Meson coupling constants at high mass and large N_c

TL;DR

This paper explores the relationship between quark-hadron duality, meson coupling constants, and the Hagedorn spectrum at large N_c, revealing that high-mass mesons have significantly larger individual couplings than their neighbors, with implications for string-like QCD models.

Contribution

It demonstrates that reconciling quark-hadron duality with a Hagedorn spectrum requires high-mass mesons to have disproportionately large coupling constants, a novel insight into meson interactions at large N_c.

Findings

Coupling constants for high-mass mesons are larger than neighboring mesons.

The ratio of squared average coupling to average of squared couplings decreases exponentially with mass.

High-precision cancellations are necessary for duality and Hagedorn spectrum compatibility.

Abstract

Quark-hadron duality implies that a process described in terms of quark loops should be the hadronic amplitude when averaged over a sufficient number of states. Ambiguities associated with the notion of quark hadron duality can be made arbitrarily small for highly excited mesons at large $N_c$. QCD is expected to form a string like description at large $N_c$ yielding an exponentially increasing Hagedorn spectrum for high mass. It is shown that in order to reconcile quantum-hadron duality with a Hagedorn spectrum, the magnitude of individual coupling constants between high-lying mesons in a typical decay process must be characteristically larger than the average of the coupling constants to mesons with nearby masses. The ratio of the square of the average coupling to the average of the coupling squared (where the average is over mesons with nearby masses) drops {\it exponentially} with the mass of the meson. Scenarios are discussed by which such a high precision cancellation can occur.