Abstract
We show that the half-integrands in the CHY representation of tree amplitudes give rise to the definition of differential forms — the scattering forms — on the moduli space of a Riemann sphere with n marked points. These differential forms have some remarkable properties. We show that all singularities are on the divisor \( {\overline{\mathrm{\mathcal{M}}}}_{0,n}\backslash {\mathrm{\mathcal{M}}}_{0,n} \). Each singularity is logarithmic and the residue factorises into two differential forms of lower points. In order for this to work, we provide a threefold generalisation of the CHY polarisation factor (also known as reduced Pfaffian) towards off-shell momenta, unphysical polarisations and away from the solutions of the scattering equations. We discuss explicitly the cases of bi-adjoint scalar amplitudes, Yang-Mills amplitudes and gravity amplitudes.
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de la Cruz, L., Kniss, A. & Weinzierl, S. Properties of scattering forms and their relation to associahedra. J. High Energ. Phys. 2018, 64 (2018). https://doi.org/10.1007/JHEP03(2018)064
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DOI: https://doi.org/10.1007/JHEP03(2018)064