Note on hidden zeros and expansions of tree-level amplitudes

TL;DR

This paper investigates hidden zeros in tree-level amplitudes across various theories, revealing their origin in bi-adjoint scalar amplitudes and addressing divergence issues in gravitational cases.

Contribution

It introduces a universal expansion framework connecting different theories' amplitudes to bi-adjoint scalar amplitudes, explaining hidden zeros and divergence elimination.

Findings

Hidden zeros are linked to zeros of bi-adjoint scalar amplitudes.

The expansion method applies to multiple theories including Yang-Mills and gravity.

A detailed mechanism for removing divergences in gravitational amplitudes is provided.

Abstract

In this note, we derive and interpret hidden zeros of tree-level amplitudes of various theories, including Yang-Mills, non-linear sigma model, special Galileon, Dirac-Born-Infeld, and gravity, by utilizing universal expansions of tree-level amplitudes which expand amplitudes of different theories to those of bi-adjoint scalar theory. Hidden zeros of above amplitudes are attributed to zeros of bi-adjoint scalar amplitudes which can be easily proved. For unordered amplitudes such as gravitational ones, the kinematic condition for zeros causes potential divergences of propagators. We also show the detailed mechanism of eliminating such divergences.