Fit to the mass spectra of the $H_c$ candidates of the selected $H_b$ decays: (a) $D^0$, (b) $D^+$, (c) $D_s^+$ mesons, and (d) the $\Lambda ^+_ c $ baryon. The data are shown as black points with error bars. The signal component is shown as the dashed (green) line and the combinatorial background component is shown as the dashed (red) line. The solid (blue) line shows all components added together.

Projections of the two-dimensional fits to the (a) $m(D^0K^{\pm})_C$ and (c) $m(D^0\myoptbar{ p}{} )_C$ mass distributions and (b, d) ${\rm ln}(\Delta\chi^{2}_{\rm V})$ for (top) $ D ^0 K^{\pm} X\mu^- \overline{\nu}_{\mu}$ candidates, and (bottom) for $ D ^0 \myoptbar{ p}{} X\overline{\nu}_{\mu}$ candidates. The curves show projections of the 2D fit. The dashed (red) curves show the $D_{s1}^{+}$ and $D_{s2}^{*+}$ resonant components in (a) and (b), and $\Lambda ^+_ c (2860)$, $\Lambda ^+_ c (2880)$ and $\Lambda ^+_ c (2940)$ resonant components in (c) and (d). The long-dashed-dotted (green) curves show the nonresonant component, the dotted (black) curves are the background components, whose shapes are determined from wrong-sign combinations, and the solid (blue) curve shows all components added together.

The ratios $f_{s}/(f_{u}+f_{d})$ and $f_{\Lambda ^0_ b }/(f_{u}+f_{d})$ in bins of $ p_{\mathrm{T}} (H_b)$. The $\overline{ B }{} {}^0_ s $ data are indicated by solid circles, while the $\Lambda ^0_ b $ by triangles. The smaller (black) error bars show the combined bin-by-bin statistical and systematic uncertainties, and the larger (blue) ones show the global systematics added in quadrature. The fits to the data are shown as the solid (green) bands, whose widths represents the $\pm 1 \sigma$ uncertainty limits on the fit shapes, and the dashed (black) lines give the total uncertainty on the fit results including the global scale uncertainty. In the highest two $ p_{\mathrm{T}}$ bins the points have been displaced from the center of the bin.

Measurement of the fraction ratios (a) $f_s/(f_u+f_d)$ and (b) $f_{\Lambda ^0_ b }/(f_u+f_d)$ as functions of $\eta$ integrated over $ p_{\mathrm{T}}$ .

Animated gif made out of all figures.

Branching fractions of semileptonic $b$-hadron decays from direct measurements for $\overline{ B }{} {}^0$ and $ B ^- $ mesons, ($\left< B\right>\equiv \left< \overline{ B }{} {}^0 +B^-\right>$), and derived for $\overline{ B }{} {}^0_ s $ and $\Lambda ^0_ b $ hadrons based on the equality of semileptonic widths and the lifetime ratios \cite{Tanabashi:2018oca,Bigi:2011gf}. Corrections to $\Gamma_{\rm SL}$ for $\overline{ B }{} {}^0_ s $ $(-1.0\pm 0.5)$% and $\Lambda ^0_ b $ $(3.0\pm 1.5)$% are applied \cite{Bigi:2011gf}. Correlations in the $\overline{ B }{} {}^0$ and $ B ^- $ branching fraction measurements have been taken into account. See Ref. \cite{Aaij:2016avz} for more information.

Charm-hadron branching fractions for the decay modes used in this analysis. Note, the $\Lambda ^+_ c $ branching fraction has been significantly improved since the previous analysis.

Global systematic uncertainties. The $D^{0}$ and $D^{+}$ branching fraction uncertainties are scaled by the fraction of each decay, $f_0$ and $f_+$ for $f_s/(f_u+f_d)$ and $f_{\Lambda ^0_ b }/(f_u+f_d)$ uncertainties.

Values of $f_s/(f_u+f_d)$ and $f_{\Lambda ^0_ b }/(f_u+f_d)$ in each $ p_{\mathrm{T}} (H_b)$ bin. The first uncertainty is statistical and incorporates both the uncertainties due to the data sample size and the finite amount of simulated events, while the second is the overall systematic uncertainty, including global and bin-dependent systematic uncertainties.

Covariance matrix for $f_s/(f_u+f_d)$ in $ p_{\mathrm{T}} (H_b)$ $ $[GeV] bins; it accounts for statistical and bin-dependent systematic uncertainties, but not the global systematic uncertainties.

Covariance matrix for $f_{\Lambda ^0_ b }/(f_u+f_d)$ in $ p_{\mathrm{T}} (H_b)$ $ $[GeV] bins; it accounts for statistical and bin-dependent systematic uncertainties, but not the global systematic uncertainties.