The nonleptonic decays $\Xi_{cc}^{++}\to\Xi_{c}^{(\prime)+}\pi^{+}$ within the nonrelativistic quark model

Abstract

In this work, we study the nonleptonic decays $\Xi_{cc}^{++}\to\Xi_{c}^{(\prime)+}\pi^{+}$ with considering $\Xi_{c}-\Xi_{c}^{\prime}$ mixing. The relevant decay amplitudes are evaluated within the framework of nonrelativistic quark model, combining the baryon spatial wave functions adopted from solving the Schr\"{o}dinger equation with a nonrelativistic potential. With the mixing angle ranging $\theta\in(-18.2^{\circ},-14.3^{\circ})$, we successfully reproduce the measured ratio $R=\mathcal{B}[\Xi_{cc}^{++}\to\Xi_{c}^{\prime+}\pi^{+}]/\mathcal{B}[\Xi_{cc}^{++}\to\Xi_{c}^{+}\pi^{+}]$ reported by the LHCb Collaboration. Furthermore, we estimate the branching fractions as $\mathcal{B}[\Xi_{cc}^{++}\to\Xi_{c}^{+}\pi^{+}]=(3.2\sim4.3)\%$ and $\mathcal{B}[\Xi_{cc}^{++}\to\Xi_{c}^{\prime+}\pi^{+}]=(4.2\sim6.0)\%$, and the asymmetry parameters as $\alpha[\Xi_{cc}^{++}\to\Xi_{c}^{+}\pi^{+}]=(-0.80\sim-0.81)$ and $\alpha[\Xi_{cc}^{++}\to\Xi_{c}^{\prime+}\pi^{+}]=(-0.61\sim-0.62)$. The measurements of absolute branching fractions and asymmetry parameters by the ongoing LHCb and Belle II experiments will be helpful for further testing our numerical results and confirming the mixing angle.