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I will try to avoid too many details. In case you want to learn more about these things I could suggest this reference: http://arxiv.org/pdf/1308.1697.pdf and from it you can find more references. First of all, the Parke-Taylor formulas is about the so called MHV (Maximal Helicity Violating) Amplitudes and with the use of the spinor-helicity formalism they ...

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