Light-meson orbital excitations in the QCD string approach

In the framework of the QCD string approach it is shown that the spin-averaged masses $\overline{M}\mathrm{}\left(\mathrm{nL}\right)\mathrm{}$ of all low-lying light mesons are well described using the string tension $\sigma$ as the only parameter. The Regge slope ${\alpha }_L^{\prime }$ and the intercept ${\alpha }_L\mathrm{}\left(0\right)\mathrm{}$ of the Regge L trajectory for $\overline{M}\mathrm{}\left(\mathrm{nL}\right)\mathrm{}$ are calculated analytically and turn out to be ${\alpha }_L^{\prime }=0.80\mathrm{}\hspace{0.5em}{\mathrm{GeV}}^{-2}$ (for $L<~4)$ and ${\alpha }_L\mathrm{}\left(0\right)=-0.34,$ in good agreement with the experimental data: ${\alpha }_{L\mathrm{expt}}^{\prime }=0.81\mathrm{}\pm 0.01\hspace{0.5em}{\mathrm{GeV}}^{-2},$ ${\alpha }_{L\mathrm{expt}}\mathrm{}\left(0\right)=-0.30\pm \mathrm{0.02.}$ To obtain this strong agreement with the data the nonperturbative quark self-energy contributions to the meson masses must be taken into account, which appear to be large and negative for small values of L, and are important for a close fit even for larger values of L. From the present analysis of the meson spectra the restriction ${\alpha }_s<~0.40$ on the strong coupling constant is required.