Gomez, Humberto2019-07-032019-07-032016-06-0111266708https://repositorio.usc.edu.co/handle/20.500.12421/257Abstract: The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm. © 2016, The Author(s).enDifferential and Algebraic GeometryField Theories in Higher DimensionsScattering AmplitudesSuperstrings and Heterotic StringsArticle