On-shell representation and further instances of the 2-split behavior of amplitudes

TL;DR

This work develops an on-shell formulation of the universal 2-split behavior for tree-level amplitudes in a broad class of theories, including gauge, gravity, and higher-derivative models. By analyzing CHY ingredients, it recasts splits as products of lower-point on-shell amplitudes and introduces kinematic shifting and transmuting operators to relate amplitudes across theories. The authors demonstrate the extension of 2-split to $(DF)^2$, $R^2$, and $R^3$ gravities, derive explicit on-shell representations via five-point examples, and generalize the framework to three-split and hidden zeros. The results illuminate the universality of the split, connect it to hidden-zero structures, and pave the way for loop extensions and massive generalizations.

Abstract

The newly discovered splitting behavior of tree-level scattering amplitudes of particles and strings has been expressed in terms of currents containing one off-shell leg. In this work, we explain how to obtain on-shell representations of the split amplitudes in different theories, thereby avoiding any ambiguity involved in the definition of the currents. Furthermore, we show that this 2-split behavior is also verified in gauge and gravity theories involving higher-dimensional operators, thereby providing additional evidence to its universal character. As a byproduct, we also generalize the transmuting operators to amplitudes in higher-derivative theories.