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The ratio of the $B^0_s$ and $B^0$ fragmentation fractions, $f_s/f_d$, in proton-proton collisions at the LHC, is obtained as a function of $B$-meson transverse momentum and collision centre-of-mass energy from the combined analysis of different $B$-decay channels measured by the LHCb experiment. The results are described by a linear function of the meson transverse momentum, or with a function inspired by Tsallis statistics. Precise measurements of the branching fractions of the $B^0_s \to J/����$ and $B^0_s \to D^-_s ��^+$ decays are performed, reducing their uncertainty by about a factor of two with respect to previous world averages. Numerous $B^0_s$ decay branching fractions, measured at the LHCb experiment, are also updated using the new values of $f_s/f_d$ and branching fractions of normalisation channels. These results reduce a major source of systematic uncertainty in several searches for new physics performed through measurements of $B^0_s$ branching fractions. All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2020-046.html (LHCb public pages)

The branching fractions of the decay $B^{+} \to p \bar p K^{+}$ for different intermediate states are measured using data, corresponding to an integrated luminosity of $1.0 fb^{-1}$, collected by the LHCb experiment. The total branching fraction, its charmless component $(M_{p\bar p} <2.85 {GeV/}c^{2})$ and the branching fractions via the resonant $c\bar c$ states $��_{c}(1S)$ and $��(2S)$ relative to the decay via a $J/��$ intermediate state are {align*} \frac{{\mathcal B}(B^{+} \to p \bar p K^{+})_{total}}{{\mathcal B}(B^{+} \to J/��K^{+} \to p \bar p K^{+})}=& \, 4.91 \pm 0.19 \, {(\rm stat)} \pm 0.14 \, {(\rm syst)}, \frac{{\mathcal B}(B^{+} \to p \bar p K^{+})_{M_{p\bar p} <2.85 {GeV/}c^{2}}}{{\mathcal B}(B^{+} \to J/��K^{+} \to p \bar p K^{+})}=& \, 2.02 \pm 0.10 \, {(\rm stat)}\pm 0.08 \, {(\rm syst)}, \frac{{\mathcal B} (B^{+} \to ��_{c}(1S) K^{+} \to p \bar p K^{+})}{{\mathcal B}(B^{+} \to J/��K^{+} \to p \bar p K^{+})} = & \, 0.578 \pm 0.035 \, {(\rm stat)} \pm 0.027 \, {(\rm syst)}, \frac{{\mathcal B} (B^{+} \to ��(2S) K^{+} \to p \bar p K^{+})}{{\mathcal B}(B^{+} \to J/��K^{+} \to p \bar p K^{+})}=& \, 0.080 \pm 0.012 \, {(\rm stat)} \pm 0.009 \, {(\rm syst)}. {align*} Upper limits on the $B^{+}$ branching fractions into the $��_{c}(2S)$ meson and into the charmonium-like states X(3872) and X(3915) are also obtained. 14 pages, 5 figures

The relative rates of B-meson decays into J/ψ and ψ(2S) mesons are measured for the three decay modes in pp collisions recorded with the LHCb detector. The ratios of branching fractions ([Formula: see text]) are measured to be [Formula: see text] where the third uncertainty is from the ratio of the ψ(2S) and J/ψ branching fractions to μ+μ-.