One-Loop Gluonic Amplitudes from Single Unitarity Cuts

Abstract

We show that one-loop amplitudes in massless gauge theories can be determined from single cuts. By cutting a single propagator and putting it on-shell, the integrand of an n-point one-loop integral is transformed into an (n+2)-particle tree level amplitude. The single-cut approach described here is complementary to the double or multiple unitarity cut approaches commonly used in the literature. In common with these approaches, if the cut is taken in four dimensions, one finds only the cut-constructible parts of the amplitude, while if the cut is in D=4-2 epsilon dimensions, both rational and cut-constructible parts are obtained. We test our method by reproducing the known results for the fully rational all-plus and mostly-plus QCD amplitudes A^{(1)}_4(1^+,2^+,3^+,4^+) and A^{(1)}_5(1^+,2^+,3^+,4^+,5^+). We also rederive expressions for the scalar loop contribution to the four-gluon MHV amplitude, A_4^{(1,N=0)}(-,-,+,+) which has both cut-constructible and rational contributions, and the fully cut-constructible n-gluon MHV amplitude in N=4 Supersymetric Yang-Mills, A_4^{(1,N=4)}(-,-,+,...,+).

31 pages, JHEP3 class, 10 figures

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• Loops and trees
• New Representations of the Perturbative S-Matrix
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• On BCFW shifts of integrands and integrals
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• One-loop monodromy relations on single cuts
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• The Q-cut Representation of One-loop Integrands and Unitarity Cut Method
• One-Loop Yang-Mills Integrands from Scattering Equations
• Integrands for QCD rational terms and N=4 SYM from massive CSW rules
• Feynman Rules for the Rational Part of One-loop QCD Corrections in the MSSM
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Obtaining One-loop Gravity Amplitudes Using Spurious Singularities
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• Integrands of Less-Supersymmetric Yang-Mills at One Loop