Light hybrid baryons in the constituent model of QCD

Abstract

Hybrid baryons, in which gluonic degrees of freedom play an explicit dynamical role, provide a key testing ground for nonperturbative quantum chromodynamics. In this work, we investigate the mass spectrum of light hybrid baryons composed of identical quarks within a phenomenological constituent framework, applied to a quark core-gluon approximation. In this approach, the hybrid baryon is described as a bound state of a color-octet three-quark core and a constituent gluon, allowing the original four-body problem to be reduced to a three-body calculation followed by an effective two-body treatment. The spectrum of the color-octet quark core is obtained by solving a semirelativistic three-quark Hamiltonian with linear confinement, Coulomb, and regularized hyperfine interactions using an oscillator basis expansion. Finite-size effects of the core are incorporated through the convolution of the effective core-gluon interaction with the spatial quark density. The resulting two-body problem, whose associated Hamiltonian has the same shape as the one of the core, is solved applying the helicity formalism and using the Lagrange mesh method. Our results predict the lightest hybrid baryons to occur at energies above $3~\mathrm{GeV}$, with negative-parity states generally lying below their positive-parity counterparts. The predicted spectra are compared with lattice QCD and QCD sum-rule calculations, showing qualitative agreement although the lowest-lying lattice QCD results are significantly lighter than the present ones. Possible extensions of the model and implications for future experimental searches are discussed.