Relativistic quantum model of confinement and the current quark masses

We consider a relativistic quantum model of confined massive spinning quarks and antiquarks which describes the leading Regge trajectories of mesons. The quarks are described by the Dirac equations and the gluon contribution is approximated by the Nambu-Goto straight-line string. The string tension and the current quark masses are the main parameters of the model. Additional parameters are phenomenological constants which approximate nonstring short-range contributions. A comparison of the measured meson masses with the model predictions allows one to determine the current quark masses (in MeV) to be $m_s=227\mathrm{}\pm 5,\hspace{0.5em}\hspace{0.5em}{m}_c=1440\mathrm{}\pm 10,$ and $m_b=4715\mathrm{}\pm 20.$ The chiral ${\mathrm{SU}}_3$ model makes it possible to estimate from here the $u$- and $d$-quark masses to be $m_u=6.2\mathrm{}\pm 0.2\mathrm{Mev}$ and $m_d=11.1\mathrm{}\pm 0.4\mathrm{Mev}.$