Measurements of $b$ hadron production ratios in protonproton collisions at a centreofmass energy of 7 TeV with an integrated luminosity of 3 pb$^{1}$ are presented. We study the ratios of strange $B$ meson to light $B$ meson production $f_s/(f_u+f_d)$ and $\Lambda_b^0$ baryon to light $B$ meson production $f_{\Lambda_b}/(f_u+f_d)$ as a function of the charmed hadronmuon pair transverse momentum $p_T$ and the $b$ hadron pseudorapidity $\eta$, for $p_T$ between 0 and 14 GeV and $\eta$ between 2 and 5. We find that $f_s/(f_u+f_d)$ is consistent with being independent of $p_{\rm T}$ and $\eta$, and we determine $f_s/(f_u+f_d)$ = 0.134$\pm$ 0.004 $^{+0.011}_{0.010}$, where the first error is statistical and the second systematic. The corresponding ratio $f_{\Lambda_b}/(f_u+f_d)$ is found to be dependent upon the transverse momentum of the charmed hadronmuon pair, $f_{\Lambda_b}/(f_u+f_d)=(0.404\pm 0.017 (stat) \pm 0.027 (syst) \pm 0.105 (Br))\times[1 (0.031 \pm 0.004 (stat) \pm 0.003 (syst))\times p_T(GeV)]$, where Br reflects an absolute scale uncertainty due to the poorly known branching fraction Br(\Lambda_c^+ \to pK^\pi^+)$. We extract the ratio of strange $B$ meson to light neutral $B$ meson production $f_s/f_d$ by averaging the result reported here with two previous measurements derived from the relative abundances of $\bar{B}_s \to D_S^+ \pi ^$ to $\bar{B}^0 \to D^+K^$ and $\bar{B}^0 \to D^+\pi^$. We obtain $f_s/f_d=0.267^{+0.021}_{0.020}$.
The logarithm of the IP distributions for (a) RS and (c) WS $D^0$ candidate combinations with a muon. The dotted curves show the false $D^0$ background, the small redsolid curves the Prompt yields, the dashed curves the Dfb signal, and the larger greensolid curves the total yields. The invariant $K^\pi^+$ mass spectra for (b) RS combinations and (d) WS combinations are also shown. 
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The logarithm of the IP distributions for (a) RS and (c) WS $D^+$ candidate combinations with a muon. The greydotted curves show the false $D^+$ background, the small redsolid curves the Prompt yields, the bluedashed curves the Dfb signal, and the larger greensolid curves the total yields. The invariant $K^\pi^+\pi^+$ mass spectra for (b) RS combinations and (d) WS combinations are also shown. 
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The logarithm of the IP distributions for (a) RS and (c) WS $ D ^+_ s $ candidate combinations with a muon. The greydotted curves show the false $ D ^+_ s $ background, the small redsolid curves the Prompt yields, the bluedashed curves the Dfb signal, the purple dashdotted curves represent the background originating from $\Lambda _ c ^+$ reflection, and the larger greensolid curves the total yields. The invariant $K^K^+\pi^+$ mass spectra for RS combinations (b) and WS combinations (d) are also shown. 
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The logarithm of the IP distributions for (a) RS and (c) WS $\Lambda_c^+$ candidate combinations with a muon. The greydotted curves show the false $\Lambda_c^+$ background, the small redsolid curves the Prompt yields, the bluedashed curves the Dfb signal, and the larger greensolid curves the total yields. The invariant $p K^\pi^+$ mass spectra for RS combinations (b) and WS combinations (d) are also shown. 
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(a) Invariant mass of $D^0 p$ candidates that vertex with each other and together with a RS muon (black closed points) and for a $\overline{p}$ (red open points) instead of a $p$; (b) fit to $D^0$ invariant mass for RS events with the invariant mass of $D^0 p$ candidate in the signal mass difference window; (c) fit to $D^0$ invariant mass for WS events with the invariant mass of $D^0 p$ candidate in the signal mass difference window. 
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Projections of the twodimensional fit to the $q^2$ and $m( D ^+_ s \mu)$ distributions of semileptonic decays including a $ D ^+_ s $ meson. The $D_s^*/D_s$ ratio has been fixed to the measured $D^*/D$ ratio in light $B$ decays (2.42$\pm$0.10), and the background contribution is obtained using the sidebands in the $K^+K^\pi^+$ mass spectrum. The different components are stacked: the background is represented by a black dotdashed line, $ D ^+_ s $ by a red dashed line, $D_s ^{*+}$ by a blue dashdouble dotted line and $ D _s^{**+}$ by a green dashdotted line. 
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Projections of the twodimensional fit to the $q^2$ and $m(\Lambda _ c ^+\mu^)$ distributions of semileptonic decays including a $\Lambda _ c ^+$ baryon. The different components are stacked: the dotted line represents the combinatoric background, the bigger dashed line (red) represents the $\Lambda _ c ^+\mu^\overline{\nu}$ component, the smaller dashed line (blue) the ${\it \Lambda _c}(2595)^+$, and the solid line represents the ${\it \Lambda _c}(2625)^+$ component. The ${\it \Lambda _c}(2595)^+/{\it \Lambda _c}(2625)^+$ ratio is fixed to its predicted value, as described in the text. 
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Measured proton identification efficiency as a function of the $\Lambda _ c ^+\mu^$ $p_{\rm T}$ for $2<\eta < 3$, $3<\eta <4$, $4<\eta < 5$ respectively, and for the selection criteria used in the $\Lambda _ c ^+\rightarrow pK^\pi^+$ reconstruction. 
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Efficiencies for $ D ^0 \mu^\overline{\nu} X$, $ D ^+ \mu^\overline{\nu} X$, $ D ^+_ s \mu^\overline{\nu} X$, $\Lambda _ c ^+\mu^\overline{\nu} X$ as a function of $\eta$ and $p_{\rm T}$. 
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Ratio between $\overline{ B }{} ^0_ s $ and light $B$ meson production fractions as a function of the transverse momentum of the $ D ^+_ s \mu^$ pair in two bins of $\eta$. The errors shown are statistical only. 
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$f_+/f_0$ as a function of $p_{\rm T}$ for $\eta$=(2,3) (a) and $\eta$=(3,5) (b). The horizontal line shows the average value. The error shown combines statistical and systematic uncertainties accounting for the detection efficiency and the particle identification efficiency. 
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Fragmentation ratio $f_{\Lambda _ b }/(f_u+f_d)$ dependence upon $p_{\rm T}(\Lambda _ c ^+\mu^)$. The errors shown are statistical only. 
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Animated gif made out of all figures. 
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Charmed hadron decay modes and branching fractions. 
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Systematic uncertainties on the relative $\overline{ B }{} ^0_ s $ production fraction. 
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Coefficients of the linear fit describing the $p_{\rm T}(\Lambda _ c ^+\mu^)$ dependence of $f_{\Lambda _ b }/(f_u+f_d)$. The systematic uncertainties included are only those associated with the bindependent MC and particle identification errors. 
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Systematic uncertainties on the absolute scale of $f_{\Lambda_b}/(f_u+f_d)$. 
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Summary of the systematic and theoretical uncertainties in the three LHCb measurements of $f_s/f_d$. 
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Uncertainties in the combined value of $f_s/f_d $. 
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Created on 16 February 2019.Citation count from INSPIRE on 16 February 2019.