ANALYTICAL EXPRESSIONS OF THREE- AND FOUR-LOOP SUNRISE FEYNMAN INTEGRALS AND FOUR-DIMENSIONAL LATTICE INTEGRALS

DOI10.1142/S0217751X08042869zbMath1165.81350arXiv0803.1007OpenAlexW3103664216MaRDI QIDQ5322492

S. Laporta

Publication date: 21 July 2009

Published in: International Journal of Modern Physics A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.1007

zbMATH Keywords

Feynman diagramelliptic integrallattice Green functionWatson integralmaster integral

Mathematics Subject Classification ID

Feynman diagrams (81T18) Numerical integration (65D30)

Related Items (8)

\({\mathbb{Q}}\)-linear dependence of certain Bessel moments ⋮ Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space ⋮ Space-time dimensionality \(\mathcal D\) as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to \(\mathcal D\) ⋮ FEYNMAN GRAPH POLYNOMIALS ⋮ On Laporta's 4-loop sunrise formulae ⋮ Analytic structure of all loop banana integrals ⋮ ON BORWEIN’S CONJECTURES FOR PLANAR UNIFORM RANDOM WALKS ⋮ Moments in Pearson's four-step uniform random walk problem and other applications of very well-poised generalized hypergeometric series

Cites Work

• Analytic treatment of the two loop equal mass sunrise graph
• Lattice perturbation theory
• High-precision \(\epsilon\)-expansions of massive four-loop vacuum bubbles
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Elliptic integral evaluations of Bessel moments and applications
• HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS
• Singular behaviour of the lattice Green function for thed-dimensional hypercubic lattice
• HARMONIC POLYLOGARITHMS
• Lattice Green function (at 0) for the 4D hypercubic lattice
• Calculation of master integrals by difference equations

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