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.