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 $σ$ as the only parameter. The Regge slope $α'_L$ and the intercept $α_L(0)$ of the Regge L-trajectory for $\bar{M}(nL)$ are calculated analytically and turn out to be $α'_L = 0.80$ GeV${}^{-2}$ (for $L \leq 4$) and $α_L(0) = -0.34$, in good agreement with the experimental data: $α'_{L {\rm exp}} = 0.81 \pm 0.01$ GeV${}^{-2}$, $α_{L {\rm exp}}(0) = -0.30 \pm 0.02$. 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 $α_s \leq 0.40$ on the strong coupling is required.