Two-loop tensor integrals in quantum field theory

Actis, Stefano; Passarino, Giampiero; Ferroglia, Andrea; Passera, M.; Uccirati, Sandro

doi:10.1016/j.nuclphysb.2004.10.018

Cited by 36 publications

(36 citation statements)

References 76 publications

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“…The presence of non-trivial structures containing integration momenta in the numerators of two-loop integrals requires to introduce tensor structures and form factors, as described in sections 7 and 9 of Ref. [49] for higher rank self-energies and vertices.…”

Section: Classification Of Two-loop Integralsmentioning

confidence: 99%

“…[47] for the scalar cases; the corresponding parametrization for tensor integrals can be found in section 9 of Ref. [49]. Extracting the UV poles from these expressions and performing some changes of variables, we get…”

Section: The Collinear-finite Part Of Vmentioning

confidence: 99%

“…[45,46] for self-energies and of Refs. [47,48,49] for vertices. For the three vertex families V G , V K and V H , we modify our approach, since two external massless particles appear and simpler results can be derived.…”

Section: Evaluation Of Massive Diagramsmentioning

confidence: 99%

“…as given in Ref. [49]. For those integrals where also ultraviolet divergences are present we need to extend the decomposition of Eq.…”

Section: B Properties Of Projectorsmentioning

confidence: 99%

“…[47] and in section 9 of Ref. [49], in close analogy with the procedure already described in section 6.2.1. The extraction of the UV poles is trivial; after an appropriate change of variables, we can write the V G functions in parametric space as…”

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confidence: 96%

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NNLO computational techniques: The cases and

et al. 2009

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A large set of techniques needed to compute decay rates at the two-loop level are derived and systematized. The main emphasis of the paper is on the two Standard Model decays H → γγ and H → gg. The techniques, however, have a much wider range of application: they give practical examples of general rules for two-loop renormalization; they introduce simple recipes for handling internal unstable particles in two-loop processes; they illustrate simple procedures for the extraction of collinear logarithms from the amplitude. The latter is particularly relevant to show cancellations, e.g. cancellation of collinear divergencies. Furthermore, the paper deals with the proper treatment of non-enhanced two-loop QCD and electroweak contributions to different physical (pseudo-)observables, showing how they can be transformed in a way that allows for a stable numerical integration. Numerical results for the two-loop percentage corrections to H → γγ, gg are presented and discussed. When applied to the process pp → gg + X → H + X, the results show that the electroweak scaling factor for the cross section is between −4% and +6% in the range 100 GeV < M H < 500 GeV, without incongruent large effects around the physical electroweak thresholds, thereby showing that only a complete implementation of the computational scheme keeps two-loop corrections under control.

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Section: Classification Of Two-loop Integralsmentioning

confidence: 99%

Section: The Collinear-finite Part Of Vmentioning

confidence: 99%

Section: Evaluation Of Massive Diagramsmentioning

confidence: 99%

“…as given in Ref. [49]. For those integrals where also ultraviolet divergences are present we need to extend the decomposition of Eq.…”

Section: B Properties Of Projectorsmentioning

confidence: 99%

mentioning

confidence: 96%

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NNLO computational techniques: The cases and

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Reduction of Feynman integrals in the parametric representation

Chen

2020

J. High Energ. Phys.

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Recently, the author proposed a new approach to reduce Feynman integrals [1]. Tensor integrals were directly parametrized by using a generator method. The resulting parametric integrals were reduced by constructing and solving linear relations. In this paper, we further show that polynomial equations for the operators that generate tensor integrals can be derived. A (incomplete) Gröbner basis is generated out of these equations. Tensor integrals can be (partially) reduced by using this basis. * wchen1@ualberta.ca

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Gauge-independent M S ¯ $$ \overline{\mathrm{MS}} $$ renormalization in the 2HDM

Denner

Jenniches

Lang

et al. 2016

J. High Energ. Phys.

159

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We present a consistent renormalization scheme for the CP-conserving TwoHiggs-Doublet Model based on MS renormalization of the mixing angles and the soft-Z 2 -symmetry-breaking scale M sb in the Higgs sector. This scheme requires to treat tadpoles fully consistently in all steps of the calculation in order to provide gauge-independent Smatrix elements. We show how bare physical parameters have to be defined and verify the gauge independence of physical quantities by explicit calculations in a general R ξ -gauge. The procedure is straightforward and applicable to other models with extended Higgs sectors. In contrast to the proposed scheme, the MS renormalization of the mixing angles combined with popular on-shell renormalization schemes gives rise to gauge-dependent results already at the one-loop level. We present explicit results for electroweak NLO corrections to selected processes in the appropriately renormalized Two-Higgs-Doublet Model and in particular discuss their scale dependence.

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Two-loop tensor integrals in quantum field theory

Cited by 36 publications

References 76 publications

NNLO computational techniques: The cases and

NNLO computational techniques: The cases and

Reduction of Feynman integrals in the parametric representation

Gauge-independent M S ¯ $$ \overline{\mathrm{MS}} $$ renormalization in the 2HDM

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