Light-meson orbital excitations in the QCD string approach

Abstract

In the framework of the QCD string approach it is shown that the spin-averaged masses $\overline{M}(\mathrm{nL})$ of all low-lying light mesons are well described using the string tension $\ensuremath{\sigma}$ as the only parameter. The Regge slope ${\ensuremath{\alpha}}_{L}^{\ensuremath{'}}$ and the intercept ${\ensuremath{\alpha}}_{L}(0)$ of the Regge L trajectory for $\overline{M}(\mathrm{nL})$ are calculated analytically and turn out to be ${\ensuremath{\alpha}}_{L}^{\ensuremath{'}}=0.80 {\mathrm{GeV}}^{\ensuremath{-}2}$ (for $L<~4)$ and ${\ensuremath{\alpha}}_{L}(0)=\ensuremath{-}0.34,$ in good agreement with the experimental data: ${\ensuremath{\alpha}}_{L\mathrm{expt}}^{\ensuremath{'}}=0.81\ifmmode\pm\else\textpm\fi{}0.01 {\mathrm{GeV}}^{\ensuremath{-}2},$ ${\ensuremath{\alpha}}_{L\mathrm{expt}}(0)=\ensuremath{-}0.30\ifmmode\pm\else\textpm\fi{}0.02.$ 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 ${\ensuremath{\alpha}}_{s}<~0.40$ on the strong coupling constant is required.