Measurements of the Branching Fractions of the Semileptonic Decays ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\ell }^{+}{\nu }_{\ell }$ and the Asymmetry Parameter of ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$

Using data samples of 89.5 and $711{\mathrm{fb}}^{-1}$ recorded at energies of $\sqrt{s}=10.52$ and 10.58 GeV, respectively, with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider, we report measurements of branching fractions of semileptonic decays ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\ell }^{+}{\nu }_{\ell }$ ($\ell =e$ or $\mu$) and the $CP$-asymmetry parameter of ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$ decay. The branching fractions are measured to be $\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{e}^{+}{\nu }_e)=(1.31\pm 0.04\pm 0.07\pm 0.38)\%$ and $\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\mu }^{+}{\nu }_{\mu })=(1.27\pm 0.06\pm 0.10\pm 0.37)\%$, and the decay parameter ${\alpha }_{\mathrm{\Xi }\pi }$ is measured to be $0.63\pm 0.03\pm 0.01$ with much improved precision compared with the current world average. The corresponding ratio $\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{e}^{+}{\nu }_e)/\mathcal{B}({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\mu }^{+}{\nu }_{\mu })$ is $1.03\pm 0.05\pm 0.07$, which is consistent with the expectation of lepton flavor universality. The first measured asymmetry parameter ${\mathcal{A}}_{CP}=({\alpha }_{{\mathrm{\Xi }}^{-}{\pi }^{+}}+{\alpha }_{{\overline{\mathrm{\Xi }}}^{+}{\pi }^{-}})/({\alpha }_{{\mathrm{\Xi }}^{-}{\pi }^{+}}-{\alpha }_{{\overline{\mathrm{\Xi }}}^{+}{\pi }^{-}})=0.024\pm 0.052\pm 0.014$ is found to be consistent with zero. The first and the second uncertainties above are statistical and systematic, respectively, while the third ones arise due to the uncertainty of the ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$ branching fraction.

Figure 1

The fits to the $M_{{\mathrm{\Xi }}^{-}{e}^{+}}$, $M_{{\mathrm{\Xi }}^{-}{\mu }^{+}}$, and $M_{{\mathrm{\Xi }}^{-}{\pi }^{+}}$ distributions of the selected (a) ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{e}^{+}{\nu }_e$, (b) ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\mu }^{+}{\nu }_{\mu }$, and (c) ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$ candidates in each $p_{{\mathrm{\Xi }}^{-}X}^{*}/p_{\max }^{*}$ bin listed at the bottom. The points with error bars represent the data from $\sqrt{s}=10.52\mathrm{GeV}$ and 10.58 GeV, the solid blue lines are the best fits, and the violet dashed lines are the fitted total backgrounds. The other components of the fits are indicated in the legends.

Figure 2

The maximum-likelihood fits to the efficiency-corrected $\cos {\theta }_{\mathrm{\Xi }}$ distributions of data to extract (a) ${\alpha }_{{\mathrm{\Xi }}^{-}{\pi }^{+}}$ and (b) ${\alpha }_{{\overline{\mathrm{\Xi }}}^{+}{\pi }^{-}}$ for ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$ and ${\overline{\mathrm{\Xi }}}_c^0\to {\overline{\mathrm{\Xi }}}^{+}{\pi }^{-}$ decays. The points with error bars represent data from the combined samples at $\sqrt{s}=10.52\mathrm{GeV}$ and 10.58 GeV, and the red solid lines are the best fits.