ALPs, the on-shell way

Abstract

We study how the coupling between axion-like particles (ALPs) and matter can be obtained at the level of on-shell scattering amplitudes. We identify three conditions that allow us to compute amplitudes that correspond to shift-symmetric Lagrangians, at the level of operators with dimension 5 or higher, and we discuss how they relate and extend the Adler's zero condition. These conditions are necessary to reduce the number of coefficients consistent with the little-group scaling to the one expected from the Lagrangian approach. We also show how our formalism easily explains that the dimension-5 interaction involving one ALP and two massless spin-1 bosons receive corrections from higher order operators only when the ALP has a non-vanishing mass. As a direct application of our results, we perform a phenomenological study of the inelastic scattering ${\ell }^{+}{\ell }^{-}\to \varphi h$ (with ${\ell }^{\pm }$ two charged leptons, $\varphi$ the ALP and $h$ the Higgs boson) for which, as a result of the structure of the 3-point and 4-point amplitudes, dimension-7 operators can dominate over the dimension-5 ones well before the energy reaches the cutoff of the theory.

32 pages + appendices; v2: minor modifications, matches version published in JHEP

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Cited by in corpus (4)

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• Renormalization of effective field theories via on-shell methods: the case of axion-like particles
• Dimension-8 SMEFT contact-terms for vector-pair production via on-shell Higgsing
• Positivity and partial wave unitarity bounds on ALP theories via amplitude methods