Note on recursion relations for the $\mathcal{Q}$-cut representation

Abstract

In this note, we study the $\mathcal{Q}$-cut representation by combining it with BCFW deformation. As a consequence, the one-loop integrand is expressed in terms of a recursion relation, i.e., $n$-point one-loop integrand is constructed using tree-level amplitudes and $m$-point one-loop integrands with $m\le n-1$. By giving explicit examples, we show that the integrand from the recursion relation is equivalent to that from Feynman diagrams or the original $\mathcal{Q}$-cut construction, up to scale free terms.

30 pages, 2 figures

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• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• Loops and trees
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Cited by in corpus (2)

• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• On-shell recursion relations for generic integrands