2
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.