Counting the number of master integrals for sunrise-type Feynman diagrams via Mellin-Barnes representation

Abstract

A number of irreducible master integrals for L-loop sunrise-type and bubble Feynman diagrams with generic values of masses and external momenta are explicitly evaluated via Mellin-Barnes representation.

28 pages, 3 figures, ver2. some typos corrected and a few references added; ver3.has some relatively minor corrections; accepted for publication in JHEP

References in corpus (10)

• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• Elliptic integral evaluations of Bessel moments
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
• Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Hypergeometric representation of the two-loop equal mass sunrise diagram
• Counting master integrals: integration by parts vs. differential reduction
• Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation

Cited by in corpus (18)

• Collider Physics at the Precision Frontier
• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• Analytic Structure of all Loop Banana Amplitudes
• Feynman integral relations from parametric annihilators
• Maximal Cuts in Arbitrary Dimension
• Feynman integrals as A-hypergeometric functions
• Landau Discriminants
• Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow
• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• Principal Landau Determinants
• Bananas: multi-edge graphs and their Feynman integrals
• Differential equations, recurrence relations, and quadratic constraints for $L$-loop two-point massive tadpoles and propagators
• GKZ-system of the 2-loop self energy with 4 propagators
• Feynman Integrals of Grassmannians
• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
• The four-propagator three-loop vacuum integral by the hypergeometry
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals
• The number of master integrals as Euler characteristic