Λ scattering equations

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.