising renormalisation”, J. High Energ. Phys., 2022:10 (2022)
John Collins, Ted C. Rogers, Nobuo Sato, “Positivity and renormalization of parton densities”, Phys. Rev. D, 105:7 (2022)
Kotikov V A., “Some Examples of Calculation of Massless and Massive Feynman Integrals”, Particles, 4:3 (2021), 361–380
J. A. M. Vermaseren, Texts & Monographs in Symbolic Computation, Anti-Differentiation and the Calculation of Feynman Amplitudes, 2021, 501
Gudrun Heinrich, “Collider physics at the precision frontier”, Physics Reports, 922 (2021), 1
Robert Beekveldt, Michael Borinsky, Franz Herzog, “The Hopf algebra structure of the R∗-operation”, J. High Energ. Phys., 2020:7 (2020)
Franz Herzog, “Geometric IR subtraction for final state real radiation”, J. High Energ. Phys., 2018:8 (2018)
F. Herzog, B. Ruijl, T. Ueda, J. A. M. Vermaseren, A. Vogt, “The five-loop beta function of Yang-Mills theory with fermions”, J. High Energ. Phys., 2017:2 (2017)
Franz Herzog, Ben Ruijl, “The R *-operation for Feynman graphs with generic numerators”, J. High Energ. Phys., 2017:5 (2017)
K. G. Chetyrkin, G. Falcioni, F. Herzog, J.A.M. Vermaseren, “Five-loop renormalisation of QCD in covariant gauges”, J. High Energ. Phys., 2017:10 (2017)
S. Penati, A. Santambrogio, D. Zanon, “Gravitational dressing of N = 2 σ-models beyond leading order”, Nuclear Physics B, 499:1-2 (1997), 479
S. Penati, A. Santambrogio, D. Zanon, “Renormalization group flows in σ-models coupled to two-dimensional dynamical gravity”, Nuclear Physics B, 483:1-2 (1997), 495
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