Measurements of $ f_s/f_d$ sensitive observables as a function of the $ B $ -meson transverse momentum, $ p_{\mathrm{T}}$ , overlaid with the fit function. The scaling factors $r_{AF}$ and $r_{E}$ are defined in the text; the variable $\mathcal{R}$ is defined in Eq. 4. The vertical axes are zero-suppressed. The uncertainties on the data points are fully independent of each other; overall uncertainties for measurements in multiple $ p_{\mathrm{T}}$ intervals are propagated via scaling parameters, as described in the text. The band associated with the fit function shows the uncertainty on the post-fit function for each sample.

Efficiency correction versus effective lifetime hypothesis for the $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi } \phi$ branching fraction. The band shows the uncertainty on the correction due to the simulated sample size for a given effective lifetime.

Fragmentation fraction ratio $ f_s/f_d$ as a function of proton-proton centre-of-mass energy.

Measurements of $ f_s/f_d$ sensitive observables as a function of the $ B $ -meson transverse momentum, $ p_{\mathrm{T}}$ , overlaid with the fit function. A Tsallis-statistics inspired function is used in this plot as described in the text. The scaling factors $r_{AF}$ and $r_{E}$ are defined in the text; the variable $\mathcal{R}$ is defined in Eq. 4. The vertical axes are zero-suppressed. The uncertainties on the data points are fully independent of each other; overall uncertainties for measurements in multiple $ p_{\mathrm{T}}$ intervals are propagated through scaling parameters, as described in the text. The band associated with the fit function shows the uncertainty on the post-fit function for each sample.

Animated gif made out of all figures.

Five sets of measurements by the LHCb experiment combined in this paper and their sensitivity to fragmentation fractions and branching fractions.

External inputs used in the hadronic and semileptonic analyses updated with respect to previous publications. The value of $\mathcal{N}_E$ is updated using Ref. [7]. The values of CKM matrix elements ratio $|V_{us}| / |V_{ud}|$ and of the meson decay constants' ratio $f_K/f_\pi$ are the same as in Ref. [9].

Observables and related parameters of the default fit. See text for a detailed explanation.

The branching fractions of $ B ^0$ and $ B ^+$ normalisation channel decays used to update previous measurements of $ B ^0_ s $ branching fractions, as reported in Ref. [7] for all but the $ B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi } K ^{*0} $ branching fraction, which is taken from the amplitude analysis in Ref [51], and corrected for the relative production fraction of $ B ^+$ and $ B ^0$ mesons at $ B $ Factories [50].

Updated branching fractions of rare $ B ^0_ s $ decays. The uncertainties are statistical, systematic, due to $ f_s/f_d$ , and due to the normalisation branching fraction. The $ B ^0_ s \rightarrow \phi\mu ^+\mu ^- $ branching fractions in different $q^2$ intervals, where $q^2$ is defined as dimuon invariant mass squared in $\text{ Ge V /}c^2$ , are normalised with respect to $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi } \phi$ . Results with the $\star$ symbol have had their normalisation branching fraction updated as well.

Updated branching fractions of $ B ^0_ s $ decays with charmonia in the final state. The uncertainties are statistical, systematic, due to $ f_s/f_d$ , and due to the normalisation branching fraction. The second, third and fourth set of branching fractions are normalised to $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi } \phi$ , $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi } \eta^{(')}$, $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi } \pi ^+ \pi ^- $ , respectively, and their third uncertainty covers the full normalisation uncertainty. Results with the $\star$ symbol have had their normalisation branching fraction updated as well.

Updated branching fractions of $ B ^0_ s $ decays with a charmless final state. The uncertainties are statistical, systematic, due to $ f_s/f_d$ , and due to the normalisation branching fraction. The last two branching fractions are normalised with respect to $ B ^0_ s \rightarrow \phi\phi$ , and their third uncertainty covers the full normalisation uncertainty. Results with the $\star$ symbol have had their normalisation branching fraction updated as well.

Updated branching fractions of $ B ^0_ s $ decays to open-charm final states. The uncertainties are statistical, systematic, due to $ f_s/f_d$ , and due to the normalisation branching fraction. The $ B ^0_ s \rightarrow D ^{\mp}_ s K ^\pm $ , $ B ^0_ s \rightarrow D ^-_ s \pi ^+ \pi ^- \pi ^+ $ and $ B ^0_ s \rightarrow D ^-_ s K ^+ \pi ^- \pi ^+ , B ^0_ s \rightarrow D _{ s 1}(2536)^- \pi ^+ $ branching fractions are normalised with respect to $ B ^0_ s \rightarrow D ^-_ s \pi ^+ $ and $ B ^0_ s \rightarrow D ^-_ s \pi ^+ \pi ^- \pi ^+ $ , respectively, and their third uncertainty covers the full normalisation uncertainty. Results with the $\star$ symbol have had their normalisation branching fraction updated as well.

Output parameters of the default fit to the data.

Output parameters of the fit to the data without external theory constraints.

Output correlation matrix of the default fit versus $ p_{\mathrm{T}}$ .

Output correlation matrix of the fit versus $ p_{\mathrm{T}}$ without theory constraints.