The Calculation Of Multi Massless Partons Interactional Amplitudes In Tree Diagrams

The standard model(SM) has been presented for a long time. There are many experiments supporting the SM even in high precision, since this beautiful theory was born. However, SM has many big problems. First, it contains too many parameters, which can not be got naturally. Second, this theory has triviality in the potential in high energy. Third, this theory has unnaturalness. Moreover, the expected fundamental particle Higgs have not been found in experiments. So many people doubt whether the SM is the fundamental theory, and there is a common idea that SM is not the final theory but a transitional theory. So people have presented many models, such as: superstring, supersymmetry, extra-dimension and so on. However, people won't accept a theory if there aren't many experiments supporting it. As a result, to search for new physics has been an interesting and important work. But many experiments involve multi-partons processes, which is difficult and complex to calculate by the large number of Feynman diagrams which appear in the perturbative expansion.Significant simplification in these calculation have been achieved in last ten years due to the use of the new simple representations for vector polarizations, a better organization of the diagrammatic expansion which is fully exploits the properties of gauge invariance. However, this method is still complex when the number of external particles becomes larger except for some special conditions.Another great progress[1] has been achieved in more recent years. They develop an alternative to usual Feynman graphs, tree amplitudes in Yang-Mills theory can be constructed from tree graphs in which the vertices are tree level maximal helicity violating (MHV) scattering amplitudes, continued off shell in a particular fashion. In the last years, a new recursion relation has been presented by Ruth Britto, Freddy Cachazo, Bo Feng, their new recursion relations for tree amplitudes in gauge theory give very compact formulas , whose relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a Feynman propagator. The two amplitudes in each term are physical in the sense that all particles are on shell and momentum conservation is preserved. In this article, I will calculate some amplitudes in detail by using their new recursion relations, and will give a simple example(six-gluons) to show that it satisfy the relation of sub-amplitude which...