ftint: Calculating gradient-flow integrals with pySecDec
Jul 23, 2024
30 pages
Published in:
- Comput.Phys.Commun. 306 (2025) 109384
- Published: Sep 20, 2024
e-Print:
- 2407.16529 [hep-ph]
DOI:
- 10.1016/j.cpc.2024.109384 (publication)
Report number:
- KA-TP-14-2024,
- TTK-24-28,
- P3H-24-050
View in:
Citations per year
Abstract: (Elsevier B.V.)
The program ftint is introduced which numerically evaluates dimensionally regularized integrals as they occur in the perturbative approach to the gradient-flow formalism in quantum field theory. It relies on sector decomposition in order to determine the coefficients of the individual orders in , where D is the space-time dimension. For that purpose, it implements an interface to the public library pySecDec. The current version works for massive and massless integrals up to three-loop level with vanishing external momenta, but the underlying method is extendable to more general cases. PROGRAM SUMMARY Program title:ftint CPC Library link to program files:https://doi.org/10.17632/bt6bkffxh9.1 Developer's repository link:https://gitlab.com/ftint/ftint Licensing provisions: MIT license Programming language:Python Supplementary material:README.md Nature of problem: The perturbative approach to the gradient-flow formalism in quantum field theory leads to integrals which closely resemble regular Feynman integrals. However, they involve exponential factors which depend on the loop and external momenta, as well as on so-called flow-time variables. In general, the latter are also integrated over a finite interval. These integrals cannot be solved immediately with standard tools. Solution method: The flow-time integrals are transformed to integrals over a hypercube by introducing Schwinger parameters. The latter are numerically evaluated using the public program pySecDec, which performs a sector decomposition and calculates the coefficients of the poles in the parameter by numerical integration, where D is the space-time dimension which occurs in dimensional regularization. Additional comments including restrictions and unusual features: In its current form, ftint is restricted to one-, two-, and three-loop integrals with vanishing external momenta. It does allow for massive propagators though, raised to virtually arbitrary integer powers.Note:
- 30 pages, 1 figure; v2: matches published version; the program ftint is available from https://gitlab.com/ftint/ftint
- Gradient flow
- Perturbation theory
- Feynman integrals
References(42)
Figures(3)
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