One-Loop Yang-Mills Integrands from Scattering Equations

Abstract

We investigate in the context of the scattering equations, how one-loop linear propagator integrands in gauge theories can be linked to integrands with quadratic propagators using a double forward limit. We illustrate our procedure through examples and demonstrate how the different parts of the derived quadratic integrand are consistent with cut-integrands derived from four-dimensional generalized unitarity. We also comment on applications and discuss possible further generalizations.

arXiv comment20 pages, 6 figures, typos corrected, added clarifications and comments. Version to be published in PRD

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• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• One-loop diagrams with quadratic propagators from the worldsheet
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Note on solutions of scattering equations
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands