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In this paper, by treating massive loop momenta as massless momenta in higher dimensions, we are able to treat all-loop scattering equations as tree ones. As an application of the new perspective, we consider the CHY-construction of bi-adjoint ϕ 3 theory. We present the explicit formula for two-loop planar integrands. We discuss in details how to subtract various forward singularities in the construction. We count the number of terms obtained by our formula and by direct Feynman diagram calculation and find the perfect match, thus provide a strong support for our results.
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Bo Feng (2016) studied this question.
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