Soft-exactness of tree-level gluon and graviton MHV amplitudes

Abstract

We discuss and present derivations of the must succinct forms for tree-level MHV gluon and MHV graviton scattering amplitudes, through appending soft-factors to lower-point MHV scattering amplitudes. For gluons, we see that the canonical spinor-helicity variables are sufficient to absorb all of the gauge redundancy needed to define transverse gluon polarization vectors. Correspondingly, the tree level gluon MHV scattering amplitudes can be cleanly and efficintly written in terms of spinor-helicity variables–and are described by the famous Parke-Taylor amplitude. However, the canonical spinor-helicity variables do not automatically enforce momentum conservation, and thus are not sufficiently redundant to absorb all of the differomorphism invariance that must be built into the graviton soft-factors. Nonetheless, appending graviton soft-factors to lower-point graviton MHV amplitudes yields the simplest known form for MHV graviton amplitudes. We briefly discuss new variables, better suited to describe perturbative scattering amplitudes in quantum gravity.