On Yangian-invariant regularisation of deformed on-shell diagrams in N=4 super-Yang-Mills theory

Abstract: We investigate Yangian invariance of deformed on-shell diagrams with D=4, N=4 superconformal symmetry. We find that invariance implies a direct relationship between the deformation parameters and the permutation associated to the on-shell graph. We analyse the connection with deformations of scattering amplitudes in N=4 super-Yang-Mills theory and the possibility of using the deformation parameters as a regulator preserving Yangian invariance. A study of higher-point tree and loop graphs suggests that manifest Yangian invariance of the amplitude requires trivial deformation parameters.