Light-front approach for heavy pentaquark transitions

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 ${\Theta }_b^{+}\to {\Theta }_c^0{\pi }^{+}\left({\rho }^{+}\right),$ ${\Theta }_c^0\to {\Theta }^{+}{\pi }^{-}\left({\rho }^{-}\right),$ ${\Sigma }_{5b}^{\prime +}\to {\Sigma }_{5c}^{\prime 0}{\pi }^{+}\left({\rho }^{+}\right),$ and ${\Sigma }_{5c}^{\prime 0}\to N_8^{+}{\pi }^{-}\left({\rho }^{-}\right)$ with ${\Theta }_Q,$ ${\Sigma }_{5Q}^{\prime },$ and $N_8$ being the heavy antisextet, heavy triplet, and light octet pentaquarks, respectively. For weakly decaying ${\Theta }_b^{+}$ and ${\Theta }_c^0,$ the branching ratios of ${\Theta }_b^{+}\to {\Theta }_c^0{\pi }^{+}$ and ${\Theta }_c^0\to {\Theta }^{+}{\pi }^{-}$ are estimated to be at the level of ${10}^{-3}$ and a few percent, respectively.