Doubly charmed baryon decays $\Xi_{cc}^{++}\to\Xi_c^{(\prime)+}\pi^+$ in the quark model

Abstract

In this work we study the doubly charmed baryon decays $\Xi_{cc}^{++}\to\Xi_c^{(\prime)+}\pi^+$ within the framework of the non-relativistic quark model (NRQM). Factorizable amplitudes are expressed in terms of transition form factors, while nonfactorizable amplitudes arising form the inner $W$-emission are evaluated using current algebra and the pole model and expressed in terms of baryonic matrix elements and axial-vector form factors. Nonperturbative parameters are then calculated using the NRQM. They can be expressed in terms of the momentum integrals of baryon wave functions, which are in turn expressed in terms of the harmonic oscillator parameters $\alpha_\rho$ and $\alpha_\lambda$ for $\rho$- and $\lambda$-mode excitation. The measured ratio $R$ of the branching fraction of $\Xi_{cc}^{++}\to \Xi^{\prime +}_c\pi^+$ relative to $\Xi_{cc}^{++}\to \Xi_c^+\pi^+$ can be accommodated in the NRQM with $\alpha_{\rho 1}$ and $\alpha_{\rho_2}$ being in the vicinity of 0.51 and 0.19, respectively, where $\alpha_{\rho 1}$ is the $\alpha_\rho$ parameter for $\Xi_{cc}^{++}$ and $\alpha_{\rho 2}$ for $\Xi_{c}^{(\prime)+}$. Decay asymmetries are predicted to be $-0.78$ and $-0.89$ for $\Xi_c^+\pi^+$ and $\Xi_c^{\prime +}\pi^+$ modes, respectively, which can be tested in the near future. We compare our results with other works and point out that although some other models can accommodate the ratio $R$, they tend to lead to a branching fraction of $\Xi_{cc}^{++}\to \Xi_c^+\pi^+$ too large compared to that inferred from the LHCb measurement of its rate relative to $\Xi_{cc}^{++}\to\Lambda_c^+ K^- \pi^+\pi^+$.