On the New Factorizations of Yang-Mills Amplitudes

TL;DR

This paper rigorously proves a new factorization pattern for tree-level Yang-Mills amplitudes, revealing their recursive structure and hidden zeros through the CHY formalism and algebraic identities.

Contribution

It validates a recently proposed factorization pattern for YM amplitudes using the CHY formalism, uncovering their recursive structure and hidden zeros.

Findings

Proves the new YM amplitude factorization pattern.

Identifies the role of singular solutions in the CHY formalism.

Reveals the recursive structure and hidden zeros of YM amplitudes.

Abstract

In this work, we prove the new factorization pattern for tree-level Yang-Mills (YM) amplitudes proposed in a companion paper. This pattern reveals a decomposition of amplitudes into a sum of gluings of lower-point amplitudes under specific kinematic constraints, making the hidden zeros of YM amplitudes manifest. Utilizing the Cachazo-He-Yuan (CHY) formalism, we rigorously derive these factorizations by systematically analyzing the contributions of singular solutions to the scattering equations. Through the identification and application of key algebraic identities, we demonstrate how cancellations among terms uncover a recursive structure intricately tied to the hidden zeros. This work not only conclusively validates the proposed factorization but also provides new insights into the geometric and algebraic organization of YM amplitudes within the CHY framework.