One-loop CHY-integrand of bi-adjoint scalar theory

In this paper, the one-loop CHY-integrands of bi-adjoint scalar theory has been reinvestigated. Differing from previous constructions, we have explicitly removed contributions from tadpole and massless bubbles when taking the forward limit of corresponding tree-level amplitudes. The way to remove those singular contributions is to exploit the idea of “picking poles”, which is to multiply a special cross ratio factor with the role of isolating terms having a particular pole structure.