Analytic Tools for Feynman Integrals

By Vladimir A. Smirnov. 2013

328 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9640d2144371c0ce3830b0be4223125824f5bfdc

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Cuts of Feynman Integrals in Baikov representation (2017, methodology): “Many methods have been introduced in order to compute MI [37].”
Production of two Z-bosons in gluon fusion in the heavy top quark approximation (2015, methodology): “We compute these diagrams using asymptotic expansions in the inverse top quark mass [25].”
Ultraviolet properties of N=8 supergravity at five loops (2018, methodology): “At high-loop orders the primary method for reducing loop integrals to a basis relies on integration-by-parts (IBP) identities [35,36].”
Post-Minkowskian effective field theory for conservative binary dynamics (2020, methodology): “Therefore, the EFT formalism in the PM scheme provides an alternative systematic machinery to compute the PM conservative dynamics of binary systems, potentially reaching the same level of success as NRGR in the PN expansion — currently at N4LO (akin of 5PM accuracy) — using the existent technology ”
Feynman integrals and hyperlogarithms (2015, background): “Many different techniques have been developed to tackle such integrals and most of them are reviewed nicely in the book [163].”
Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order (2014, methodology): “We have computed the kernels K (2a) and K (2b) using the methods of asymptotic expansion [17] and in that way confirmed the results provided in Ref.”
FIRE5: A C++ implementation of Feynman Integral REduction (2014, methodology): “: yes Number of processors used: the program has been tested on computers with up to 32 cores, but it is not a requirement Supplementary material: The article, install instructions, http://science.sander.su Keywords: Feynman diagrams, Multiloop Feynman integrals, Dimensional regularization, Computer”
FIRE6: Feynman Integral REduction with modular arithmetic (2019, methodology): “A classical approach is to apply integration by parts (IBP) relations [1] (see Chapter 6 of [2] for a review) and reduce all integrals to a smaller set, the so-called master integrals.”
Virtual corrections to Higgs boson pair production in the large top quark mass limit (2014, methodology): “To cure these problems, the large-mass expansion procedure [19] is applied to Feynman diagrams that contribute to the full theory amplitude.”
The bulk dual of SYK: cubic couplings (2017, methodology): “For any fixed n,m, k, one can evaluate I (1) nmk and I (2) nmk using standard Mellin-Barnes techniques [28,29].”
Magnus and Dyson series for Master Integrals (2014, methodology): “[4, 5], is one of the most effective techniques for computing dimensionally regulated multi-loop integrals and has led to significant achievements in the context of multi-loop corrections.”