Study on the mixing of ${\Xi }_c$ and ${\Xi }_c^{\prime }$ by the transition ${\Xi }_b\to {\Xi }_c^{{(}^{\prime })}$

Abstract

Recently, the LHCb collaboration has observed the decays ${\Xi }_b^0\to {\Xi }_c^{+}{D}_s^{-}$ and ${\Xi }_b^{-}\to {\Xi }_c^0{D}_s^{-}$. They measured the relative branching fractions times the ratio of beauty-baryon production cross-sections $\mathcal{R}(\frac{{\Xi }_b^0}{{\Lambda }_b})\equiv \frac{\sigma ({\Xi }_b^0)}{\sigma ({\Lambda }_b^0)}\times \frac{B({\Xi }_b^0\to {\Xi }_c^{+}{D}_s^{-})}{B({\Lambda }_b^0\to {\Lambda }_c^{+}{D}_s^{-})}$ and $\mathcal{R}(\frac{{\Xi }_b^{-}}{{\Lambda }_b})\equiv \frac{\sigma ({\Xi }_b^{-})}{\sigma ({\Lambda }_b^0)}\times \frac{B({\Xi }_b^{-}\to {\Xi }_c^0{D}_s^{-})}{B({\Lambda }_b^0\to {\Lambda }_c^{+}{D}_s^{-})}$. Once the ratio $\frac{\sigma ({\Xi }_b^0)}{\sigma ({\Lambda }_b^0)}$ or $\frac{\sigma ({\Xi }_b^{-})}{\sigma ({\Lambda }_b^0)}$ is known, one can determine the relative branching fractions which can be used to exam the mixing of ${\Xi }_c$ and ${\Xi }_c^{\prime }$. In previous literature, ${\Xi }_c$ and ${\Xi }_c^{\prime }$ were assumed to belong to SU(3)${}_F$ antitriple and sextet, respectively. However, recent experimental measurements such as the ratio $\Gamma ({\Xi }_{cc}\to {\Xi }_c{\pi }^{+})/\Gamma ({\Xi }_{cc}\to {\Xi }_c^{\prime }{\pi }^{+})$ indicate the spin-flavor structures of ${\Xi }_c$ and ${\Xi }_c^{\prime }$ are a mixture of ${\Xi }_c^{\bar{3}}$ and ${\Xi }_c^6$. The exact value of mixing angle $\theta$ is still under debate. In theoretical models, the mixing angle was fitted to be about $16.27^{\circ }\pm 2.30^{\circ }$ or $85.54^{\circ }\pm 2.30^{\circ }$ based on decay channels ${\Xi }_{cc}\to {\Xi }_{cc}^{{(}^{\prime })}$. While in lattice calculation, a small angle ($1.2^{\circ }\pm 0.1^{\circ }$) is preferred. To address such discrepancy and test the mixing of ${\Xi }_c$ and ${\Xi }_c^{\prime }$, here we propose the analysis of semileptonic and non-leptonic decays of ${\Xi }_b\to {\Xi }_c$ and ${\Xi }_b\to {\Xi }_c^{{}^{\prime }}$. We calculate the decay rate of ${\Xi }_b\to {\Xi }_c$ and ${\Xi }_b\to {\Xi }_c^{{}^{\prime }}$ based on light-front quark model and study the effect of the mixing angle on the ratios of weak decays ${\Xi }_b\to {\Xi }_c$ and ${\Xi }_b\to {\Xi }_c^{{}^{\prime }}$.....

Comments: 12 pages, 4 figures and 8 tables