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arXiv · 2311.09284

All Loop Scattering For All Multiplicity

Nima Arkani-Hamed·Hadleigh Frost·Giulio Salvatori·Pierre-Guy Plamondon·Hugh Thomas
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Abstract

This is part of a series of papers describing the new curve integral formalism for scattering amplitudes of the colored scalar tr$\phi^3$ theory. We show that the curve integral manifests a very surprising fact about these amplitudes: the dependence on the number of particles, $n$, and the loop order, $L$, is effectively decoupled. We derive the curve integrals at tree-level for all $n$. We then show that, for higher loop-order, it suffices to study the curve integrals for $L$-loop tadpole-like amplitudes, which have just one particle per color trace-factor. By combining these tadpole-like formulas with the the tree-level result, we find formulas for the all $n$ amplitudes at $L$ loops. We illustrate this result by giving explicit curve integrals for all the amplitudes in the theory, including the non-planar amplitudes, through to two loops, for all $n$.

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Nima Arkani-Hamed, Hadleigh Frost, Giulio Salvatori, Pierre-Guy Plamondon, Hugh Thomas. 2023-11-15. All Loop Scattering For All Multiplicity. https://arxiv.org/abs/2311.09284

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