Cornering Large-$N_c$ QCD with Positivity Bounds

TL;DR

This paper uses positivity bounds and analytic structures of meson scattering amplitudes in large-$N_c$ QCD to constrain low-energy parameters, revealing a structure of kinks and explaining meson coupling behaviors.

Contribution

It introduces new analytical tools and amplitude deformations to explore the parameter space, connecting positivity bounds with meson coupling patterns and high-energy amplitude assumptions.

Findings

Kinks in parameter space correspond to single light pole amplitudes.

Meson couplings to pions decrease with increasing spin.

Deformations of UV-complete amplitudes lie near the boundaries of allowed regions.

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.