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Recently it has been shown that in gauge theories amplitudes to anyperturbation order can be obtained by glueing together simple three-pointon-shell amplitudes. These three-point amplitudes in turn are fixed by localityand Lorentz invariance. This factorization into three-point on-shell amplitudesfollows from the BCFW recursion relations and the Feynman-tree theorem. In anexplicit example, that is, the four-gluon amplitude with all plus helicities,we illustrate the method. In conventional calculation this amplitudecorresponds to one-loop box diagrams.

Application of BCFW-recursion relations and the Feynman-tree theorem to the four gluon amplitude with all plus helicities