Reduction of Feynman integrals in the parametric representation

Chen, Wen

doi:10.1007/jhep02(2020)115

Cited by 3 publications

(3 citation statements)

References 42 publications

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“…We note that the work presented in this paper is part of a recent revival of interest in the mathematical structure of Feynman integrals in parameter space, and presents interesting potential connections to several current research topics in this context. In particular, a study of IBP relations from the viewpoint of D-modules, starting from the Feynman parameter representation, was carried on in [33,34]; other relevant connections include the applications of intersection theory [36][37][38][39][40], the use of syzygy relations in reduction algorithms [41,42], the study of generalised hypergeometric systems [43], and the reduction of tensor integrals in parameter space [44][45][46]. More generally, for the first time in several decades we are witnessing a rapid growth of our understanding of the mathematical properties of Feynman integrals, in particular with regards to analyticity and monodromy (see, for example, [35,[47][48][49][50], and the lectures in ref.…”

Section: Jhep03(2024)096mentioning

confidence: 99%

Integration-by-parts identities and differential equations for parametrised Feynman integrals

Artico,

Magnea

2024

J. High Energ. Phys.

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Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. We provide a different viewpoint on these important tools by working in Feynman-parameter space, and using its projective geometry. Our work is based upon little-known results pre-dating the modern era of loop calculations [16–19, 30, 31]: we adapt and generalise these results, deriving a very general expression for sets of IBP identities in parameter space, associated with a generic Feynman diagram, and valid to any loop order, relying on the characterisation of Feynman-parameter integrands as projective forms. We validate our method by deriving and solving systems of differential equations for several simple diagrams at one and two loops, providing a unified perspective on a number of existing results.

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Section: Jhep03(2024)096mentioning

confidence: 99%

Integration-by-parts identities and differential equations for parametrised Feynman integrals

Artico,

Magnea

2024

J. High Energ. Phys.

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“…The calculations of the double-real-virtual and double-virtual-real correction is more complicated and the -expansion seems inevitable in order to carry out the loop integrals. Though challenging, recent developments for the computation of phase-space integrals with step functions [197][198][199][200] bring new opportunities to obtain the α 3 s order soft function analytically.…”

Section: 3mentioning

confidence: 99%

“…The problem of step functions in phase space integrals can be solved by using the method developed in refs. [197][198][199]. The idea is that a theta function has an integral representation similar to the alpha parametrization of a propagator.…”

Section: 3mentioning

confidence: 99%

The Path forward to N$^3$LO

Caola¹,

Chen²,

Duhr³

et al. 2022

Preprint

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The LHC experiments will achieve percent level precision measurements of processes key to some of the most pressing questions of contemporary particle physics: What is the nature of the Higgs boson? Can we successfully describe the interaction of fundamental particles at high energies? Is there physics beyond the Standard Model at the LHC? The capability to predict and describe such observables at next-to-nextto-next-to-leading order (N 3 LO) in QCD perturbation theory is paramount to fully exploit these experimental measurements. We describe the current status of N 3 LO predictions and highlight their importance in the upcoming precision phase of the LHC. Furthermore, we identify key conceptual and mathematical developments necessary to see wide-spread N 3 LO phenomenology come to fruition.

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Next-to-Next-to-Leading-Order QCD Corrections to Pion Electromagnetic Form Factors

Chen,

Feng

et al. 2024

Phys. Rev. Lett.

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We calculate the next-to-next-to-leading-order (NNLO) QCD radiative correction to the pion electromagnetic form factor with large momentum transfer. We explicitly verify the validity of the collinear factorization to two-loop order for this observable and obtain the respective IR-finite two-loop hard-scattering kernel in the closed form. The NNLO QCD correction turns out to be positive and significant. Incorporating this new ingredient of correction, we then make a comprehensive comparison between the finest theoretical predictions and numerous data for both space- and timelike pion form factors. Our phenomenological analysis provides a strong constraint on the second Gegenbauer moment of the pion light-cone distribution amplitude obtained from recent lattice QCD studies. Published by the American Physical Society 2024

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Reduction of Feynman integrals in the parametric representation

Cited by 3 publications

References 42 publications

Integration-by-parts identities and differential equations for parametrised Feynman integrals

Integration-by-parts identities and differential equations for parametrised Feynman integrals

The Path forward to N$^3$LO

Next-to-Next-to-Leading-Order QCD Corrections to Pion Electromagnetic Form Factors

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