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All Loop Scattering For All Multiplicity

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arxiv 2311.09284 v2 pith:X5O4GKG3 submitted 2023-11-15 hep-th

All Loop Scattering For All Multiplicity

classification hep-th
keywords amplitudescurveintegralsloopformulasintegralloopsresult
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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Cited by 12 Pith papers

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