Linear radial Regge trajectories for mesons with any quark flavor

Saint Petersburg State University, 7/9 Universitetskaya nab., St.Petersburg, 199034, Russia

^* e-mail: s.afonin@spbu.ru
^** e-mail: i.pusenkov@spbu.ru

Published online: 28 October 2016

Abstract

In the Regge phenomenology, the radial spectrum of light mesons is given by a linear relation M²_n = 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 − m₁ − m₂)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.