Cornering Large-$N_c$ QCD with Positivity Bounds

Abstract

The simple analytic structure of meson scattering amplitudes in the large-$N_c$ 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-$N_c$ QCD.

38 pages, 7 figures

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• Positivity Bounds on Massive Vectors
• Non-Forward UV/IR Relations
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Bootstrapping gauge theories
• A Celestial Route to AdS Bulk Locality
• On the number of Regge trajectories for dual amplitudes
• Positivity bounds in scalar-QED EFT at one-loop level
• Strings from Almost Nothing
• The $\pi \pi$ scattering amplitude at large $N_{\text{c}}$
• The Rise of Linear Trajectories
• Bootstrap Method in Theoretical Physics
• Worldsheet for Generalized Veneziano Amplitudes