From Jacobi off-shell currents to integral relations

Llanes, Jurado, Jose; Rodrigo, Germán; Bobadilla, William J. Torres

doi:10.1007/jhep12(2017)122

Cited by 38 publications

(38 citation statements)

References 53 publications

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“…In this section, we report the results of [1]. For the sake of simplicity, although analogous to gauge theories coupled to matter, we focus on the study of the integral relations generated from the Jacobi off-shell current gg → gg.…”

Section: Colour-kinematics Dualitymentioning

confidence: 99%

“…It was noticed in [1] that in order to eliminate redundant terms in (2.8), the reference momenta q i have to be chosen to be equal for internal and external gluons. This request, together with the decomposition of off-shell momenta p i into massless ones,…”

Section: Numerators From Jacobi Off-shell Currentsmentioning

confidence: 99%

“…For the 2 → 2 case, we write relations for Feynman integrals with three loop propagators. In [1], we study particular example of gg → ss showing that higher rank numerators can be replaced by lower ones. This outcome indeed allows for an optimisation in the evaluation of Feynman integrals.…”

Section: One-loop Integral Relationsmentioning

confidence: 99%

“…2. The algorithm we use to perform the integrand reduction by means of AIDA is described as follows 1 1 Further details will be provided in: P. Mastrolia, T. Peraro, A. Primo and W. J. Torres Bobadilla (in preparation).…”

Section: µE Elastic Scatteringmentioning

confidence: 99%

“…In this talk, we discuss the new one-loop integral relations [1] that emerge as a consequence of the Colour-Kinematics duality (CKD) [2] and Loop-Tree duality formalism (LTD) [3,4]. Relations at integral level have been considered from a string theory perspective [5,6] and also from the modern techniques based on unitarity based methods [7,8].…”

Section: Introductionmentioning

confidence: 99%

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Interplay of colour kinematics duality and analytic calculation of multi-loop scattering amplitudes: one and two loops

Bobadilla¹,

William²

2018

Proceedings of 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) —

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In this talk, we review recent developments towards the calculation of multi-loop scattering amplitudes. In particular, we discuss how the colour-kinematics duality can provide new integral relations at one-loop level via the Loop-Tree duality formalism. On the other hand, in order to compute scattering amplitudes at one-and two-loop level, numerically and analytically, we describe the preliminary automation of the adaptive integrand decomposition algorithm. We show preliminary results on the analytic reduction of the µe-elastic scattering at one-and two-loop level.13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)

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Section: Colour-kinematics Dualitymentioning

confidence: 99%

Section: Numerators From Jacobi Off-shell Currentsmentioning

confidence: 99%

Section: One-loop Integral Relationsmentioning

confidence: 99%

Section: µE Elastic Scatteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Interplay of colour kinematics duality and analytic calculation of multi-loop scattering amplitudes: one and two loops

Bobadilla¹,

William²

2018

Proceedings of 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) —

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Causal representation of multi-loop Feynman integrands within the loop-tree duality

Aguilera-Verdugo

Hernández-Pinto

Rodrigo

et al. 2021

J. High Energ. Phys.

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145

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The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops and internal configurations, in terms of causal propagators only. Thus, providing very compact and causal integrand representations to all orders. In order to do so, we reconstruct their analytic expressions from numerical evaluation over finite fields. This procedure implicitly cancels out all unphysical singularities. We also interpret the result in terms of entangled causal thresholds. In view of the simple structure of the dual expressions, we integrate them numerically up to four loops in integer space-time dimensions, taking advantage of their smooth behaviour at integrand level.

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Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes

Garozzo

Queimada

Schlotterer

2019

J. High Energ. Phys.

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We construct new representations of tree-level amplitudes in D-dimensional gauge theories with deformations via higher-mass-dimension operators α F 3 and α 2 F 4 . Based on Berends-Giele recursions, the tensor structure of these amplitudes is compactly organized via off-shell currents. On the one hand, we present manifestly cyclic representations, where the complexity of the currents is systematically reduced. On the other hand, the duality between color and kinematics due to Bern, Carrasco and Johansson is manifested by means of non-linear gauge transformations of the currents. We exploit the resulting notion of Bern-Carrasco-Johansson gauge to provide explicit and manifestly local double-copy representations for gravitational amplitudes involving α R 2 and α 2 R 3 operators. arXiv:1809.08103v1 [hep-th] 21 Sep 2018 45 A.3 Gauge algebra 47 B The explicit form of gauge scalars towards BCJ gauge 50 B.1 The local building block h 12345 50 B.2 An alternative expression for H 1234 51 B.3 The Berends-Giele version H 12345 52 C Deriving a BCJ representation for (YM+F 3 +F 4 ) amplitudes 52 -1 -1 The low-energy effective action of the open bosonic string involves another operator ∼ ζ2α 2 F 4 at the mass dimensions in (1.1) which will not be discussed in this article. Said ζ2α 2 F 4 -operator is also known from the superstring and cannot be reconciled with the BCJ duality [18]. 2 See [ 23,24] for earlier work on the interplay of the KLT relations at the three-and four-point level with gravitational matrix elements of R 2 , R 3 operators and F 3 , F 4 -deformed gauge-theory amplitudes.3 In slight abuse of terminology, we will usually refer to the matrix elements from higher-mass-dimension operators as "amplitudes". In the case at hand, we will be interested in contributions from single-or doubleinsertions of α R 2 operators and single-insertions of α 2 R 3 4 See [27,28] for generating series of Berends-Giele currents, their non-linear gauge transformations and BCJ gauge in ten-dimensional SYM.5 Said higher-derivative extension of the NLSM is defined by the ζ2α 2 -order of abelian Z-theory [44].

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From Jacobi off-shell currents to integral relations

Cited by 38 publications

References 53 publications

Interplay of colour kinematics duality and analytic calculation of multi-loop scattering amplitudes: one and two loops

Interplay of colour kinematics duality and analytic calculation of multi-loop scattering amplitudes: one and two loops

Causal representation of multi-loop Feynman integrands within the loop-tree duality

Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes

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