Toolbox for multiloop Feynman diagrams calculations using $R^{*}$ operation

Batkovich, Dmitrii; Kompaniets, M. V.

doi:10.48550/arxiv.1411.2618

Cited by 2 publications

(2 citation statements)

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“…Our computation has been made possible by the development of a refined algorithm [31], implemented in Form [40][41][42], for the determination of the ultraviolet and infrared divergences of arbitrary tensor self-energy integrals via the R * operation [32][33][34][35] -for another recent diagrammatic implementation of R * for scalar integrals and its application to ϕ 4 theory at six loops, see refs. [48,49] -and the Forcer program [28][29][30] for the parametric reduction of four-loop self-energy integrals. It should be noted that this approach is quite different from those taken in refs.…”

Section: Discussionmentioning

confidence: 99%

The five-loop beta function of Yang-Mills theory with fermions

Herzog

Ruijl

Ueda

et al. 2017

J. High Energ. Phys.

313

278

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Abstract:We have computed the five-loop corrections to the scale dependence of the renormalized coupling constant for Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum Electrodynamics (QED). Our analytical result, obtained using the background field method, infrared rearrangement via a new diagram-by-diagram implementation of the R * operation and the Forcer program for massless four-loop propagators, confirms the QCD and QED results obtained by only one group before. The numerical size of the five-loop corrections is briefly discussed in the standard MS scheme for QCD with n f flavours and for pure SU(N ) Yang-Mills theory. Their effect in QCD is much smaller than the four-loop contributions, even at rather low scales.

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Section: Discussionmentioning

confidence: 99%

The five-loop beta function of Yang-Mills theory with fermions

Herzog

Ruijl

Ueda

et al. 2017

J. High Energ. Phys.

313

278

View full text Add to dashboard Cite

show abstract

“…Our use of this approach has been made possible by the development of (a) Forcer [26][27][28], a Form [29][30][31] program for the parametric reduction of four-loop self-energy integrals, and (b) a program [32] efficiently implementing the R * operation, see refs. [33][34][35][36][37], locally for the evaluation of L -loop pole terms in terms of (L −1)-loop integrals. In order to cope with the computations for H → gg, which are far more demanding than those required to determine the five-loop beta function [38,39], the latter program has undergone substantial modifications and extensions.…”

Section: Introductionmentioning

confidence: 99%

On Higgs decays to hadrons and the R-ratio at N4LO

Herzog

Ruijl

Ueda

et al. 2017

J. High Energ. Phys.

131

243

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We present the first determination of Higgs-boson decay to hadrons at the nextto-next-to-next-to-next-to-leading order of perturbative QCD in the limit of a heavy top quark and massless light flavours. This result has been obtained by computing the absorptive parts of the relevant five-loop self-energy for a general gauge group and combining the outcome with the corresponding coefficient function already known to this order in QCD. Our new result reduces the uncertainty due to the truncation of the perturbation series to a fraction of the uncertainty due to the present error of the strong coupling constant. We have also performed the corresponding but technically simpler computations for direct Higgs decay to bottom quarks and for the electromagnetic R-ratio in e + e − → hadrons, thus verifying important fifth-order results obtained only by one group so far.

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Toolbox for multiloop Feynman diagrams calculations using $R^{*}$ operation

Cited by 2 publications

References 0 publications

The five-loop beta function of Yang-Mills theory with fermions

The five-loop beta function of Yang-Mills theory with fermions

On Higgs decays to hadrons and the R-ratio at N4LO

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