QCDloop: A repository for one-loop scalar integrals

This is a repository of one-loop scalar Feynman integrals, evaluated close to four dimensions. For integrals with all massive internal lines the integrals are all known, both analytically and numerically. This website therefore concentrates on integrals with some internal masses vanishing; in general, these integrals contain infra-red and collinear singularities which are here regulated dimensionally. The integrals are described in a PDF file for every known integral. The general divergent box integral can be calculated using one of sixteen basis integrals which are given here. The general divergent triangle integral can be calculated using one of six triangle basis integrals which are also given here. The browser must be set to use hypertex-aware tool, such as Acrobat reader, and for best viewing, should open the pdf files in the browser. For general notation for the loop integrals click here

Box integrals definitions and generalities

Basis set of 16 divergent box integrals

Index of all box integrals currently in the repository

Triangle integrals

Basis set of 6 divergent triangle integrals

Finite triangle integrals

Bubble integrals

Bubble integrals with vanishing or degenerate masses

Tadpole integral

The results in this web-site are also available in the paper arXiv:0712.1851 by R.K. Ellis and G. Zanderighi
The corresponding gfortran/fortran77 code which calculates an arbitrary one-loop scalar integral, finite or divergent can be downloaded,
QCDLoop-1.98.tar.gz (version 1.981, date 2021-Apr-30). If you encounter any problems with the code, please notify the authors.

We gratefully acknowledge comments on previous versions of the code from
Stefano Actis, Andre van Hameren, Francesco Tramontano, Kirill Melnikov, Gudrun Heinrich, Jacek Holeczek, Adrian Signer, and Markus Schulze.

Other associated tools for one-loop diagrams:-
Looptools
the FF package by G.J. van Oldenborgh

R. Keith Ellis

Last modified: Thu Feb 25 17:43:23 GMT 2021