Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 306 / 3 / c / Solution

Fix $z_1=0$, $z_2=1$, and $z_4=\infty$, and write $z_3=z$. Its scattering equation isso in the hard limitEvaluating the Koba-Nielsen factor at this saddle and using $s+t+u=O(m_{\mathrm{tachyon}}^2)$ yields, with the logarithms defined by analytic continuation,The omitted terms grow more slowly than the displayed fixed-angle $s\log s$ terms.