FIRCLA, one-loop correction to and basis of Feynman integrals in higher dimensions

Jegerlehner, F.; Tarasov, O. V.

doi:10.1016/s0920-5632(03)80149-4

Cited by 16 publications

(19 citation statements)

References 11 publications

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“…The one-loop electroweak and QCD radiative corrections to the most important production mechanisms have been completed only recently [517][518][519][520][521][522][523][524][525][526][527][528][529] and their main effects will be summarized.…”

Section: Higgs Production Processes In Lepton Collisionsmentioning

confidence: 99%

“…4.9. The corrections have been calculated some time ago [517] and reanalyzed recently in the context of the full e + e − → Hνν process [518][519][520].…”

Section: The Higgs-strahlung Processmentioning

confidence: 99%

“…In Ref. [520], the results have been obtained as a MAPLE output using the program DIANA [531] without an explicit evaluation. In Ref.…”

Section: The Ww Fusion Processmentioning

confidence: 99%

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The anatomy of electroweak symmetry breaking

2008

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Section: Higgs Production Processes In Lepton Collisionsmentioning

confidence: 99%

“…4.9. The corrections have been calculated some time ago [517] and reanalyzed recently in the context of the full e + e − → Hνν process [518][519][520].…”

Section: The Higgs-strahlung Processmentioning

confidence: 99%

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The anatomy of electroweak symmetry breaking

2008

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“…for d = 4 one meets a division by zero, 0 0 . In [29], however, an interesting approach has been proposed, which can also be applied to handle this case. In fact, the idea is to go to even higher dimensions, which provides good numerical stability.…”

Section: Numerical Evaluation Of Higher-dimensional Scalar Integralsmentioning

confidence: 99%

New results for algebraic NLO - Tensor reduction of Feynman integrals

Riemann¹,

Fleischer²,

Yundin³

2013

Proceedings of 10th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) —

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We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5-point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d + 2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1-to 4-point functions in the generic dimension d = 4 − 2ε. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d + 2)-dimensional 5-point function can be evaluated.

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“…There was one attempt to use the Davydychev-Tarasov reduction for the description of oneloop contributions to the process e þ e À ! H " [32], and the numerical problems due to the five-point functions were discussed in some detail. To a large extent they root in the appearance of inverse powers of Gram determinants.…”

Section: Introductionmentioning

confidence: 99%

Complete reduction of one-loop tensor 5- and 6-point integrals

et al. 2009

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We perform a complete analytical reduction of general one-loop Feynman integrals with five and six external legs for tensors up to rank R ¼ 3 and 4, respectively. An elegant formalism with extensive use of signed minors is developed for the cancellation of inverse Gram determinants. The 6-point tensor functions of rank R are expressed in terms of 5-point tensor functions of rank R À 1, and the latter are reduced to scalar four-, three-, and two-point functions. The resulting compact formulas allow both for a study of analytical properties and for efficient numerical programming. They are implemented in FORTRAN and MATHEMATICA.

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FIRCLA, one-loop correction to and basis of Feynman integrals in higher dimensions

Cited by 16 publications

References 11 publications

The anatomy of electroweak symmetry breaking

The anatomy of electroweak symmetry breaking

New results for algebraic NLO - Tensor reduction of Feynman integrals

Complete reduction of one-loop tensor 5- and 6-point integrals

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