Soft Limits and Factorizations of the Pfaffian Formula

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:

Scattering of Massless Particles in Arbitrary Dimension: Soft Limits and Factorization, v2

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:

  1. Minor mistakes corrected;
  2. 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;
  3. Detailed discussions on the behavior of the integration measure by Faddeev-Popov method has been added.

Previous versions can still be found here:

Scattering of Massless Particles in Arbitrary Dimension: Soft Limits and Factorization, v1


Last updated on: 29/08/2013.


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