In this note, we study the $\mathcal{Q}$-cut representation by combining itwith BCFW deformation. As a consequence, the one-loop integrand is expressed interms of a recursion relation, i.e., $n$-point one-loop integrand isconstructed using tree-level amplitudes and $m$-point one-loop integrands with$m\leq n-1$. By giving explicit examples, we show that the integrand from therecursion relation is equivalent to that from Feynman diagrams or the original$\mathcal{Q}$-cut construction, up to scale free terms.
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机译：在本说明中，我们通过结合BCFW变形来研究$ \ mathcal {Q} $-cut表示。结果，单回路被积是用递归关系表示的，即，使用树级幅度和$ m $点单回路被积以$ m \ leq n构造$ n $点单回路被积。 -1 $。通过给出明确的示例，我们证明了递归关系中的被积物等效于费曼图或原始的$ \ mathcal {Q} $-cut构造中的被积物，并且按比例缩放了自由项。
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