Abstract:
The formalism of the R∗R∗ operation [1] is developed; it generalizes the RR 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
(ℜ+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 ℜ.
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
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J. A. M. Vermaseren, Texts & Monographs in Symbolic Computation, Anti-Differentiation and the Calculation of Feynman Amplitudes, 2021, 501
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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)
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S. Penati, A. Santambrogio, D. Zanon, “Gravitational dressing of N = 2 σ-models beyond leading order”, Nuclear Physics B, 499:1-2 (1997), 479
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S. Penati, A. Santambrogio, D. Zanon, “Dressing of the beta-function in sigma-models coupled by two dimensional gravity”, Nuclear Physics B - Proceedings Supplements, 57:1-3 (1997), 216
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