Off-Shell CHY Amplitudes and Feynman Graphs
Louise Dolan, Peter Goddard
TL;DR
This paper develops a polynomial formulation of off-shell CHY scattering equations, linking them directly to off-shell Feynman graphs in massless $ ^3$ theory, and introduces a recurrence relation for individual graphs.
Contribution
It introduces a new polynomial form of off-shell CHY equations and a recurrence relation for off-shell Feynman graph amplitudes, extending the CHY formalism off shell.
Findings
Polynomial form of off-shell CHY equations derived.
Explicit off-shell Feynman graph amplitudes expressed via CHY.
Recurrence relation for individual off-shell Feynman graphs established.
Abstract
A polynomial form is established for the off-shell CHY scattering equations proposed by Lam and Yao. Re-expressing this in terms of independent Mandelstam invariants provides a new expression for the polynomial scattering equations, immediately valid off shell, which makes it evident that they yield the off-shell amplitudes given by massless Feynman graphs. A CHY expression for individual Feynman graphs, valid even off shell, is established through a recurrence relation.
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