Quark spin content of the proton, hyperon semileptonic decays, and the decay width of the $\Theta^{+}$ pentaquark

Abstract

Using the exisiting experimental data for hyperon semileptonic decays and the flavor-singlet axial-vector charge $g_{A}^{(0)}$ from polarized deep inelastic scattering of the proton, we derive the decay width of the $\Theta^{+}$ pentaquark baryon. We take into account the effects of flavor SU(3) symmetry breaking within the framework of the chiral quark-soliton model. All dynamical parameters of the model are fixed by using the five experimental hyperon semileptonic decay constants and flavor singlet axial-vector charge. We obtain the numerical results of the decay width of the $\Theta^{+}$ pentaquark baryon as a function of the pion-nucleon sigma term $\Sigma_{\pi N}$ and investigate the dependence of the decay width of the $\Theta^{+}$ on the $g_{A}^{(0)}$, varying the $g_{A}^{(0)}$ within the range of the experimental uncertainty. We demonstrate that the combined values of all known semileptonic decays with the generally accepted value of $g_{A}^{(0)} \approx 0.3$ for the proton are compatible with a small decay width $\Gamma_{\Theta KN}$ of the $\Theta^{+}$ pentaquark, i.e. $\Gamma_{\Theta KN} \leq 1$ MeV.