Topic
Loop integral
About: Loop integral is a research topic. Over the lifetime, 288 publications have been published within this topic receiving 16635 citations.
Papers published on a yearly basis
Papers
TL;DR: Algorithms for the construction of the systems using integration-by-parts identities and methods of solutions by means of expansions in factorial series and Laplace transformation and procedures for generating and solving systems of differential equations in masses and momenta for master integrals are shown.
Abstract: We describe a new method of calculation of generic multiloop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using integration-by-parts identities and methods of solutions by means of expansions in factorial series and Laplace transformation. We also describe new algorithms for the identification of master integrals and the reduction of generic Feynman integrals to master integrals, and procedures for generating and solving systems of differential equations in masses and momenta for master integrals. We apply our method to the calculation of the master integrals of massive vacuum and self-energy diagrams up to three loops and of massive vertex and box diagrams up to two loops. Implementation in a computer program of our approach is described. Important features of the implementation are: the ability to deal with hundreds of master integrals and the ability to obtain very high precision results expanded at will in the number of dimensions.
1,276 citations
TL;DR: It is argued that a good choice of basis for (multi)loop integrals can lead to significant simplifications of the differential equations, and criteria for finding an optimal basis are proposed.
Abstract: Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi)loop integrals can lead to significant simplifications of the differential equations, and propose criteria for finding an optimal basis. This builds on experience obtained in supersymmetric field theories that can be applied successfully to generic quantum field theory integrals. It involves studying leading singularities and explicit integral representations. When the differential equations are cast into canonical form, their solution becomes elementary. The class of functions involved is easily identified, and the solution can be written down to any desired order in ϵ within dimensional regularization. Results obtained in this way are particularly simple and compact. In this Letter, we outline the general ideas of the method and apply them to a two-loop example.
1,223 citations
TL;DR: In this article, the authors presented a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory, and proved that their N = 4 ansatz is correct.
1,222 citations
TL;DR: In this article, the authors show how the use of tools already employed in inclusive calculations can be suitably extended to the computation of loop integrals appearing in the virtual corrections to exclusive observables, namely two-loop four-point functions with massless propagators and up to one off-shell leg.
1,204 citations
TL;DR: In this paper, a new method of massive Feynman diagram calculation is presented, which provides a fairly simple procedure for obtaining the result without D -space integrals for dimensional regularization.
1,181 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 9 |
| 2019 | 27 |
| 2018 | 34 |
| 2017 | 24 |
| 2016 | 24 |