We study all tree-level split helicity gluon amplitudes by using the recently proposed BCFW recursion relation and Hodges diagrams in ambitwistor space. We pick out the contributing diagrams and find that all of them can be divided into triangles in a suitable way. We give the explicit expressions for all of these amplitudes. As an example, we reproduce the six gluon split NMHV amplitudes in momentum space.
Scattering amplitudes computed by superstring perturbation theory are known to holomorphically split into chiral half integrands at fixed internal loop momentum. It is established by direct computation that upon reduction to the ordinary moduli space, the chiral half integrands of the superstring match those computed by the ambitwistor string in the limit of zero tension ($α'\rightarrow\infty$). Subtleties that arise at higher genus due to the nonprojectedness of the supermoduli space are considered and arguments as to their resolution are furnished.
The infinite tower of positive-helicity soft gravitons in any minimally coupled, tree-level, asymptotically flat four-dimensional (4D) gravity was recently shown to generate a $w_{1+\infty}$ asymptotic symmetry algebra. It is natural to ask whether this classical algebra acquires quantum corrections at loop level. We explore this in quantum self-dual gravity, whose amplitudes acquire known one-loop exact all-plus helicity quantum corrections. We show using collinear splitting formulae that, remarkably, the $w_{1+\infty}$ algebra persists in quantum self-dual gravity without corrections.
We present a world-sheet formula for all tree level scattering amplitudes, in all trace sectors, of four dimensional $\mathcal{N} \leq 4$ supersymmetric Einstein-Yang-Mills theory, based on the refined scattering equations. This generalizes previously known formulas for all-trace purely bosonic, or supersymmetric single-trace amplitudes. We find this formula by applying a new chiral splitting formula for all CHY Pfaffians in 4d, into two determinants, of positive and negative helicity respectively. The splitting of CHY Pfaffians is shown to be a special case of the splitting of $T\mathbb{M}$ v…
We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric Yang-Mills theory. With the exception of massless bubbles, all integrands have unambiguous, leading singularities as coefficients defined in field theory; for the massless bubbles on external legs, we find two natural choices which lead to different integrands that highlight distinct aspects of field theory. For concreteness, we give the all-multiplicity integrands for MHV amplitudes, and the split-helicity amplitude integrand for six-particle NM…
This article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor decomposition and avoids also dimensional splitting. Because of the latter, commutation between Lorentz index contraction and loop integration is preserved within this prescription, which entails certain technical advantages. The usage of these D-dimensional polarized amplitude projectors results in helicity amplitudes that can be expressed solely in terms of…
Massless-Massive Amplitude Correspondence I: Helicity-chirality Matching and On-shell Higgsing
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院）；International Center for Theoretical Physics Asia-Pacific（亚太理论物理中心）；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
The structure of tree-level scattering amplitudes for collinear massless bosons is studied beyond their leading splitting function behavior. These near-collinear limits at sub-leading order are best studied using the Cachazo-He-Yuan (CHY) formulation of the S-matrix based on the scattering equations. We compute the collinear limits for gluons, gravitons and scalars. It is shown that the CHY integrand for an n-particle gluon scattering amplitude in the collinear limit at sub-leading order is expressed as a convolution of an (n-1)-particle gluon integrand and a collinear kernel integrand, which …
