Abstract
The simple analytic structure of meson scattering amplitudes in the large-Nc limit, combined with positivity of the spectral density, provides precise predictions on low-energy observables. Building upon previous studies, we explore the allowed regions of chiral Lagrangian parameters and meson couplings to pions. We reveal a structure of kinks at all orders in the chiral expansion and develop analytical tools to show that kinks always correspond to amplitudes with a single light pole. We build (scalar- and vector-less) deformations of the Lovelace-Shapiro and Coon UV-complete amplitudes, and show that they lie close to the boundaries. Moreover, constraints from crossing-symmetry imply that meson couplings to pions become smaller as their spin increases, providing an explanation for the success of Vector Meson Dominance and holographic QCD. We study how these conclusions depend on assumptions about the high-energy behavior of amplitudes. Finally, we emphasize the complementarity between our results and Lattice computations in the exploration of large-Nc QCD.
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Acknowledgments
F.R. thanks Jan Albert, Adam Falkowski, Felipe Figueroa, Davide Lombardo, Marcos Marino, Leonardo Rastelli, Antonio Rodriguez, Jullian Sonner, Matteo Tacchi and Piotr Tourkine for important discussions. F.S. thanks Filippo Nardi for useful conversations. F.S. and F.R. acknowledge the support of the European Consortium for Astroparticle Theory in the form of an Exchange Travel Grant. We are grateful to the Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA+ (Project ID 39083149), for its hospitality and support during the workshop Amplitudes meet BSM. C.F. is supported by the fellowship FPU18/04733 from the Spanish Ministry of Science, Innovation and Universities. A.P. has been supported by the Catalan ICREA Academia Program, and the grants 2014-SGR-1450, PID2020-115845GB-I00/AEI/10.13039/501100011033. The work of F.R. is supported by the Swiss National Science Foundation under grants no. 200021-205016 and PP00P2-206149.
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Fernandez, C., Pomarol, A., Riva, F. et al. Cornering large-Nc QCD with positivity bounds. J. High Energ. Phys. 2023, 94 (2023). https://doi.org/10.1007/JHEP06(2023)094
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DOI: https://doi.org/10.1007/JHEP06(2023)094