Very recently F. Cachazo, S. He and I have proposed a new formula (arXiv:1307.2199) for the complete tree-level S-matrix of Yang-Mills and gravity in any dimension, which is based on an integration of the Pfaffian of a skew-symmetric matrix depending on momentum and polarization vectors, over the moduli space of n punctures on a Riemann sphere.
This post is to supplement the paper by providing a detailed proof that our formula satisfies correct soft limits and factorizations both for gluons and gravitons, the most up-to-date notes of which can be found in the following link:
Notice: Any comments and remarks are welcome, either by sending us e-mails (preferred) or replying directly to this post. The document here will be updated if we have a better version in future. — Freddy, Song and Ellis.
Updates in Version 2:
- Minor mistakes corrected;
- A slightly different convention for the formula has been chosen (which however agrees with that in our previous work arXiv:1306.6575), so that it exactly matches the results from the standard spin-helicity formalism when restricting to 4-dimensions;
- Detailed discussions on the behavior of the integration measure by Faddeev-Popov method has been added.
Previous versions can still be found here:
Last updated on: 29/08/2013.