Solving recurrence relations for multi-loop Feynman integrals

DOI10.1016/J.NUCLPHYSB.2003.09.003zbMath1058.81606arXivhep-ph/0307088OpenAlexW2132801079MaRDI QIDQ1411196

Matthias Steinhauser, Vladimir A. Smirnov

Publication date: 26 October 2003

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-ph/0307088

zbMATH Keywords

parametric representationcoefficient functionslinear master-integral combination

Mathematics Subject Classification ID

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

Related Items (8)

INTEGRATION BY PARTS: AN INTRODUCTION ⋮ TWO-LOOP VACUUM DIAGRAMS IN BACKGROUND FIELD AND THE HEISENBERG–EULER EFFECTIVE ACTION ⋮ The one loop \( \overline{\text{MS}} \) static potential in the Gribov-Zwanziger lagrangian ⋮ Analytic computing methods for precision calculations in quantum field theory ⋮ Fermionic corrections to the three-loop matching coefficient of the non-relativistic vector current ⋮ Cuts of Feynman integrals in Baikov representation ⋮ Four loop massless propagators: an algebraic evaluation of all master integrals ⋮ Feynman integral relations from parametric annihilators

Cites Work

• Applied asymptotic expansions in momenta and masses
• Evaluating double and triple (?) boxes
• Three-loop vacuum integrals in FORM and REDUCE
• Five-loop vacuum polarization in pQCD: \(O(m_q^2 \alpha_s^4 n_f^2)\) contribution
• HIGH-PRECISION CALCULATION OF MULTILOOP FEYNMAN INTEGRALS BY DIFFERENCE EQUATIONS
• Equivalence of recurrence relations for Feynman integrals with the same total number of external and loop momenta.

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