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 ℓ+ℓ− → ϕh (with ℓ± two charged leptons, ϕ 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.
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Acknowledgments
We thank M. Ramos, G. Guedes, J. Roosmale Nepveu, and specially C.-Y. Yao and J. Kley for useful discussion. We are also grateful to S. De Angelis, Q. Bonnefoy, G. Durieux and Y. Shadmi for insightful comments on an early draft. E.B. acknowledges financial support from “Fundação de Amparo à Pesquisa do Estado de São Paulo” (FAPESP) under contract 2019/04837-9, as well as partial support from “Conselho Nacional de Deselvolvimento Científico e Tecnológico” (CNPq). G.M.S. acknowledges financial support from “Fundação de Amparo à Pesquisa do Estado de São Paulo” (FAPESP) under contracts 2020/14713-2 and 2022/07360-1. This work is supported by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy EXC 2121 “Quantum Universe” - 390833306. This work has been also partially funded by the Deutsche Forschungsgemeinschaft under the grant 491245950. This project has received funding from the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie Staff Exchange grant agreement No 101086085 - ASYMMETRY. This project has received funding /support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 860881-HIDDeN.
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Bertuzzo, E., Grojean, C. & Salla, G.M. ALPs, the on-shell way. J. High Energ. Phys. 2024, 175 (2024). https://doi.org/10.1007/JHEP05(2024)175
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DOI: https://doi.org/10.1007/JHEP05(2024)175