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

TL;DR

This paper explores the Q-cut representation for one-loop integrands in massless field theories, demonstrating its equivalence to traditional unitarity cut methods and detailing the computational technique.

Contribution

It introduces a detailed method for deriving one-loop integrands using the Q-cut representation, connecting it with established unitarity cut techniques.

Findings

Q-cut representation reproduces traditional unitarity cut integrands

Method includes summation over all Q-cuts and helicity states

Provides a cross-check for the new integrand construction

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.