An Algorithm to Compute Born Scattering Amplitudes without Feynman Graphs
F. Caravaglios, M. Moretti
TL;DR
By exploiting the relation between Γ and the connected Green function generator, Z, a formula is provided which does not require the use of the Feynman graphs and it is suitable to implement a numerical routine.
Abstract
In this paper we suggest an {\it 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 I\negthinspace{I} (finding a very good agreement with previous calculation) with and without the emission of one observable photon.