A Stroll through the Loop-Tree Duality

Aguilera-Verdugo, José de Jesús; Driencourt-Mangin, Félix; Hernández-Pinto, Roger J.; Plenter, Judith; Prisco, Renato Maria; Ramírez-Uribe, Selomit; Rentería-Olivo, Andrés E.; Rodrigo, Germán; Sborlini, Germán F. R.; Bobadilla, William J. Torres; Tramontano, Francesco

doi:10.3390/sym13061029

Cited by 24 publications

(14 citation statements)

References 114 publications

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“…The purpose of this review is to explain novel technologies pointing towards a more efficient calculation of the loop contributions. In particular, these developments are done in the context of the Loop-Tree Duality (LTD) formalism [15][16][17][18][19]. The main advantage of this formalism is that Feynman loop integrals in Minkowski space are transformed into sums of phase-space integrals of tree-level like objects, i.e.…”

Section: Introductionmentioning

confidence: 99%

Geometry and causal flux in multi-loop Feynman diagrams

Sborlini

2022

Supl. Rev. Mex. Fis.

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In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand level representation of scattering amplitudes which only contains physical singularities. These so-called causal representations can be derived from connected binary partitions of Feynman diagrams, properly entangled according to specific rules. We will focus on the detection of flux orientations which are compatible with causality, describing the implementation of a quantum algorithm to identify such configurations.

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Section: Introductionmentioning

confidence: 99%

Geometry and causal flux in multi-loop Feynman diagrams

Sborlini

2022

Supl. Rev. Mex. Fis.

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“…With the purpose of simplifying the numerical implementation, we have been developing a strategy that aims to achieve the cancellation of singularities before integration: this is the so-called local cancellation. This approach is based on the Loop-Tree Duality (LTD) [7][8][9][10][11][12][13] to re-write the loop amplitudes as dual contributions defined in an Euclidean space. In this way, after introducing proper mappings, it is possible to relate the kinematics of the real and dual components, leading to a unified description and a natural integrand-level cancellation of IR singularities [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Geometry and causality for efficient multiloop representations

Sborlini

2022

SciPost Phys. Proc.

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Multi-loop scattering amplitudes constitute a serious bottleneck in current high-energy physics computations. Obtaining new integrand level representations with smooth behaviour is crucial for solving this issue, and surpassing the precision frontier. In this talk, we describe a new technology to rewrite multi-loop Feynman integrands in such a way that non-physical singularities are avoided. The method is inspired by the Loop-Tree Duality (LTD) theorem, and uses geometrical concepts to derive the causal structure of any multi-loop multi-leg scattering amplitude. This representation makes the integrand much more stable, allowing faster numerical simulations, and opens the path for novel re-interpretations of higher-order corrections in QFT.

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“…This methodology has been deeply studied [32][33][34][35][36][37] and many applications have been developed [38][39][40][41][42][43][44][45][46][47]. In recent years the LTD has evolved in a significant way [48][49][50][51][52][53][54][55][56][57]. This progress was based on its most remarkable property, the existence of a manifestly causal representation, which was conjectured for the first time in Ref.…”

Section: Introductionmentioning

confidence: 99%