Tree (set theory)

Physics

Scattering amplitude

Grassmannian

Hypergeometric function

Pure mathematics

Mathematics

Mathematical physics

Fourier transform

Particle physics

Quantum chromodynamics

Gluon

Mathematical analysis

Celestial sphere

Amplitude

Mellin transform

Quantum electrodynamics

Astrophysics

Massless particle

Quantum mechanics

Infinity

Physics Letters B

Pasterski, Shao and Strominger have recently proposed that massless scattering amplitudes can be mapped to correlators on the celestial sphere at infinity via a Mellin transform. We apply this prescription to arbitrary n-point tree-level gluon amplitudes. The Mellin transforms of MHV amplitudes are given by generalized hypergeometric functions on the Grassmannian Gr(4,n), while generic non-MHV amplitudes are given by more complicated Gelfand A-hypergeometric functions.

Tree-level gluon amplitudes on the celestial sphere