Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders

Aguilera-Verdugo, J. J.; Driencourt-Mangin, Félix; Plenter, Judith; Ramírez-Uribe, Selomit; Rodrigo, Germán; Sborlini, Germán F. R.; Bobadilla, William J. Torres; Tracz, Szymon

doi:10.48550/arxiv.1904.08389

Cited by 6 publications

(14 citation statements)

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“…4. We summarize the conclusions of a very recent paper [3], emphasizing the advantages of the LTD approach to deal with generic multi-loop multi-leg processes. Finally, we present the conclusions and future research directions in Sec.…”

Section: Introductionmentioning

confidence: 86%

“…In consequence, a natural four-dimensional representation of any IR-safe physical observables emerges from our formalism. Also, we have recently exploted our method to describe the origin of causal and anomalous thresholds, at one-loop level and beyond [3]. We demonstrated that the dual prescription is crucial to achieve a proper cancellation of unphysical and spurious singularities.…”

Section: Outlook and Conclusionmentioning

confidence: 99%

“…So, let us apply this to analyze the singular behaviour of one-loop amplitudes; a complete study at two-loops and beyond is presented in Ref. [3].…”

Section: Thresholds and Unphysical Singularitiesmentioning

confidence: 99%

“…For more details about anomalous thresholds within the LTD approach at one-loop and beyond, we refer the reader to Ref. [3].…”

Section: Anomalous Thresholdsmentioning

confidence: 99%

“…with k ji a combination of momenta [3]. Since the denominators of different dual propagators consist in products of different λ ±± i j , the limits λ ±± i j → 0 indicate the location of the singular points of the integrands.…”

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confidence: 99%

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Analysis of singularities and the four-dimensional representation of physical observables within the LTD formalism

Sborlini¹

2019

Preprint

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In the past years, we have been developing a novel technique, called Four-Dimensional Unsubtraction (FDU) which aims to obtain purely four-dimensional representations of the matrix elements contributing to physical observables. In this talk, we describe the application of the loop-tree duality (LTD) theorem to represent loop amplitudes in terms of tree-level like objects, focusing on the origin of possible singularities of scattering amplitudes. In particular, we analyze the regions responsible of infrared and threshold singularities. With this information, we aim to extend the FDU formalism to NNLO and beyond.

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Section: Introductionmentioning

confidence: 86%

Section: Outlook and Conclusionmentioning

confidence: 99%

“…So, let us apply this to analyze the singular behaviour of one-loop amplitudes; a complete study at two-loops and beyond is presented in Ref. [3].…”

Section: Thresholds and Unphysical Singularitiesmentioning

confidence: 99%

“…For more details about anomalous thresholds within the LTD approach at one-loop and beyond, we refer the reader to Ref. [3].…”

Section: Anomalous Thresholdsmentioning

confidence: 99%

mentioning

confidence: 99%

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Analysis of singularities and the four-dimensional representation of physical observables within the LTD formalism

Sborlini¹

2019

Preprint

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The infrared structure of perturbative gauge theories

et al. 2023

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Loop-Tree Duality for Multiloop Numerical Integration

et al. 2019

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Loop Tree Duality (LTD) offers a promising avenue to numerically integrate multi-loop integrals directly in momentum space. It is well-established at one loop, but there have been only sparse numerical results at two loops. We provide a formal derivation for a novel multi-loop LTD expression and study its threshold singularity structure. We apply our findings numerically to a diverse set of up to four-loop finite topologies with kinematics for which no contour deformation is needed. We also lay down the ground work for constructing such a deformation. Our results serve as an important stepping stone towards a generalised and efficient numerical implementation of LTD, applicable to the computation of virtual corrections.

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Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders

Cited by 6 publications

References 0 publications

Analysis of singularities and the four-dimensional representation of physical observables within the LTD formalism

Analysis of singularities and the four-dimensional representation of physical observables within the LTD formalism

The infrared structure of perturbative gauge theories

Loop-Tree Duality for Multiloop Numerical Integration

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