An algorithm to compute Born scattering amplitudes without Feynman graphs

In this paper we suggest an iterative algorithm to compute automatically the scattering matrix elements of any given effective lagrangian, Γ. By exploiting the relation between Γ and the connected Green function generator, Z, we provide a formula which does not require the use of the Feynman graphs and it is suitable to implement a numerical routine. By means of this algorithm we have built a relatively simple and fast fortran code which we have used to calculate, at the tree level, the rate of four fermion production at LEP II (finding a very good agreement with previous calculation) with and without the emission of one observable photon. OUTP 9528P SHEP 95-22 Introduction The computation of the matrix element of physical processes is often a difficult task. With the increasing collider energies the complexity of the required computations has grown considerably. When the number of final particles is high, even to evaluate the corresponding tree level Feynman diagrams becomes hard and the final formula is often an intricated function of several variables, inadequate for practical use. For this reason, many authors made a lot of work to simplify these calculations. Very good achievements have been obtained: the helicity amplitude technique [1] shows how to manipulate the Feynman rules to compute by hand some extremely difficult multi-particle processes which otherwise would be impossible to handle, color decomposition, recursion INFN Fellow European Community Fellow, CHRX-CT93-0132 contract, Human Capital and Mobility Program