Excited Hadrons and Quark-Hadron Duality

TL;DR

This paper reviews how quark-hadron duality explains the mass patterns of mesons and baryons, validating a Regge form for resonance masses and extracting specific radial and angular slope parameters from experimental data.

Contribution

It introduces a phenomenological validation of the Regge mass formula for hadrons, connecting duality with two-body dynamics and providing precise slope measurements.

Findings

Radial mass dependence aligns with two-body dynamics.

Distinct radial slopes for mesons and baryons.

Similar angular slopes for different hadron types.

Abstract

We review how Quark-Hadron Duality (QHD) for (u,d) flavors at high energies and in the scaling regime suggests a radial and angular behaviour of mesonic and baryonic resonance masses of the Regge form $M^2_{nJ} = \mu^2 n + \beta^2 J + M_0^2 $. The radial mass dependence is asymptotically consistent with a common two-body dynamics for mesons and baryons in terms of the quark-antiquark ($q \bar q)$ and quark-diquark ($qD$) degrees of freedom, respectively. This formula is validated phenomenologically within an uncertainty determined by half the width of the resonances, $\Delta M_{nJ}^2 \sim \Gamma_{nJ} M_{nJ}$. With this error prescription we find from the non-strange PDG hadrons different radial slopes $\mu^2_{\bar qq}=1.34(4) {\rm GeV}^2$ and $\mu^2_{qD}=0.75(3) {\rm GeV}^2$, but similar angular slopes $\beta_{\bar q q}^2 \sim \beta_{ q D}^2 \sim 1.15 {\rm GeV}^2$.