Linear radial Regge trajectories for mesons with any quark flavor

In the Regge phenomenology, the radial spectrum of light mesons is given by a linear relation $M_n^2=a(n+b)$, where $a$ is a universal slope, the dimensionless intercept $b$ depends on quantum numbers, and $n$ enumerates the excited states in radial recurrences. The usual extensions of this relation to heavy quarkonia in the framework of hadron string models typically lead to strong nonlinearities which seem to be at variance with the available experimental data. Introducing a radially static string picture of mesons, we put forward a linear generalization $(M_n-m_1-m_2)^2=a(n+b)$, where $m_{1,2}$ are quark masses. The vector channel contains enough experimental states to check this new relation and a good agreement is observed. It is shown that this generalization leads to a simple estimate of current quark masses from the radial spectra.