One-loop integrand from generalised scattering equations

Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured CPk-1, are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster algebras. Recently connections between one-loop integrands for bi-adjoint cubic scalar theory and Dn cluster polytope have been established. In this paper using the Gr (3, 6) cluster algebra, we relate the singularities of (3, 6) amplitude to four-point one-loop integrand in the bi-adjoint cubic scalar theory through the D4 cluster polytope. We also study factorisation properties of the (3, 6) amplitude at various boundaries in the worldsheet.