Light-front approach for heavy pentaquark transitions

Abstract

Assuming the two-diquark structure for the pentaquark state as advocated in the Jaffe-Wilczek model, there exist exotic parity-even antisextet and parity-odd triplet heavy pentaquark baryons. The theoretical estimate of charmed and bottom pentaquark masses is quite controversial and it is not clear whether the ground-state heavy pentaquark lies above or below the strong-decay threshold. We study the weak transitions of heavy pentaquark states using the light-front quark model. In the heavy quark limit, heavy-to-heavy pentaquark transition form factors can be expressed in terms of three Isgur-Wise functions: two of them are found to be normalized to unity at zero recoil, while the third one is equal to 1/2 at the maximum momentum transfer, in accordance with the prediction of the large-${N}_{c}$ approach or the quark model. Therefore, the light-front model calculations are consistent with the requirement of heavy quark symmetry. Numerical results are obtained for form factors and Isgur-Wise functions are presented. Decay rates of the weak decays ${\ensuremath{\Theta}}_{b}^{+}\ensuremath{\rightarrow}{\ensuremath{\Theta}}_{c}^{0}{\ensuremath{\pi}}^{+}({\ensuremath{\rho}}^{+}),$ ${\ensuremath{\Theta}}_{c}^{0}\ensuremath{\rightarrow}{\ensuremath{\Theta}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}({\ensuremath{\rho}}^{\ensuremath{-}}),$ ${\ensuremath{\Sigma}}_{5b}^{\ensuremath{'}+}\ensuremath{\rightarrow}{\ensuremath{\Sigma}}_{5c}^{\ensuremath{'}0}{\ensuremath{\pi}}^{+}({\ensuremath{\rho}}^{+}),$ and ${\ensuremath{\Sigma}}_{5c}^{\ensuremath{'}0}\ensuremath{\rightarrow}{N}_{8}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}({\ensuremath{\rho}}^{\ensuremath{-}})$ with ${\ensuremath{\Theta}}_{Q},$ ${\ensuremath{\Sigma}}_{5Q}^{\ensuremath{'}},$ and ${N}_{8}$ being the heavy antisextet, heavy triplet, and light octet pentaquarks, respectively. For weakly decaying ${\ensuremath{\Theta}}_{b}^{+}$ and ${\ensuremath{\Theta}}_{c}^{0},$ the branching ratios of ${\ensuremath{\Theta}}_{b}^{+}\ensuremath{\rightarrow}{\ensuremath{\Theta}}_{c}^{0}{\ensuremath{\pi}}^{+}$ and ${\ensuremath{\Theta}}_{c}^{0}\ensuremath{\rightarrow}{\ensuremath{\Theta}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ are estimated to be at the level of ${10}^{\ensuremath{-}3}$ and a few percent, respectively.