The Q-cut Representation of One-loop Integrands and Unitarity Cut Method

Abstract

Recently, a new construction for complete loop integrands of massless field theories has been proposed, with on-shell tree-level amplitudes delicately incorporated into its algorithm. This new approach reinterprets integrands in a novel form, namely the Q-cut representation. In this paper, by deriving one-loop integrands as examples, we elaborate in details the technique of this new representation, e.g., the summation over all possible Q-cuts as well as helicity states for the non-scalar internal particle in the loop. Moreover, we show that the integrand in the Q-cut representation naturally reduces to the integrand in the traditional unitarity cut method for each given cut channel, providing a cross-check for the new approach.

33 pages, 5 figures, 3 appendices

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Cited by in corpus (16)

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• Prescriptive Unitarity
• Gluons and gravitons at one loop from ambitwistor strings
• Elliptic scattering equations
• $\Lambda$ Scattering Equations
• 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 Yang-Mills Integrands from Scattering Equations
• A scattering amplitudes approach to hard thermal loops
• A differential operator for integrating one-loop scattering equations
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• On differential operators and unifying relations for $1$-loop Feynman integrands
• Note on recursion relations for the $\mathcal{Q}$-cut representation
• General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in Q-cut representaion