Nonleptonic decays of ${\Xi }_{cc}\to {\Xi }_c\pi$ with ${\Xi }_c-{\Xi }_c^{\prime }$ mixing

Abstract

Aiming on testing the ${\Xi }_c-{\Xi }_c^{\prime }$ mixing, we study the decays of ${\Xi }_{cc}\to {\Xi }_c\pi$ with ${\Xi }_{cc}=({\Xi }_{cc}^{++},{\Xi }_{cc}^{+})$, ${\Xi }_c=({\Xi }_c^{(\prime )+},{\Xi }_c^{(\prime )0})$ and $\pi =({\pi }^{+},{\pi }^0)$. The soft-meson limit is considered along with the pole model, and the baryon matrix elements are evaluated by the bag model with and without removing the center-of-mass motion (CMM). We find that the four-quark operator matrix elements are about twice larger once the unwanted CMM is removed. We obtain that $\mathcal{R}=\mathcal{B}({\Xi }_{cc}^{+}\to {\Xi }_c^{\prime +}{\pi }^{+})/\mathcal{B}({\Xi }_{cc}^{+}\to {\Xi }_c^{+}{\pi }^{+})=0.87_{-0.11}^{+0.17}$ and $1.45$ with and without removing the CMM, where the former is close to the lower bound and the later is well consistent with $\mathcal{R}=1.41\pm 0.17\pm 0.10$ measured at LHCb. In addition, we show that after including the mixing, the up-down asymmetry of $\alpha ({\Xi }_{cc}^{+}\to {\Xi }_c^{(\prime )0}{\pi }^{+})$ flips sign. Explicitly, we obtain that $\alpha ({\Xi }_{cc}^{+}\to {\Xi }_c^{\prime +}{\pi }^0)=0.52$ and $\alpha ({\Xi }_{cc}^{+}\to {\Xi }_c^0{\pi }^{+})=0.31$ with and without the CMM corrections, respectively, which are all negative if the mixing is absence. As a bonus, a positive value of $\alpha ({\Xi }_{cc}^{+}\to {\Xi }_c^{\prime 0}{\pi }^{+})$ in experiments can also serve as the evidence of the $W$-exchange contributions.

Comments: 17 pages, 1 figure, accepted by Physical Review D