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Measurement of $f_s / f_u$ variation with proton-proton collision energy and $B$-meson kinematics

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Abstract

The ratio of the $\mathrm{B}^0_\mathrm{s}$ and $\mathrm{B}^+$ fragmentation fractions $f_\mathrm{s}$ and $f_u$ is studied with $B^0_\mathrm{s}\to\mathrm{J}/\psi \phi $ and $B^+\to\mathrm{J}/\psi K^+$ decays using data collected by the LHCb experiment in proton-proton collisions at 7, 8 and 13$\text{ TeV}$ center-of-mass energies. The analysis is performed in bins of $\mathrm{B}$-meson momentum, longitudinal momentum, transverse momentum, pseudorapidity and rapidity. The fragmentation-fraction ratio $f_\mathrm{s} / f_u$ is observed to depend on the $\mathrm{B}$-meson transverse momentum with a significance of $6.0 \sigma$. This dependency is driven by the 13$\text{ TeV}$ sample ($8.7 \sigma$) while the results for the other collision energies are not significant when considered separately. Furthermore the results show a $4.8 \sigma$ evidence for an increase of $f_\mathrm{s} / f_u$ as a function of collision energy.

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Mass distributions of (a) $ B^+\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^+$ and (b) $ B^0_s\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$ candidates in the 2012 data. The result of the fit is drawn with a blue solid line. The model components are denoted with red dashed line for the signal, green dot-dashed line for the combinatorial background, magenta triple-dot-dashed line for misidentified $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^+$ and cyan triple-dot-dashed line for misidentified the inclusive $ B^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^+ \pi^-$ contribution.

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Efficiency-corrected $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi $ and $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ $ yield ratios ( $\mathcal{R}$ ) at different $ pp $ collision energies with the total (uncorrelated, including statistical) uncertainties denoted by dashed (solid) error bars. The fit result is shown with the blue solid line, the blue band denotes the $ 68\%$ confidence region. The 13 $\text{ Te V}$ measurements are shifted horizontally for clarity.

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Efficiency-corrected $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$ and $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ $ yield ratios ( $\mathcal{R}$ ) in bins of (a) $ { p_{\mathrm{T}} ^{ B }}$ , (c) $ {p_{\mathrm{L}}^{ B }}$ and (d) $ {\eta^{ B }}$ . The ratios are scaled to match the measured $ f_s/f_d$ value (horizontal blue lines, the $\pm1\sigma$ interval is indicated by the dashed blue lines) at the positions indicated by the vertical gray lines. The red dashed lines denote the results of the exponential fits used to estimate the statistical significances of the variations (see text). In (b) the results as a function of $ { p_{\mathrm{T}} ^{ B }}$ are obtained separately in the three collision energies.

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The $ B $ -meson mass distributions of (left column) $ B^+\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^+$ and (right column) $ B^0_s\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$ candidates in LHCb data collected in 2011, 2012, 2015, and 2016, shown from top to bottom in that order. The result of the fit is drawn with a blue solid line. The model components are denoted with the dashed lines: signal in red, combinatorial background in green, misidentified $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^+$ in magenta and the misidentified inclusive $ B^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^+ \pi^-$ contribution in light blue.

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Efficiency-corrected $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$ and $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ $ yield ratios ( $\mathcal{R}$ ) in bins of $ B $ -meson momentum $ { p ^{ B }}$ (left) and rapidity $ {y^{ B }}$ (right). The ratios are scaled to match the measured $ f_s/f_d$ value (horizontal blue lines, the $\pm1\sigma$ interval is indicated by the dashed blue lines) at the positions indicated by the vertical gray lines. The red dashed line denotes the result of the exponential fit used to estimate the statistical significance of the variation (see text), and the red band denotes the $ 68\%$ confidence region.

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Efficiency-corrected $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$ and $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ $ yield ratios ( $\mathcal{R}$ ) in bins of $ B $ -meson transverse momentum $ { p_{\mathrm{T}} ^{ B }}$ , shown for the $ B $ -meson longitudinal-momentum ranges: (top) low range ([0,75) $\text{ Ge V /}c$ ), (middle) medium range ([75,125) $\text{ Ge V /}c$ ), and (bottom) high range ([125,700] $\text{ Ge V /}c$ ). The ratios are scaled to match the measured $ f_s/f_d$ value (horizontal blue lines, the $\pm1\sigma$ interval is indicated by the dashed blue lines) at the positions indicated by the vertical gray lines. The red dashed line denotes the result of the exponential fit used to estimate the variation (see text), and the red band denotes the $ 68\%$ confidence region.

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Efficiency-corrected $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$ and $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ $ yield ratios ( $\mathcal{R}$ ) in bins of $ {\Delta y} $ for different samples. The ratios are scaled to match the measured $ f_s/f_d$ value.

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Tables and captions

Efficiency-corrected $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$ and $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ $ yield ratios ( $\mathcal{R}$ ) and uncertainties ($\sigma_{\rm{tot}}$), including the statistical uncertainty ($\sigma_{\rm{stat}}$) and the fully correlated and uncorrelated systematic uncertainties among the samples ($\sigma^{\rm{uncor}}_{\rm{syst}}$, $\sigma^{\rm{cor}}_{\rm{syst}}$). Individual contributions from tracking efficiency ($\sigma^{\rm{track}}_{\rm{syst}}$), acceptance, reconstruction and selection efficiency ($\sigma^{\rm{sel}}_{\rm{syst}}$) and fit model ($\sigma^{\rm{fit}}_{\rm{syst}}$) are shown separately. Correlations stem from the common tracking and fit model uncertainties.

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The efficiency-corrected yield ratio ($\mathcal{R}$) in bins of $ B $ -meson transverse momentum in (a) low, (b) medium, and (c) high $ B $ -meson longitudinal-momentum regions. Uncertainties include both statistical and systematic sources.

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The measured efficiency-corrected yield ratio ($\mathcal{R}$) in bins of the kinematic variables. Uncertainties include both statistical and systematic sources.

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Efficiency-corrected $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$ and $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ $ yield ratios in bins of $ B $ -meson transverse momentum $ { p_{\mathrm{T}} ^{ B }}$ , separately for the three $ pp$ collision energies.

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Supplementary Material [file]

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This ZIP file contains supplemetary material for the publication LHCb-PAPER-2019-020. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps : The figures in variuous formats

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Created on 19 February 2021.