Note on New KLT relations

TL;DR

This paper re-derives a known MHV amplitude using symmetric KLT relations and proves the equivalence of two recently discovered KLT relations, providing a direct validation of their correctness.

Contribution

It presents a direct derivation of Mason-Skinner MHV amplitude and proves the equivalence of two new KLT relations using regularized definitions.

Findings

Re-derivation of Mason-Skinner MHV amplitude.

Proof of equivalence between S_{n-2} and S_{n-3} KLT relations.

First direct check of the new KLT formula using regularized definitions.

Abstract

In this short note, we present two results about KLT relations discussed in recent several papers. Our first result is the re-derivation of Mason-Skinner MHV amplitude by applying the S_{n-3} permutation symmetric KLT relations directly to MHV amplitude. Our second result is the equivalence proof of the newly discovered S_{n-2} permutation symmetric KLT relations and the well-known S_{n-3} permutation symmetric KLT relations. Although both formulas have been shown to be correct by BCFW recursion relations, our result is the first direct check using the regularized definition of the new formula.