Abstract
We revisit the familiar construction of one-loop scattering amplitudes via generalized unitarity in light of the recently understood properties of loop integrands prior to their integration. We show how in any four-dimensional quantum field theory, the integrand -level factorization of infrared divergences leads to twice as many constraints on integral coefficients than are visible from the integrated expressions. In the case of planar, maximally supersymmetric Yang-Mills amplitudes, we demonstrate that these constraints are both sufficient and necessary to imply the finiteness and dual-conformal invariance of the ratios of scattering amplitudes. We present a novel regularization of the scalar box integrals which makes dual-conformal invariance of finite observables manifest term by term, and describe how this procedure can be generalized to higher loop-orders. Finally, we describe how the familiar scalar boxes at one-loop can be upgraded to ‘chiral boxes’ resulting in a manifestly infrared-factorized, box-like expansion for all one-loop integrands in planar, \( \mathcal{N}=4 \) super Yang-Mills. Accompanying this note is a Mathematica pack-age which implements our results, and allows for the efficient numerical evaluation of any one-loop amplitude or ratio function.
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Bourjaily, J., Caron-Huot, S. & Trnka, J. Dual-conformal regularization of infrared loop divergences and the chiral box expansion. J. High Energ. Phys. 2015, 1 (2015). https://doi.org/10.1007/JHEP01(2015)001
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DOI: https://doi.org/10.1007/JHEP01(2015)001