Hybrid baryons in large-NcQCD

Abstract

We study the properties and couplings of hybrid baryons in the large-${N}_{c}$ expansion. These are color-neutral baryon states which contain in addition to ${N}_{c}$ quarks also one constituent gluon. Hybrid baryons with both symmetric and mixed symmetric orbital wave functions are considered. We introduce a Hartree description for these states, similar to the one used by Witten for ordinary baryons. It is shown that the Hartree equations for ${N}_{c},{(N}_{c}\ensuremath{-}1)$ quarks for symmetric (mixed symmetric) states in hybrid baryons coincide with those in ordinary baryons in the large-${N}_{c}$ limit. The energy due to the gluon field is of order ${N}_{c}^{0}{\ensuremath{\Lambda}}_{\mathrm{QCD}}$ and can be interpreted as the mass of a constituent gluon. Under the assumption of color confinement, our results prove the existence of hybrid baryons made up of heavy quarks in the large ${N}_{c}$ limit and provide a justification for the constituent gluon picture of these states. The couplings of the hybrid baryons to mesons of arbitrary spin are computed in the quark model. Using constraints from the large ${N}_{c}$ scaling laws for the meson-baryon scattering amplitudes, we write down consistency conditions for the meson couplings of the hybrid baryons. These consistency conditions are solved explicitly with results in agreement with those in the quark model for the respective couplings.