Physics Asked on June 1, 2021
In Matthew Schwartz Quantum Field Theory and Standard Model the author presents the Parke-Taylor formula
$tilde{M}(1^+2^+…j^-…k^-…n^+) = frac{langle j k rangle^4}{langle 1 2 rangle langle 2 3 rangle langle 3 4 rangle … langle n 1 rangle}$
(Chapter 27 Gluon scattering and the spinor-helicity formalism, page.550) to calculate MHW amplitudes for $n$-gluon amplitudes. Moreover the reader can find an explicit example of this formula on page 558
$tilde{M}(1^-2^-3^+4^+5^+6^+7^+) = frac{langle 1 2 rangle^4}{langle 7 1 rangle langle 1 2 rangle langle 2 3 rangle langle 3 4 rangle langle 4 5 rangle langle 5 6 rangle langle 6 7 rangle }$
So far so good. But one thing makes me wonder: How can I see which gluons are incoming and which ones are outgoing? Is there some "convention" that I am missig, e.g. all particles with one helicity are incoming and the rest of the particles with the other helicity are outgoing? Otherwise I simply do not understand, whether $tilde{M}(1^-2^-3^+4^+5^+6^+7^+)$ refers to $tilde{M}(1^- + 2^- rightarrow 3^+ + 4^+ + 5^+ + 6^+ + 7^+)$, $tilde{M}(1^- + 2^- + 3^+ rightarrow 4^+ + 5^+ + 6^+ + 7^+)$ or $tilde{M}(1^- + 2^- + 3^+ + 4^+ rightarrow 5^+ + 6^+ + 7^+)$ and so on.
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