Note on universal description of heavy and light mesons

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.