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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Cited by in corpus (6)

• Integrands of loop amplitudes within loop-tree duality
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• One-loop diagrams with quadratic propagators from the worldsheet
• A scattering amplitudes approach to hard thermal loops
• On-shell recursion relations for generic integrands