Hidden zeros for higher-derivative YM and GR amplitudes at tree-level

TL;DR

This work shows that hidden zeros extend to tree-level amplitudes in YM and GR with higher-derivative corrections, including $F^3$, $R^2$, and $R^3$ terms. By exploiting universal expansions that express amplitudes as sums over BAS amplitudes with polynomial coefficients, the authors connect hidden zeros in BAS to those in higher-derivative YM and GR amplitudes, and address propagator divergences in unordered graviton configurations with a robust cancellation mechanism. They demonstrate concrete hidden zeros in $F^3$ and in $R^2$/$R^3$ amplitudes, supported by 4- and 5-point examples and general proofs, establishing finite effective expansions compatible with KK relations. The results provide a framework for constraining and potentially constructing higher-derivative amplitudes on-shell, with implications for recursion and the understanding of low-energy stringy corrections.”

Abstract

We extend the recently discovered phenomenon of hidden zeros to tree amplitudes for Yang-Mills (YM) and general relativity (GR) theories with higher-derivative interactions. This includes gluon amplitudes with a single insertion of the local $F^3$ operator, as well as graviton amplitudes at sub-leading and sub-sub-leading orders in the low-energy expansion of bosonic closed string amplitudes -- referred to as $R^2$ and $R^3$ amplitudes, respectively. The kinematic condition for hidden zeros leads to unavoidable propagator singularities in unordered graviton amplitudes. We investigate in detail the systematic cancellation of these divergences, which resolves ambiguities in the proof of hidden zeros. Our approach is based on universal expansions that express tree amplitudes as linear combinations of bi-adjoint scalar amplitudes.

Figures (1)

• Figure 1: Examples of $\Gamma$.