# Measurement of b hadron production fractions in 7 TeV pp collisions

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Measurements of $b$ hadron production ratios in proton-proton collisions at a centre-of-mass 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 hadron-muon 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 hadron-muon 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}$. ## Figures and captions  The logarithm of the IP distributions for (a) RS and (c) WS$D^0$candidate combinations with a muon. The dotted curves show the false$D^0$background, the small red-solid curves the Prompt yields, the dashed curves the Dfb signal, and the larger green-solid curves the total yields. The invariant$K^-\pi^+$mass spectra for (b) RS combinations and (d) WS combinations are also shown. fig1.pdf [71 KiB] HiDef png [374 KiB] Thumbnail [224 KiB] *.C file The logarithm of the IP distributions for (a) RS and (c) WS$D^+$candidate combinations with a muon. The grey-dotted curves show the false$D^+$background, the small red-solid curves the Prompt yields, the blue-dashed curves the Dfb signal, and the larger green-solid curves the total yields. The invariant$K^-\pi^+\pi^+$mass spectra for (b) RS combinations and (d) WS combinations are also shown. fig2.pdf [78 KiB] HiDef png [369 KiB] Thumbnail [269 KiB] *.C file The logarithm of the IP distributions for (a) RS and (c) WS$ D ^+_ s $candidate combinations with a muon. The grey-dotted curves show the false$ D ^+_ s $background, the small red-solid curves the Prompt yields, the blue-dashed curves the Dfb signal, the purple dash-dotted curves represent the background originating from$\Lambda _ c ^+$reflection, and the larger green-solid curves the total yields. The invariant$K^-K^+\pi^+$mass spectra for RS combinations (b) and WS combinations (d) are also shown. fig3.pdf [73 KiB] HiDef png [386 KiB] Thumbnail [238 KiB] *.C file The logarithm of the IP distributions for (a) RS and (c) WS$\Lambda_c^+$candidate combinations with a muon. The grey-dotted curves show the false$\Lambda_c^+$background, the small red-solid curves the Prompt yields, the blue-dashed curves the Dfb signal, and the larger green-solid curves the total yields. The invariant$p K^-\pi^+$mass spectra for RS combinations (b) and WS combinations (d) are also shown. fig4.pdf [70 KiB] HiDef png [334 KiB] Thumbnail [203 KiB] *.C file (a) Invariant mass of$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$candidate in the signal mass difference window. fig5.pdf [73 KiB] HiDef png [321 KiB] Thumbnail [238 KiB] *.C file Projections of the two-dimensional fit to the$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^+$mass spectrum. The different components are stacked: the background is represented by a black dot-dashed line,$ D ^+_ s $by a red dashed line,$D_s ^{*+}$by a blue dash-double dotted line and$ D _s^{**+}$by a green dash-dotted line. fig6.pdf [62 KiB] HiDef png [253 KiB] Thumbnail [139 KiB] *.C file Projections of the two-dimensional fit to the$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)^+$ratio is fixed to its predicted value, as described in the text. fig7.pdf [62 KiB] HiDef png [186 KiB] Thumbnail [141 KiB] *.C file Measured proton identification efficiency as a function of the$\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. fig8.pdf [60 KiB] HiDef png [95 KiB] Thumbnail [70 KiB] *.C file 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}$. fig9.pdf [108 KiB] HiDef png [267 KiB] Thumbnail [284 KiB] *.C file Ratio between$\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$. The errors shown are statistical only. fig10.pdf [59 KiB] HiDef png [64 KiB] Thumbnail [52 KiB] *.C file$f_+/f_0$as a function of$p_{\rm T}$for$\eta$=(2,3) (a) and$\eta$=(3,5) (b). The horizontal line shows the average value. The error shown combines statistical and systematic uncertainties accounting for the detection efficiency and the particle identification efficiency. fig11.pdf [60 KiB] HiDef png [74 KiB] Thumbnail [57 KiB] *.C file Fragmentation ratio$f_{\Lambda _ b }/(f_u+f_d)$dependence upon$p_{\rm T}(\Lambda _ c ^+\mu^-)$. The errors shown are statistical only. fig12.pdf [60 KiB] HiDef png [118 KiB] Thumbnail [82 KiB] *.C file Animated gif made out of all figures. PAPER-2011-018.gif Thumbnail ## Tables and captions  Charmed hadron decay modes and branching fractions. Table_1.pdf [52 KiB] HiDef png [56 KiB] Thumbnail [28 KiB] tex code Systematic uncertainties on the relative$\overline{ B }{} ^0_ s $production fraction. Table_2.pdf [56 KiB] HiDef png [124 KiB] Thumbnail [58 KiB] tex code Coefficients of the linear fit describing the$p_{\rm T}(\Lambda _ c ^+\mu^-)$dependence of$f_{\Lambda _ b }/(f_u+f_d)$. The systematic uncertainties included are only those associated with the bin-dependent MC and particle identification errors. Table_3.pdf [28 KiB] HiDef png [51 KiB] Thumbnail [25 KiB] tex code Systematic uncertainties on the absolute scale of$f_{\Lambda_b}/(f_u+f_d)$. Table_4.pdf [57 KiB] HiDef png [149 KiB] Thumbnail [65 KiB] tex code Summary of the systematic and theoretical uncertainties in the three LHCb measurements of$f_s/f_d$. Table_5.pdf [59 KiB] HiDef png [109 KiB] Thumbnail [48 KiB] tex code Uncertainties in the combined value of$f_s/f_d \$. Table_6.pdf [54 KiB] HiDef png [78 KiB] Thumbnail [36 KiB] tex code

Created on 06 March 2021.