Reduction of feynman diagrams

Melrose, D. B.

doi:10.1007/bf02832919

Cited by 181 publications

(264 citation statements)

References 4 publications

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“…Doing so one observes that I n N can be expressed by only 6 (N − 1)-point graphs for arbitrary N ≥ 6. Here we make contact to a result in [9,18], where a similar relation has been derived for the IR finite case in integer dimensions by using 4-dimensional Schouten identities.…”

Section: Derivationmentioning

confidence: 58%

Reduction formalism for dimensionally regulated one-loop N-point integrals

Binoth¹,

Guillet²,

2000

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We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce Npoint scalar functions with generic 4-dimensional external momenta to box integrals in (4 − 2 ) dimensions. We derive a formula valid for arbitrary N and give an explicit expression for N = 6.Further a tensor reduction method for N -point tensor integrals is presented. We prove that generically higher dimensional integrals contribute only to order for N ≥ 5. The tensor reduction can be solved iteratively such that any tensor integral is expressible in terms of scalar integrals. Explicit formulas are given up to N = 6.

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Section: Derivationmentioning

confidence: 58%

Reduction formalism for dimensionally regulated one-loop N-point integrals

Binoth¹,

Guillet²,

2000

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“…The existence of this decomposition is one of the most important results for one-loop calculations; its origin relies on simple Lorentz invariance which allows a decomposition of tensor integrals to invariant form factors and on the four-dimensional nature of space time which allows scalar higher point integrals to be reduced to sums of boxes. Thus a scalar pentagon in D dimensions can be written as a sum of the five box diagrams obtainable by removing one propagator if we neglect terms of order ǫ [49,50,51]. The general one loop N -point integral in D = 4 − 2ǫ dimensions for N ≥ 6 can be recursively obtained as a linear combination of pentagon integrals [49,50], provided that the external momenta are restricted to four dimensions.…”

Section: Preliminary Remarksmentioning

confidence: 99%

“…Thus a scalar pentagon in D dimensions can be written as a sum of the five box diagrams obtainable by removing one propagator if we neglect terms of order ǫ [49,50,51]. The general one loop N -point integral in D = 4 − 2ǫ dimensions for N ≥ 6 can be recursively obtained as a linear combination of pentagon integrals [49,50], provided that the external momenta are restricted to four dimensions. This will be discussed in detail in the later sections.…”

Section: Preliminary Remarksmentioning

confidence: 99%

“…Some illustrative results are presented in Section 4. Second, using the van Neerven -Vermaseren basis, it is straightforward to show that in four dimensions the scalar five-point Feynman integral is given by a linear combination of scalar box integrals [49,50]. Third, using the van Neerven -Vermaseren basis it is easy to understand that in four dimensions the integrand of any one-loop Feynman diagram in any renormalizable theory is given by a linear combination of rational functions containing products of four, three, two or one Feynman denominators and with the numerators of a very restrictive form, see Section 5.…”

Section: The Van Neerven -Vermaseren Basismentioning

confidence: 99%

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One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts

et al. 2012

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The success of the experimental program at the Tevatron re-inforced the idea that precision physics at hadron colliders is desirable and, indeed, possible. The Tevatron data strongly suggests that one-loop computations in QCD describe hard scattering well. Extrapolating this observation to the LHC, we conclude that knowledge of many short-distance processes at next-to-leading order may be required to describe the physics of hard scattering. While the field of oneloop computations is quite mature, parton multiplicities in hard LHC events are so high that traditional computational techniques become inefficient. Recently new approaches based on unitarity have been developed for calculating one-loop scattering amplitudes in quantum field theory. These methods are especially suitable for the description of multi-particle processes in QCD and are amenable to numerical implementations. We present a systematic pedagogical description of both conceptual and technical aspects of the new methods.

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“…There is a vast literature on this subject [40,41,42,43,44,45,46]. The tensor reduction relations we will use for our calculation of the 5-and 6-gluon amplitudes are quite simple.…”

Section: Review Of Tensor Reduction Of the One-loop Amplitudementioning

confidence: 99%

The rational parts of one-loop QCD amplitudes III: The six-gluon case

Xiao

Yang

et al. 2006

Nuclear Physics B

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The rational parts of 6-gluon one-loop amplitudes with scalars circulating in the loop are computed by using the newly developed method for computing the rational parts directly from Feynman integrals. We present the analytic results for the two MHV helicity configurations: (1 − 2 + 3 + 4 − 5 + 6 + ) and (1 − 2 + 3 − 4 + 5 + 6 + ), and the two NMHV helicity configurations: (1 − 2 − 3 + 4 − 5 + 6 + ) and (1 − 2 + 3 − 4 + 5 − 6 + ). Combined with the previously computed results for the cut-constructible part, our results are the last missing pieces for the complete partial helicity amplitudes of the 6-gluon one-loop QCD amplitude. *

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Reduction of feynman diagrams

Cited by 181 publications

References 4 publications

Reduction formalism for dimensionally regulated one-loop N-point integrals

Reduction formalism for dimensionally regulated one-loop N-point integrals

One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts

The rational parts of one-loop QCD amplitudes III: The six-gluon case

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