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General structure

The CompHEP  symbolic output can be used for further manipulation with an answer which has been obtained by means of the built-in symbolic calculator. It might be a summation of all diagrams to a common denominator expression, a symbolic integration of answer, a representation of answer as a function of special set of variables and so on. We have tried to present results in the form which can be easily used for different purposes.

All diagram contributions for one subprocess are stored in one file. The subprocess ordering number is attached to the file name. For example, the symb1.red and symb1.m files are generated to present the symbolic answer of the first subprocess in the Reduce  [Hearn&Fitch] and Mathematica  [Wolfram] format correspondingly.

The structure of the output file can be described by the following scheme:

Initial declarations;

$initSum()$;

Answer for the first diagram;

$addToSum()$;

Answer for the second diagram;

$addToSum()$;

    ...................

    ...................

$finishSum()$;

'Initial declarations' includes the declaration of vector variables for momenta and the conservation law relations for them, the declaration of independent parameters involved in calculation and numerical values of them, the declaration of constrained parameters and substitution rules for them, and, at last, the declaration of the process name. The momenta are named $p1,p2,p3,...$. They are assigned to particles according to a particle sequence in the process name. The signs of momenta are defined in such a way that the sum of momenta of incoming particles is equal to the sum of momenta of outgoing particles. The list of substitutions of numerical values for independent parameters is written down in variable $parameters$. The list of substitutions for the constrained parameters is stored in variable $substitutions$. The lists of incoming and outgoing particles are stored in variables $inParticles$ and $outParticles$ respectively.

CompHEP  writes down subsequently expressions for diagram contributions and after any record it calls a summation procedure $addToSum()$. Just before and after summation the procedures $initSum()$ and $finishSum()$ are called. These three procedures must be written by the user and loaded in advance. Such a construction of the output allows one to use it for different purposes creating appropriate procedures.

Now we shall explain the structure of diagram contribution. It is started from a pseudo-graphic diagram image like in Fig.. After that assignments for $totFactor$, $numerator$, $denominator$ variables follow:

$totFactor$ is a ration function depending on model parameters;

$numerator$ is a polynomial of model parameters and momenta scalar products;

$denominator$ is presented as a product of propagator denominators

$$propDen(P,Mass,Width)\;,$$

where $P$, $Mass$, and $Width$ are the momentum, mass, and width of the corresponding virtual particle. In the case $Width=0$ $propDen$ must be defined as $(Mass^2-P^2)$. The treatment of the $Width$ argument can be arranged by the user as he likes.

In these terms the diagram contribution to the squared matrix element may be expressed in the following way:

$$totFactor \frac{numerator}{denominator}\;\;.$$

As it was mentioned above (Section ) the result obtained by summation of all diagrams must be symmetrized in the case of identical outgoing particles. This work may be done by the $finishSum()$ procedure.