DIANA

a program for automation of Feynman diagram evaluation

Last modified: Wednesday July 26 17:25:57 MET DST 2006

Aim

News

• http://www.physik.uni-bielefeld.de/~tentukov
• tentukov@physik.uni-bielefeld.de

Recent high precision experiments require, on the side of the theory, high-precision calculations resulting in the evaluation of higher loop diagrams in the Standard Model (SM). For specific processes thousands of multiloop Feynman diagrams do contribute, and it turns out to be impossible to perform these calculations by hand. This makes the request for automation a high-priority task.

Several different packages have been developed with different areas of applicability (see a good review by R.Harlander and M.Steinhauser). For example, FEYNARTS /FEYNCALC are MATHEMATICA packages convenient for various aspects of the calculation of radiative corrections in the SM. There are several FORM packages for evaluating multiloop diagrams, like MINCER, and a package by L.Avdeev for the calculation of 3-loop bubble integrals with one non-zero mass. Other packages for automation are GRACE and COMPHEP, which partially perform full calculations, from the process definition to the cross-section values.

A somewhat different approach is pursued by XLOOPS. A graphical user interface makes XLOOPS an `easy-to-handle' program package, but is mainly aimed to the evaluation of single diagrams. To deal with thousands of diagrams, it is necessary to use special techniques like databases and special controlling programs. In T.van Ritbergen et al., Int. J. Mod. Phys. C6 (1995) 513 for evaluating more than 11000 diagrams the special database-like program MINOS was developed. It calls the relevant FORM programs, waits until they finished, picks up their results and repeats the process without any human interference.

The package GEFICOM, developed for computation of higher order processes involving a large number of diagrams, is based on cooperative usage of several software tools such as Mathematica, FORM, Fortran, etc.

It seems impossible to develop an universal package, which will be efficient for all tasks. It appears absolutely necessary that various groups produce their own solutions of handling the problem of automation: various ways will be of different efficiency, have different domains of applicability, and last but not least, should eventually allow for completely independent checks of the final results. This point of view motivated us to seek our own way of automatic evaluation of Feynman diagrams.

Our aim is to create some universal software tool for piloting the process of generating the source code in multi-loop order for analytical or numerical evaluations and to keep the control of the process in general. Based on this instrument, we can attempt to build a complete package performing the computation of any given process in the framework of any concrete model.

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What does the program do?

For generating Feynmann diagrams we use a well-known program QGRAF. Its output consists of a list of diagrams, described in a combinatorial fashion.

The program consists of two parts:

• Analyzer of diagrams.
• Interpreter of a special text manipulating language (TM).

The TM language is very simple TeX-like language for creating source code.

Analyzer reads QGRAF output and passes necessary information to interpreter. For each diagram the interpreter performs the TM-program using data received from analyzer. Thus, the program:
Reads QGRAF output. For each diagram it:

1. Determines the topology.
2. Looking for it in the table of all known topologies and distributes momenta.
3. Creates an internal representation of diagram in terms of vertices and propagators.
4. Executes the TM-program to insert explicit expressions for the vertices, propagators etc. The TM-program produces input text for FORM ( or some other language), and executes the latter (optionally).

Using the TM language, advanced users can develop further extensions, e.g. including FORTRAN, to create a postscript file for the picture of the current diagram, etc.

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To translate the program you need one of the UNIX OS, the C compiler (preferably GNU C compiler), and 'make' utility.

The program and Makefile were tested on Linux (gcc), OSF1( both gcc and native digital cc), HP_UX (gcc) and SunOS (both gcc and native cc compilers).

To use Diana you need the package QGRAF.

To use Diana's autocreation facility you must have QGRAF version 2.0

To use graphics topology editor for Diana you need the X Window System and the Qt GUI Toolkit version 1.x (developed and tested on versions 1.43 and 1.44). The topology editor is written on C++, so you need some c++ compiler, preferably GNU g++ compiler.

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ATTENTION!
The sources were not updated for a long time.

Binary distribution for Linux Intel x86 is available now (statically linked executable ELF files, 1053827 bytes).

At present, we have no any installation tools, only Makefile and explanations in Readme and INSTALL files.

Here are several .tar.gz. archives:

• Full package contains the c-sources, makefiles, TM-resources, documentation and examples. The size of this file is about 400 Mb. This archive does not contain the topology editor.
• C-sources.
• TM-resources.
• Documentation. The documentation now is strongly under developing. Nevertheless, there are several drafts from which the attentive reader can get full information about the current Diana state:
  • diana.ps - the first draft of the manual. It is written in very poor English:(, and it is obsolete in many aspects.
  • diana2.ps - the brief summary of changing from the version 1 to the version 2.
• Examples.
• Sources of the topology editor.

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• hep-ph/9905560 M. Tentyukov, J. Fleischer. DIANA, a program for Feynman Diagram Evaluation talk given at 6th International Workshop on Software Engineering, Artificial Intelligence, Neural Nets, Genetic Algorithms, Symbolic Algebra, Automatic Calculation (AIHENP 99), Heraklion, Crete, Greece, 12-16 April, 1999
• hep-ph/9904258 M. Tentyukov, J. Fleischer. A Feynman Diagram Analyser DIANA
• hep-ph/9802243 M. Tentyukov, J. Fleischer. Automation of Feynman Diagram Evaluation Proceedings of XII International Workshop in Samara (Russia), 4 - 10 September 1997 (NPI MSU 99)
• hep-ph/9711437 J. Fleischer, M. Tentyukov, O.L. Veretin. Multi-Loop Calculations in the Standard Model: Techniques and applications Acta Phys.Polon. B28 (1997) 2333-2350.
• hep-ph/9904256 J. Fleischer, F. Jegerlehner, M. Tentyukov, O. Veretin. Non factorizable $O(\alpha\alpha_s)$ corrections to the process $Z\to b\bar{b}$ Phys.Lett. B459 (1999) 625-630.

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