Bootstrapping mesons at large $N$: Regge trajectory from spin-two maximization

TL;DR

This paper uses bootstrap methods to explore large N QCD mesons, revealing a Regge trajectory with low-lying states closely matching real-world meson masses, highlighting a novel spectral assumption and extremal solution.

Contribution

It introduces a new bootstrap approach to large N QCD mesons, assuming a spin-two resonance above the rho meson, leading to a Regge trajectory consistent with experimental data.

Findings

Regge trajectory derived from bootstrap matches real meson spectrum

Extremal solution reveals a spectrum of low-lying meson states

Spectral assumption about spin-two resonance is validated

Abstract

We continue the investigation of large $N$ QCD from a modern bootstrap perspective, focusing on the mesons. We make the natural spectral assumption that the $2 \to 2$ pion amplitude must contain, above the spin-one rho meson, a massive resonance of spin two. By maximizing its coupling we find a very interesting extremal solution of the dual bootstrap problem, which appears to contain at least a full Regge trajectory. Its low-lying states are in uncanny quantitative agreement with the meson masses in the real world.