Abusing qgraf

Nogueira, P.

doi:10.1016/j.nima.2005.11.151

Cited by 33 publications

(28 citation statements)

References 7 publications

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“…The gradient-flow formalism in perturbation theory can be formulated in terms of a Lagrangian field theory, where the flow equations (2) We have implemented the Feynman rules into the program qgraf [21,22], which generates the Feynman diagrams for the desired matrix elements. Its output is then transformed to FORM [23,24] notation by q2e/exp [25,26].…”

Section: Methodsmentioning

confidence: 99%

The two-loop energy–momentum tensor within the gradient-flow formalism

2018

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The gradient-flow formulation of the energy-momentum tensor of QCD is extended to NNLO perturbation theory. This means that the Wilson coefficients which multiply the flowed operators in the corresponding expression for the regular energy-momentum tensor are calculated to this order. The result has been obtained by applying modern tools of regular perturbation theory, reducing the occurring two-loop integrals, which also include flow-time integrations, to a small set of master integrals which can be calculated analytically.

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Section: Methodsmentioning

confidence: 99%

The two-loop energy–momentum tensor within the gradient-flow formalism

2018

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“…We generate the Feynman diagrams including symmetry factors and signs (from closed fermion loops) with the help of the program qgraf [24,25]. In the notation of this program, the propagators for the gluon, the ghost, and a single quark flavor can be defined as…”

Section: Generation Of Feynman Diagram Expressionsmentioning

confidence: 99%

Results and techniques for higher order calculations within the gradient-flow formalism

Artz¹,

Harlander²,

Lange³

et al. 2019

J. High Energ. Phys.

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We describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradient-flow formalism. This includes a collection of all relevant Feynman rules of the five-dimensional field theory and the composite operators considered in this paper. Tools from standard perturbative calculations are used to obtain Green's functions at finite flow time t at higher orders in perturbation theory. The three-loop results for the quark condensate at finite t and the conversion factor for the "ringed" quark fields to the MS scheme are presented as applications. We also re-evaluate an earlier result for the three-loop gluon condensate, improving on its accuracy.

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“…While we refer to the literature for more detailed descriptions of our chain of computer-algebra programs [7,10] and for technical details concerning our procedure for integral reduction and evaluation [11][12][13][14], let us briefly summarize the main components of our strategy here. As is standard procedure in perturbative multiloop calculations, we start with expressions produced by the diagram generator qgraf [15,16] linked with some own FORM [17][18][19] codes. Taking the required set of 2-and 3-point functions, we perform the group algebra with the help of color [20].…”

Section: Computational Strategymentioning

confidence: 99%