ar X iv : h ep - p h / 98 02 24 3 v 1 4 F eb 1 99 8 Automation of Feynman diagram evaluation

A C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented. Recent high precision experiments require, on the side of the theory, high-precision calculations resulting in the evaluation of higher loop diagrams in the Standart 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. For example, FEYNARTS / FEYNCALC [1] 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 [2], and a package [3] for the calculation of 3-loop bubble integrals with one non-zero mass. Other packages for automation are GRACE [4] and COMHPEP [5], which partially perform full calculations, from the process definition to the cross-section values. A somewhat different approach is persued by XLOOPS [6]. 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 neccessary to use special techniques like databases and special controlling programs. In [7] 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. It seems impossible to develop an universal package, which will be effective 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 first step is dedicated to the automation of the muons two-loop anomalous magnetic moment (AMM) 1 2 (g − 2) µ. For this purpose the package TLAMM was developed [8]. The algorithm is implemented as a FORM-based program package. For generating and automatically evaluating any number of two-loop self-energy diagrams, a special C-program has been written. This program creates the initial FORM-expression for every diagram generated by QGRAF [10], executes the corresponding subroutines and sums up the various contributions. In the SM …