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| CMS-BPH-21-007 ; CERN-EP-2025-176 | ||
| Measurement of $ {\mathrm{B}} $ meson production fraction ratios in proton-proton collisions at $ \sqrt{s} = $ 13 TeV using open-charm and charmonium decays | ||
| CMS Collaboration | ||
| 10 February 2026 | ||
| Submitted to Physical Review D | ||
| Abstract: Production fraction ratios of $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ mesons are measured in proton-proton collisions at $ \sqrt{s} = $ 13 TeV using a special data set recorded in 2018 with high-rate triggers designed to collect an unbiased sample of $ 10^{10} \mathrm{b} $ hadrons with the CMS experiment at the LHC\@. These data allow the use of the open-charm decays of $ {\mathrm{B}} $ mesons ($ {\mathrm{B}}_{(\mathrm{s})} \!\to\! \pi\mathrm{D}_{(\mathrm{s})} $) where the $ \mathrm{D} $ meson decays into fully hadronic final states. Production fraction ratios as functions of $ {\mathrm{B}} $ meson transverse momentum ($ p_{\mathrm{T}} $) and rapidity ($ y $) are measured using the open-charm decays in the kinematic range of 8 $ < p_{\mathrm{T}} < $ 60 GeV and $ |y| < $ 2.25. In addition, the same data are used to measure the relative production fraction ratios with the charmonium decay channels ($ {\mathrm{B}}_{(\mathrm{s})} \!\to\! \mathrm{X}{\mathrm{J}/\psi} $ with $ \mathrm{X} $ indicating a $ \mathrm{K^+} $, $ \mathrm{K^*}(892)^0 $, or $ \phi(1020) $ meson) with the $ {\mathrm{J}/\psi} $ meson decaying into a pair of muons. By utilizing known branching fractions, precision theoretical calculations, and the open-charm results, the production fraction ratios in the charmonium samples are determined with an absolute normalization for the first time. These results also improve several world-average values of the ratios of branching fractions of $ {\mathrm{B}} $ meson decays to charmonium and open-charm states. Finally, we test isospin invariance in $ {\mathrm{B}} $ meson production in proton-proton collisions and observe that it holds within the experimental precision. | ||
| Links: e-print arXiv:2602.1027 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Representative Feynman diagrams for the open-charm (upper) and charmonium (lower) decays of the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ mesons. |
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Figure 1-a:
Representative Feynman diagrams for the open-charm (upper) and charmonium (lower) decays of the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ mesons. |
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Figure 1-b:
Representative Feynman diagrams for the open-charm (upper) and charmonium (lower) decays of the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ mesons. |
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Figure 2:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution (corrected by the $ \mathrm{D} $ meson mass) used to extract the signal in the open-charm channels. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
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Figure 2-a:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution (corrected by the $ \mathrm{D} $ meson mass) used to extract the signal in the open-charm channels. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
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Figure 2-b:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution (corrected by the $ \mathrm{D} $ meson mass) used to extract the signal in the open-charm channels. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
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Figure 2-c:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution (corrected by the $ \mathrm{D} $ meson mass) used to extract the signal in the open-charm channels. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
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Figure 3:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution used to extract the signal in the charmonium channels of the tag-side analysis. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
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Figure 3-a:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution used to extract the signal in the charmonium channels of the tag-side analysis. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
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Figure 3-b:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution used to extract the signal in the charmonium channels of the tag-side analysis. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
png pdf |
Figure 3-c:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution used to extract the signal in the charmonium channels of the tag-side analysis. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
png pdf |
Figure 4:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution used to extract the signal in the charmonium channels of the probe-side analysis. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
png pdf |
Figure 4-a:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution used to extract the signal in the charmonium channels of the probe-side analysis. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
png pdf |
Figure 4-b:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution used to extract the signal in the charmonium channels of the probe-side analysis. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
png pdf |
Figure 4-c:
Examples of fits to the $ {\mathrm{B}} $ candidate mass distribution used to extract the signal in the charmonium channels of the probe-side analysis. The upper, middle, and lower plots correspond to the $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ decays, respectively. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) of the fit is shown in each plot. The lower panels illustrate the pull, defined as the deviation of data from the fit function, normalized by the statistical uncertainty in each bin. |
png pdf |
Figure 5:
The production fraction ratios $ f_\mathrm{s}/f_\mathrm{d} $ (upper row) and $ f_\mathrm{s}/f_\mathrm{u} $ (lower row) as functions of $ p_{\mathrm{T}} $ (left column) and $ |y| $ (right column), measured using open-charm decays. The vertical error bars show the combined statistical and bin-to-bin uncorrelated systematic uncertainty. The global uncertainties are not included. The red line is the average over the full reconstructed kinematic range, and the blue dashed line is the linear fit result. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) values for the constant fit and linear fit are given. Parameters inside angle brackets are averages over $ p_{\mathrm{T}} $ where the absolute normalization may be affected by the $ p_{\mathrm{T}} $ dependence. |
png pdf |
Figure 5-a:
The production fraction ratios $ f_\mathrm{s}/f_\mathrm{d} $ (upper row) and $ f_\mathrm{s}/f_\mathrm{u} $ (lower row) as functions of $ p_{\mathrm{T}} $ (left column) and $ |y| $ (right column), measured using open-charm decays. The vertical error bars show the combined statistical and bin-to-bin uncorrelated systematic uncertainty. The global uncertainties are not included. The red line is the average over the full reconstructed kinematic range, and the blue dashed line is the linear fit result. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) values for the constant fit and linear fit are given. Parameters inside angle brackets are averages over $ p_{\mathrm{T}} $ where the absolute normalization may be affected by the $ p_{\mathrm{T}} $ dependence. |
png pdf |
Figure 5-b:
The production fraction ratios $ f_\mathrm{s}/f_\mathrm{d} $ (upper row) and $ f_\mathrm{s}/f_\mathrm{u} $ (lower row) as functions of $ p_{\mathrm{T}} $ (left column) and $ |y| $ (right column), measured using open-charm decays. The vertical error bars show the combined statistical and bin-to-bin uncorrelated systematic uncertainty. The global uncertainties are not included. The red line is the average over the full reconstructed kinematic range, and the blue dashed line is the linear fit result. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) values for the constant fit and linear fit are given. Parameters inside angle brackets are averages over $ p_{\mathrm{T}} $ where the absolute normalization may be affected by the $ p_{\mathrm{T}} $ dependence. |
png pdf |
Figure 5-c:
The production fraction ratios $ f_\mathrm{s}/f_\mathrm{d} $ (upper row) and $ f_\mathrm{s}/f_\mathrm{u} $ (lower row) as functions of $ p_{\mathrm{T}} $ (left column) and $ |y| $ (right column), measured using open-charm decays. The vertical error bars show the combined statistical and bin-to-bin uncorrelated systematic uncertainty. The global uncertainties are not included. The red line is the average over the full reconstructed kinematic range, and the blue dashed line is the linear fit result. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) values for the constant fit and linear fit are given. Parameters inside angle brackets are averages over $ p_{\mathrm{T}} $ where the absolute normalization may be affected by the $ p_{\mathrm{T}} $ dependence. |
png pdf |
Figure 5-d:
The production fraction ratios $ f_\mathrm{s}/f_\mathrm{d} $ (upper row) and $ f_\mathrm{s}/f_\mathrm{u} $ (lower row) as functions of $ p_{\mathrm{T}} $ (left column) and $ |y| $ (right column), measured using open-charm decays. The vertical error bars show the combined statistical and bin-to-bin uncorrelated systematic uncertainty. The global uncertainties are not included. The red line is the average over the full reconstructed kinematic range, and the blue dashed line is the linear fit result. The $ \chi^2 $ per degree of freedom ($ \chi^2/\mathrm{ndof} $) values for the constant fit and linear fit are given. Parameters inside angle brackets are averages over $ p_{\mathrm{T}} $ where the absolute normalization may be affected by the $ p_{\mathrm{T}} $ dependence. |
png pdf |
Figure 6:
The relative production fraction ratios $ \mathcal{R}_\mathrm{s} $ (upper row) and $ \mathcal{R}_\mathrm{s}^\mathrm{d} $ (lower row) as functions of $ p_{\mathrm{T}} $ (left column) and $ |y| $ (rigtht column), measured using charmonium decays. For comparison, the recent CMS [7] and LHCb [4] measurements are also presented. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. Values enclosed in angle brackets represent averages over $ p_{\mathrm{T}} $, where the absolute normalization may be affected by the $ p_{\mathrm{T}} $ dependence. |
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Figure 6-a:
The relative production fraction ratios $ \mathcal{R}_\mathrm{s} $ (upper row) and $ \mathcal{R}_\mathrm{s}^\mathrm{d} $ (lower row) as functions of $ p_{\mathrm{T}} $ (left column) and $ |y| $ (rigtht column), measured using charmonium decays. For comparison, the recent CMS [7] and LHCb [4] measurements are also presented. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. Values enclosed in angle brackets represent averages over $ p_{\mathrm{T}} $, where the absolute normalization may be affected by the $ p_{\mathrm{T}} $ dependence. |
png pdf |
Figure 6-b:
The relative production fraction ratios $ \mathcal{R}_\mathrm{s} $ (upper row) and $ \mathcal{R}_\mathrm{s}^\mathrm{d} $ (lower row) as functions of $ p_{\mathrm{T}} $ (left column) and $ |y| $ (rigtht column), measured using charmonium decays. For comparison, the recent CMS [7] and LHCb [4] measurements are also presented. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. Values enclosed in angle brackets represent averages over $ p_{\mathrm{T}} $, where the absolute normalization may be affected by the $ p_{\mathrm{T}} $ dependence. |
png pdf |
Figure 6-c:
The relative production fraction ratios $ \mathcal{R}_\mathrm{s} $ (upper row) and $ \mathcal{R}_\mathrm{s}^\mathrm{d} $ (lower row) as functions of $ p_{\mathrm{T}} $ (left column) and $ |y| $ (rigtht column), measured using charmonium decays. For comparison, the recent CMS [7] and LHCb [4] measurements are also presented. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. Values enclosed in angle brackets represent averages over $ p_{\mathrm{T}} $, where the absolute normalization may be affected by the $ p_{\mathrm{T}} $ dependence. |
png pdf |
Figure 6-d:
The relative production fraction ratios $ \mathcal{R}_\mathrm{s} $ (upper row) and $ \mathcal{R}_\mathrm{s}^\mathrm{d} $ (lower row) as functions of $ p_{\mathrm{T}} $ (left column) and $ |y| $ (rigtht column), measured using charmonium decays. For comparison, the recent CMS [7] and LHCb [4] measurements are also presented. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. Values enclosed in angle brackets represent averages over $ p_{\mathrm{T}} $, where the absolute normalization may be affected by the $ p_{\mathrm{T}} $ dependence. |
png pdf |
Figure 7:
The production fraction ratios $ f_\mathrm{d}/f_\mathrm{u} $ as functions of $ p_{\mathrm{T}} $ (left) and $ |y| $ (right) measured using both the open-charm and charmonium decays, without an assumption of isospin invariance. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. The global uncertainties of 5.7% for the open-charm analysis 4.8% for both charmonium analyses are not shown. |
png pdf |
Figure 7-a:
The production fraction ratios $ f_\mathrm{d}/f_\mathrm{u} $ as functions of $ p_{\mathrm{T}} $ (left) and $ |y| $ (right) measured using both the open-charm and charmonium decays, without an assumption of isospin invariance. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. The global uncertainties of 5.7% for the open-charm analysis 4.8% for both charmonium analyses are not shown. |
png pdf |
Figure 7-b:
The production fraction ratios $ f_\mathrm{d}/f_\mathrm{u} $ as functions of $ p_{\mathrm{T}} $ (left) and $ |y| $ (right) measured using both the open-charm and charmonium decays, without an assumption of isospin invariance. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. The global uncertainties of 5.7% for the open-charm analysis 4.8% for both charmonium analyses are not shown. |
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Figure 8:
Comparison of the $ f_\mathrm{d}/f_\mathrm{u} $ measurements across different channels. The ``Combined'' value, shown above the black dashed line, is obtained from a combined $ \chi^{2} $ fit of the measurements from two statistically independent channels: the open-charm and tag-side charmonium. Additionally, the plot presents the previous CMS result [7] for comparison. The blue dashed line at unity corresponds to $ f_{\mathrm{d}} = f_{\mathrm{u}} $. |
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Figure 9:
The $ \mathcal{R}_\mathrm{s}^\mathrm{d} $ and $ \mathcal{R}_\mathrm{s} $ values measured in the charmonium analysis, converted to $ f_\mathrm{s}/f_\mathrm{d} $ (left) and $ f_\mathrm{s}/f_\mathrm{u} $ (right) using the absolute normalizations $ c_{\mathrm{s}\mathrm{d}} $ and $ c_{\mathrm{s}\mathrm{u}} $, respectively. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. For comparison, PFR measurements from the open-charm analysis, LEP [47], and CMS [7] (converted to $ f_\mathrm{s}/f_\mathrm{u} $ using $ c_{\mathrm{s}\mathrm{u}} $) are overlaid, along with the $ p_{\mathrm{T}} $ trend of $ f_\mathrm{s}/f_\mathrm{d} $ observed by LHCb [5] with its uncertainties displayed as the gray band. The $ f_\mathrm{s}/f_\mathrm{d} $ ($ f_\mathrm{s}/f_\mathrm{u} $) global uncertainties are 6.3% (7.4%) for the open-charm channel and 8.4% (8.9%) for both the charmonium channel and the previous CMS result. |
png pdf |
Figure 9-a:
The $ \mathcal{R}_\mathrm{s}^\mathrm{d} $ and $ \mathcal{R}_\mathrm{s} $ values measured in the charmonium analysis, converted to $ f_\mathrm{s}/f_\mathrm{d} $ (left) and $ f_\mathrm{s}/f_\mathrm{u} $ (right) using the absolute normalizations $ c_{\mathrm{s}\mathrm{d}} $ and $ c_{\mathrm{s}\mathrm{u}} $, respectively. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. For comparison, PFR measurements from the open-charm analysis, LEP [47], and CMS [7] (converted to $ f_\mathrm{s}/f_\mathrm{u} $ using $ c_{\mathrm{s}\mathrm{u}} $) are overlaid, along with the $ p_{\mathrm{T}} $ trend of $ f_\mathrm{s}/f_\mathrm{d} $ observed by LHCb [5] with its uncertainties displayed as the gray band. The $ f_\mathrm{s}/f_\mathrm{d} $ ($ f_\mathrm{s}/f_\mathrm{u} $) global uncertainties are 6.3% (7.4%) for the open-charm channel and 8.4% (8.9%) for both the charmonium channel and the previous CMS result. |
png pdf |
Figure 9-b:
The $ \mathcal{R}_\mathrm{s}^\mathrm{d} $ and $ \mathcal{R}_\mathrm{s} $ values measured in the charmonium analysis, converted to $ f_\mathrm{s}/f_\mathrm{d} $ (left) and $ f_\mathrm{s}/f_\mathrm{u} $ (right) using the absolute normalizations $ c_{\mathrm{s}\mathrm{d}} $ and $ c_{\mathrm{s}\mathrm{u}} $, respectively. The error bars include both statistical and bin-to-bin uncorrelated systematic uncertainties. For comparison, PFR measurements from the open-charm analysis, LEP [47], and CMS [7] (converted to $ f_\mathrm{s}/f_\mathrm{u} $ using $ c_{\mathrm{s}\mathrm{u}} $) are overlaid, along with the $ p_{\mathrm{T}} $ trend of $ f_\mathrm{s}/f_\mathrm{d} $ observed by LHCb [5] with its uncertainties displayed as the gray band. The $ f_\mathrm{s}/f_\mathrm{d} $ ($ f_\mathrm{s}/f_\mathrm{u} $) global uncertainties are 6.3% (7.4%) for the open-charm channel and 8.4% (8.9%) for both the charmonium channel and the previous CMS result. |
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Figure 10:
Comparison of the $ f_\mathrm{s}/f_\mathrm{u} $ measurements at high $ p_{\mathrm{T}} $ ($ p_{\mathrm{T}} > $ 18 GeV) across different channels. The blue dashed line and shaded band represent the LEP measurement and its uncertainty [47], respectively, included for comparison. The $ \mathcal{R}_\mathrm{s} $ values obtained in the charmonium analysis in the tag-side category and the previous CMS measurement [7] are converted to $ f_\mathrm{s}/f_\mathrm{u} $ using the absolute normalization factor $ c_{\mathrm{s}\mathrm{u}} $. |
| Tables | |
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Table 1:
Summary of the single-muon $ {\mathrm{B}} $ parking triggers used in this analysis. |
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Table 2:
Inputs for the open-charm PFR measurements. |
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Table 3:
Summary of the preselection requirements for $ {\mathrm{B}} $ candidates in the open-charm analysis. The $ \text{---} $ entries indicate that the selection does not apply to this channel. |
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Table 4:
Summary of the selection requirements for $ {\mathrm{B}} $ candidates in the charmonium analysis. The $ \text{---} $ entries indicate that the selection does not apply to this channel. |
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Table 5:
Fit functions used in the open-charm and charmonium analyses. The $ \text{---} $ entries indicate that the background does not apply to this channel. |
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Table 6:
Summary of MC corrections for the open-charm and charmonium channels. |
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Table 7:
Sources and values of the systematic uncertainties affecting the measured PFRs in the open-charm analysis. The bin-to-bin-uncorrelated uncertainties are presented as ranges, which indicate the range of uncertainties across different $ p_{\mathrm{T}} $ and $ |y| $ bins. The $ \text{---} $ entries indicate that the uncertainty does not apply. The reported values are the relative systematic uncertainties in percent. |
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Table 8:
Sources of bin-to-bin uncorrelated systematic uncertainty affecting the measured $ \mathcal{R}_\mathrm{s} $, $ \mathcal{R}_\mathrm{s}^\mathrm{d} $, and $ f_\mathrm{d}/f_\mathrm{u} $ values for the tag-side and probe-side categories in the charmonium analysis. The uncertainties are presented as ranges, which indicate the range of the uncertainties across different $ p_{\mathrm{T}} $ and $ |y| $ bins. The $ \text{---} $ entries indicate that the uncertainty does not apply. The reported values are the relative systematic uncertainty in percent. |
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Table 9:
Summary of the channels employed in each measurement of $ f_\mathrm{s}/f_\mathrm{u} $, $ f_\mathrm{s}/f_\mathrm{d} $, $ \mathcal{R}_\mathrm{s} $, $ \mathcal{R}_\mathrm{s}^\mathrm{d} $, $ f_\mathrm{d}/f_\mathrm{u} $, and in determining the absolute normalizations for $ \mathcal{R}_\mathrm{s} $ and $ \mathcal{R}_\mathrm{s}^\mathrm{d} $. The $ \text{---} $ entries indicate the channel is not included. |
| Summary |
| In summary, the relative production fractions of $ {\mathrm{B}^{+}} $, $ {\mathrm{B}^0} $, and $ \mathrm{B}_{s}^{0} $ mesons have been measured in proton-proton collisions at $ \sqrt{s} = $ 13 TeV using a special data set recorded in 2018 with the CMS experiment at the LHC, corresponding to an integrated luminosity of 41.6 fb$^{-1}$. This data set, collected with high-rate triggers, provided an unprecedented unbiased sample of $ 10^{10} \mathrm{b} $ hadrons. Production fraction ratios as functions of $ {\mathrm{B}} $ meson transverse momentum and absolute rapidity were measured using open-charm decays in the range of 8 $ < p_{\mathrm{T}} < $ 60 GeV and $ |y| < $ 2.25. The same data set was also used to measure these ratios in the charmonium decay channels, with the $ {\mathrm{J}/\psi} $ meson decaying into a pair of muons, to determine the dependence of these ratios on $ {\mathrm{B}} $ meson kinematics. We also reported PFR values averaged over $ p_{\mathrm{T}} $. The absolute normalization from the charmonium to open-charm channels is determined using known branching fractions, precision theoretical calculations, and the corresponding charmonium and open-charm results. This normalization is constructed as a double ratio of the two analyses, thereby canceling any potential $ p_{\mathrm{T}} $ dependence of the production fraction ratios. This makes these quantities universal constants that can be applied to any charmonium analysis and allows, for the first time, the extraction of production fraction ratios in the charmonium channels with an absolute normalization, rather than just as a shape measurement. The measurements are also used to extract $ {\mathrm{B}^{+}} $, $ \mathrm{B}_{s}^{0} $, and $ {\mathrm{B}^0} $ branching fraction ratios of open-charm decays to charmonium decays, improving by $ \approx 40% $ upon the precision of the world-average value for the $ \mathrm{B}_{s}^{0} $ decays. |
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