Note on universal description of heavy and light mesons

TL;DR

This paper observes a universal linear relation in the squared masses of excited vector mesons across all quark flavors and proposes a reparametrization model that treats quarks as static sources with relativistic interactions.

Contribution

It introduces a new, model-independent way to describe meson spectra using a universal slope and intercept, accounting for different quark masses.

Findings

Linear $m_n^2$ spectrum holds across all quark flavors.

Heavy mesons exhibit even better linearity than light ones.

Proposed model treats quarks as static sources with relativistic interactions.

Abstract

The experimental spectrum of excited S-wave vector mesons with hidden quark flavor reveals a remarkable property: For all flavors, it is approximately linear in mass squared, $m_n^2\approx a(n+b)$, $n$ is the radial quantum number. We draw attention to the fact that such a universal behavior for any quark mass cannot be obtained in a natural way within the usual semirelativistic potential and string-like models - if the Regge-like behavior is reproduced for the mesons made of the light quarks, the trajectories become essentially nonlinear for the heavy-quark sector. In reality, however, the linearity for the heavy mesons appears to be even better than for the light ones. In addition, the slope a is quite different for different quark flavors. This difference is difficult to understand within the QCD string approach since the slope measures the interaction strength among quarks. We propose a simple way for reparametrization of the vector spectrum in terms of quark masses and universal slope and intercept. Our model-independent analysis suggests that the quarks of any mass should be regarded as static sources inside mesons while the interaction between quarks is substantially relativistic.