Unstable rotational states of string models and width of a hadron

Abstract

Rotational states (planar uniform rotations) of various string hadron models are tested for stability with respect to small disturbances. These models include an open or closed string carrying $n$ massive points (quarks), and their rotational states result in a set of quasilinear Regge trajectories. It is shown that rotations of the linear string baryon model $q\mathrm{\text{\ensuremath{-}}}q\mathrm{\text{\ensuremath{-}}}q$ and the similar states of the closed string are unstable, because spectra of small disturbances for these states contain complex frequencies, corresponding to exponentially growing modes of disturbances. Rotations of the linear model are unstable for any values of points' masses, but for the closed string we have the threshold effect. This instability is important for describing excited hadrons; in particular, it increases predictions for their width $\ensuremath{\Gamma}$. Predicted large values $\ensuremath{\Gamma}$ for $N$, $\ensuremath{\Delta}$ and strange baryons in comparison with experimental data result in unacceptability of the linear string model $q\mathrm{\text{\ensuremath{-}}}q\mathrm{\text{\ensuremath{-}}}q$ for describing these baryon states.