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

Mikhail Yu. Kalmykov, Bernd A. Kniehl

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.

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.

Paper Structure

This paper contains 11 sections, 79 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Mellin--Barnes integral versus Horn hypergeometric function
  3. What happens if the monodromy is reducible?
  4. $L$-loop sunrise diagram
  5. $L$-loop sunrise diagram with $R$ massive lines
  6. $L$-loop bubble diagram
  7. $L$-loop bubble diagram with $R$ massive lines
  8. Independent verification
  9. Conclusions
  10. $L$-loop V-type diagram
  11. Sunrise diagram and Bessel functions

Figures (3)

  • Figure 1: $L$-loop sunrise diagram.
  • Figure 2: $L$-loop bubble diagram.
  • Figure 3: $L$-loop V-type diagram.