Off-shell CHY amplitudes and Feynman graphs

Abstract

A polynomial form is established for the off-shell CHY scattering equations proposed by Lam and Yao. Re-expressing this in terms of independent Mandelstam invariants provides a new expression for the polynomial scattering equations, immediately valid off shell, which makes it evident that they yield the off-shell amplitudes given by massless 𝜙3 Feynman graphs. A CHY expression for individual Feynman graphs, valid even off shell, is established through a recurrence relation.