TVID: Three-loop Vacuum Integrals from Dispersion relations

Abstract

TVID is a program for the numerical evaluation of general three-loop vacuum integrals with arbitrary masses. It consists of two parts. An algebraic module, implemented in Mathematica, performs the separation of the divergent pieces of the master integrals and identifies special cases. The numerical module, implemented in C, carries out the numerical integration of the finite pieces. In this note, the structure of the program is explained and a few usage examples are given.

TVID is based on the formalism described in arXiv:1609.09159

References in corpus (4)

• HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables
• HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4
• Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
• Evaluation of the general 3-loop vacuum Feynman integral

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• Comparison of the EFT Hybrid and Three-Loop Fixed-Order Calculations of the Lightest MSSM Higgs Boson Mass
• Matching relations for decoupling in the Standard Model at two loops and beyond
• The vacuum seagull: evaluating a 3-loop Feynman diagram with 3 mass scales
• Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
• Three-loop effective potential of general scalar theory via differential equations
• Multi-loop calculations: numerical methods and applications