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 $\bar{M}(nL)$ 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 ${\alpha }_L(0)$ of the Regge L-trajectory for $\bar{M}(nL)$ are calculated analytically and turn out to be ${\alpha }_L^{\prime }=0.80$ GeV${}^{-2}$ (for $L\le 4$) and ${\alpha }_L(0)=-0.34$, in good agreement with the experimental data: ${\alpha }_{L\exp }^{\prime }=0.81\pm 0.01$ GeV${}^{-2}$, ${\alpha }_{L\exp }(0)=-0.30\pm 0.02$. To obtain this strong agreement with the data the nonperturbative quark self-energy contributions to the meson masses must be taken into account, which appeared to be large and negative for small values of L, and are even for larger values of L important for a close fit. From the present analysis of the meson spectra the restriction ${\alpha }_s\le 0.40$ on the strong coupling is required.

Comments: 18 pages RevTeX, 1 figure