Planar Radiation Zeros and Scattering Equations in Field Theory Amplitudes

We will present planar radiation zeros in biadjoint scalar, Yang-Mills theory or Einstein-Hilbert theories. Radiation zero refers to configurations in phase space for which the scattering amplitude vanishes. We studied “planar zeros”, which apply to processes where all momenta lie on a plane. Gauge planar zeros in the maximally helicity violating sector amplitudes live in the projective space spanned by the stereographic coordinates labelling the direction of flight of the external momenta. This implies that planar zeros are realized within the soft limit of the emitted particles. Gravitational amplitudes always vanish within the planar limit for non-helicity conserving configurations. String α'-corrections have also been calculated. We have used color-kinematics duality to compute gravitational amplitudes together with the Cachazo-He-Yuan formalism. The latter is based upon a rational map between the space of null D-dimensional momentum vectors and the moduli space of punctured Riemann spheres, the so-called scattering equa-

tions. We have shown that Sudakov parametrization simplifies the computations of their solutions.