W. Wayne Zhao | Searcharxiv

arXiv2026

Surface Water Wave Scattering and the Hydrotope

We study the classical tree-level scattering amplitudes of deep-water surface gravity waves using the methods of high-energy physics. For scattering in one horizontal dimension and in the two-negative-wavenumber sector we obtain a closed formula for $n$-wave scattering. Up to a kinematic prefactor, the amplitude is the volume of a classic polytope -- a box sliced by a hyperplane, which we dub the hydrotope, whose purpose in life is simply to organize the sign patterns of the "chambers" characterizing all the different regions of the two-minus kinematic space. The general formula was discovered by Claude Opus 4.6 working under our guidance, beginning with our earlier discovery of a one-term expression valid in the "simplest" kinematic chamber. Our results resolve the puzzle raised by Y.V. Lvov's 1997 computation of the five-wave amplitudes, unifying and extending it to all multiplicities.

hep-th↗

arXiv2024

Five-dimensional spinor helicity for all masses and spins

We develop a spinor helicity formalism for five-dimensional scattering amplitudes of any mass and spin configuration. While five-dimensional spinor helicity variables have been previously studied in the context of N=2,4 supersymmetric Yang-Mills scattering amplitudes with spin less than two arXiv:2202.08257, we propose an alternative viewpoint that stems from d-dimensional spinor helicity variables avoiding the use of the exceptional low-dimensional isomorphism $SO(4,1) \cong USp(2,2)$ and the decomposition of a massive momentum into the sum of two massless momenta. By enumerating all possible independent little group tensors, we systematically build the full space of five-dimensional three-point tree-level scattering amplitudes for any configuration of spins and masses. Furthermore, we provide a prescription for computing the high energy limit of scattering amplitudes written in our spinor helicity variables. We also expect that our formalism will be applicable to effective field theories with higher spin, in particular, the scattering of highly spinning black holes in five dimensions.

hep-th↗