2017/09/30 by Roman N. Lee, Alexander V. Smirnov, Vladimir A. Smirnov · 3 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Differential equation #Dimensional regularization #Feynman diagram #Feynman integral #Integral equation #Mathematical analysis #Mathematical physics #Mathematics #Order of integration (calculus) #Particle physics theoretical and experimental studies #Regularization (linguistics) #Singular integral #Variable (mathematics) #Zero (linguistics) #hep-ph
paper · pdf · doi:10.1007/jhep03(2018)008
References added, functionality of the presented code extended
openalex created_date 2017/10/06 · arxiv created 2017/11/14 · openalex publication_date 2018/03/01 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
A bstract We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ϵ.