A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques

Abstract

We use configuration space methods to write down one-dimensional integral representations for one- and two-loop sunrise diagrams (also called Bessel moments) which we use to numerically check on the correctness of the second order differential equations for one- and two-loop sunrise diagrams that have recently been discussed in the literature.

11 pages, no figures, published version

References in corpus (12)

• Differential Equations for Feynman Graph Amplitudes
• Analytic treatment of the two loop equal mass sunrise graph
• Elliptic integral evaluations of Bessel moments
• The Master Differential Equations for the 2-loop Sunrise Selfmass Amplitudes
• On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order
• On the evaluation of sunset-type Feynman diagrams
• Threshold expansion of the sunset diagram
• Threshold expansion of Feynman diagrams within a configuration space technique
• A new technique for computing the spectral density of sunset-type diagrams: integral transformation in configuration space
• Elliptic integral evaluation of a Bessel moment by contour integration of a lattice Green function
• Laurent series expansion of sunrise-type diagrams using configuration space techniques
• Relativistic phase space: dimensional recurrences

Cited by in corpus (26)

• The elliptic dilogarithm for the sunset graph
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• The kite integral to all orders in terms of elliptic polylogarithms
• The $\epsilon$-form of the differential equations for Feynman integrals in the elliptic case
• A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries
• The two-loop sunrise graph with arbitrary masses
• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
• Analytic results for the planar double box integral relevant to top-pair production with a closed top loop
• The unequal mass sunrise integral expressed through iterated integrals on ${\overline{\mathcal{M}}}_{1,3}$
• The iterated structure of the all-order result for the two-loop sunrise integral
• Analytic continuation and numerical evaluation of the kite integral and the equal mass sunrise integral
• On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
• The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case
• $\epsilon$-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
• Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities
• Cuts and Isogenies
• An Analytic Approach to Sunset Diagrams in Chiral Perturbation Theory: Theory and Practice
• Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves
• The sunrise integral and elliptic polylogarithms
• The analytic leading color contribution to the Higgs-gluon form factor in QCD at NNLO
• A walk on sunset boulevard
• Discontinuities of banana integrals in dispersion relation representation
• Generalizations of polylogarithms for Feynman integrals
• Differential equations for Feynman integrals beyond multiple polylogarithms
• Position-space representation of charged particles' propagators in a constant magnetic field as an expansion over Landau levels