Three-loop planar master integrals for heavy-to-light form factors

Chen, Long-Bin; Wang, Jian

doi:10.1016/j.physletb.2018.10.035

Cited by 7 publications

(2 citation statements)

References 81 publications

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“…These corrections can be usually expressed in terms of generalized polylogarithms (GPLs) [28][29][30][31]. While sometimes higher-order massive corrections can also be expressed in terms of GPLs [32][33][34][35][36], they reveal in general a more complicated structure. This is for instance the case of the two MIs of the equal-mass two-loop sunrise.…”

Section: Introductionmentioning

confidence: 99%

A numerical routine for the crossed vertex diagram with a massive-particle loop

Bonciani

Degrassi

Giardino

et al. 2019

Computer Physics Communications

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We present an evaluation of the two master integrals for the crossed vertex diagram with a closed loop of top quarks that allows for an easy numerical implementation. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular points. The different series are then matched numerically with high accuracy in intermediate points. The expansions allow a fast and precise numerical calculation of the two master integrals in all the regions of the phase space. A numerical routine that implements these expansions is presented.

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Section: Introductionmentioning

confidence: 99%

A numerical routine for the crossed vertex diagram with a massive-particle loop

Bonciani

Degrassi

Giardino

et al. 2019

Computer Physics Communications

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“…However, the master integrals can be shown to satisfy differential equations [21][22][23], which after the reduction to a canonical form [24,25], can be in some cases solved, iteratively. Although various results have been obtained in presence of the massive particles [26][27][28][29][30][31][32][33][34], the final results are often represented as (iterated) integrals whose integrands consist of polylogarithms and other irrational functions, which still require numerical integration.…”

Section: Introductionmentioning

confidence: 99%

Evaluating multi-loop Feynman integrals numerically through differential equations

Mandal

Zhao

2019

J. High Energ. Phys.

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The computation of Feynman integrals is often the bottleneck of multi-loop calculations. We propose and implement a new method to efficiently evaluate such integrals in the physical region through the numerical integration of a suitable set of differential equations, where the initial conditions are provided in the unphysical region via the sector decomposition method. We present numerical results for a set of two-loop integrals, where the non-planar ones complete the master integrals for gg → γγ and qq → γγ scattering mediated by the top quark.

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Identifying regions in wide-angle scattering via graph-theoretical approaches

2024

J. High Energ. Phys.

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The method of regions, which provides a systematic approach for computing Feynman integrals involving multiple kinematic scales, proposes that a Feynman integral can be approximated and even reproduced by summing over integrals expanded in certain regions. A modern perspective of the method of regions considers any given Feynman integral as a specific Newton polytope, defined as the convex hull of the points associated with Symanzik polynomials. The regions then correspond one-to-one with the lower facets of this polytope.As Symanzik polynomials correspond to the spanning trees and spanning 2-trees of the Feynman graph, a graph-theoretical study of these polynomials may allow us to identify the complete set of regions for a given expansion. In this work, our primary focus is on three specific expansions: the on-shell expansion of generic wide-angle scattering, the soft expansion of generic wide-angle scattering, and the mass expansion of heavy-to-light decay. For each of these expansions, we employ graph-theoretical approaches to derive the generic forms of the regions involved in the method of regions. The results, applicable to all orders, offer insights that can be leveraged to investigate various aspects of scattering amplitudes.

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Three-loop planar master integrals for heavy-to-light form factors

Cited by 7 publications

References 81 publications

A numerical routine for the crossed vertex diagram with a massive-particle loop

A numerical routine for the crossed vertex diagram with a massive-particle loop

Evaluating multi-loop Feynman integrals numerically through differential equations

Identifying regions in wide-angle scattering via graph-theoretical approaches

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