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Abstract: We study -on-shell constructibility- of tree amplitudes from recursionrelations in general 4-dimensional local field theories with any type ofparticles, both massless and massive. Our analysis applies to renormalizable aswell as non-renormalizable interactions, with or without supersymmetry. Wefocus on recursion relations that arise from complex deformations of allexternal momenta. Under certain conditions, these -all-line shift recursionrelations- imply the MHV vertex expansion. We derive a simple sufficientcriterion for the validity of the all-line shift recursion relations. Itdepends only on the mass dimensions of the coupling constants and on the sum ofhelicities of the external particles. Our proof is strikingly simple since itjust relies on dimensional analysis and little-group transformation properties.In particular, the results demonstrate that all tree amplitudes with n>4external states are constructible in any power-counting renormalizable theory.Aspects of all-line shift constructibility are illustrated in numerousexamples, ranging from pure scalar theory and the massless Wess-Zumino model totheories with higher-derivative interactions, gluon-Higgs fusion, and Z-bosonscattering. We propose a sharp physical interpretation of our constructibilitycriterion: the all-line shift fails precisely for those classes of n-pointamplitudes that can receive local contributions from independentgauge-invariant n-field operators.

Autor: Timothy Cohen, Henriette Elvang, Michael Kiermaier

Fuente: https://arxiv.org/

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