Multiloop integrand reduction for dimensionally regulated amplitudes

Mastrolia, Pierpaolo; Mirabella, Edoardo; Ossola, Giovanni; Peraro, Tiziano

doi:10.1016/j.physletb.2013.10.066

Cited by 49 publications

(67 citation statements)

References 21 publications

(33 reference statements)

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“…A more intimate connection among the idea of reduction under the integral sign and analyticity and unitarity has been pointed out recently. Using basic principles of algebraic geometry [7,8,[21][22][23], have shown that the structure of the multi-particle poles is determined by the zeros of the denominators involved in the corresponding multiple cut. This new approach to integrand reduction methods allows for their systematization and for their all-loop extension.…”

Section: Introductionmentioning

confidence: 99%

On the four-dimensional formulation of dimensionally regulated amplitudes

et al. 2014

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Elaborating on the four-dimensional helicity scheme, we propose a pure four-dimensional formulation (FDF) of the d-dimensional regularization of one-loop scattering amplitudes. In our formulation particles propagating inside the loop are represented by massive internal states regulating the divergences. The latter obey Feynman rules containing multiplicative selection rules which automatically account for the effects of the extra-dimensional regulating terms of the amplitude. We present explicit representations of the polarization and helicity states of the four-dimensional particles propagating in the loop. They allow for a complete, four-dimensional, unitarity-based construction of d-dimensional amplitudes. Generalized unitarity within the FDF does not require any higher-dimensional extension of the Clifford and the spinor algebra. Finally we show how the FDF allows for the recursive construction of d-dimensional one-loop integrands, generalizing the fourdimensional open-loop approach.

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Section: Introductionmentioning

confidence: 99%

On the four-dimensional formulation of dimensionally regulated amplitudes

et al. 2014

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“…While the GOSAM code will be further improved, it will be interesting to observe whether the extension of integrand-level techniques [87][88][89][90] to higher orders will succeed and provide a comparable level of automation, at least for the calculation of the virtual parts.…”

Section: Discussionmentioning

confidence: 99%

GoSam @ LHC: algorithms and applications to Higgs production

Cullen¹,

Mirabella²,

Schlenk³

et al. 2014

Proceedings of 11th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) —

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“…In the framework of the integrand reduction method [1,3,9,10,11,29], the computation of dimensionally regulated -loop integrals…”

Section: Adaptive Integrand Decomposition 31 Integrand Recurrence Rementioning

confidence: 99%

Adaptive Integrand Decomposition

Mastrolia¹,

Peraro²,

Primo³

et al. 2016

Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2016)

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We present a simplified variant of the integrand reduction algorithm for multiloop scattering amplitudes in d = 4 − 2ε dimensions, which exploits the decomposition of the integration momenta in parallel and orthogonal subspaces, d = d + d ⊥ , where d is the dimension of the space spanned by the legs of the diagrams. We discuss the advantages of a lighter polynomial division algorithm and how the orthogonality relations for Gegenbauer polynomilas can be suitably used for carrying out the integration of the irreducible monomials, which eliminates spurious integrals. Applications to one-and two-loop integrals, for arbitrary kinematics, are discussed. Loops and Legs in Quantum Field Theory

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Multiloop integrand reduction for dimensionally regulated amplitudes

Cited by 49 publications

References 21 publications

On the four-dimensional formulation of dimensionally regulated amplitudes

On the four-dimensional formulation of dimensionally regulated amplitudes

GoSam @ LHC: algorithms and applications to Higgs production

Adaptive Integrand Decomposition

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