Generalized $2$-split for higher-derivative YM and GR amplitudes at tree-level

TL;DR

This paper explores the generalized 2-split method for higher-derivative Yang-Mills and Gravity amplitudes at tree level, revealing they do not factorize simply but as sums of multiple contributions, and introduces the concept of hidden zero phenomena.

Contribution

It extends the 2-split framework to higher-derivative theories, uncovering new factorization properties and the hidden zero phenomenon in these amplitudes.

Findings

Higher-derivative amplitudes do not factorize into a single product.

Amplitudes decompose into sums of multiple 2-split contributions.

Discovery of the hidden zero phenomenon in these amplitudes.

Abstract

We study the generalized $2$-split of higher-derivative amplitudes, including Yang-Mills (YM) and Gravity (GR) amplitudes with special insertions of higher-derivative vertices, by expanding them into ${\rm YM}\oplus{\rm BAS}$, ${\rm GR}\oplus{\rm YM}$, and ${\rm GR}\oplus{\rm YM}\oplus{\rm BAS}$ amplitude, respectively. By leveraging the established $2$-split properties of these constituent theories, we show that these higher-derivative amplitudes -- which also exhibit another newly discovered phenomenon called hidden zero -- do not factorize into a single product of two currents. Instead, their factorization universally appears as a sum of multiple $2$-split contributions.