Fragmentation-fraction ratio $f_{{\mathrm{\Xi }}_b}\mathrm{/}{f}_{{\mathrm{\Lambda }}_b}$ in $b$- and $c$-baryon decays

We study the ratio of fragmentation fractions, $f_{{\mathrm{\Xi }}_b}\mathrm{/}{f}_{{\mathrm{\Lambda }}_b}$, from the measurement of ${\mathrm{\Xi }}_b^0\to {\mathrm{\Xi }}_c^{+}{\pi }^{-}$ and $\Lambda_b^0\to \Lambda_c^+\pi^-$with$\Xi_{c}^{+}/\Lambda_{c}^{+}\to p K^-\pi^+$. With the branching fraction $\mathcal{B}({\mathrm{\Xi }}_c^{+}\to p{K}^{-}{\pi }^{+})=(2.2\pm 0.8)\mathrm{\%}$ obtained under the U-spin symmetry, the fragmentation ratio is determined as $f_{{\mathrm{\Xi }}_b}\mathrm{/}{f}_{{\mathrm{\Lambda }}_b}$=$0.054\pm 0.020$. To reduce the above uncertainties, we suggest to measure the branching fractions of $\Xi_c^+\to p \overline K^{*0}$and$\Lambda_c^+\to \Sigma^+ K^{*0}$ at BESIII, Belle(II) and LHCb.