EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2019-209 LHCb-PAPER-2019-020

Measurement of $f_{s}/f_{u}$ variation with proton-proton collision energy and
$B$-meson kinematics

LHCb collaboration†††Authors are listed at the end of this Letter.

The ratio of the ${B}^{0}_{s}$ and ${B}^{+}$ fragmentation fractions $f_{s}$
and $f_{u}$ is studied with
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ and
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$ decays
using data collected by the LHCb experiment in proton-proton collisions at 7,
8 and 13 TeV center-of-mass energies. The analysis is performed in bins of
$B$-meson momentum, longitudinal momentum, transverse momentum, pseudorapidity
and rapidity. The fragmentation-fraction ratio $f_{s}/\kern-1.00006ptf_{u}$ is
observed to depend on the $B$-meson transverse momentum with a significance of
$6.0\,\sigma$. This dependency is driven by the 13 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 $f_{s}/\kern-1.00006ptf_{u}$ as a function of collision
energy.

Published in Phys. Rev. Lett. 124 (2020) 122002

© 2024 CERN for the benefit of the LHCb collaboration. CC-BY-4.0 licence.

The proton-proton ($pp$) collisions at the LHC produce copious pairs of $b$
and $\overline{b}$ quarks, which immediately hadronize into the full spectrum
of $b$ hadrons. The knowledge of $b$-hadron production rates is crucial in
order to measure their branching fractions.

The fragmentation fractions $f_{u}$, $f_{d}$, $f_{s}$, and $f_{\rm baryon}$
are defined as probabilities for a $b$ quark to hadronize into a ${B}^{+}$,
${B}^{0}$, ${B}^{0}_{s}$ meson or a $b$ baryon, respectively.111The inclusion
of the charge-conjugate modes is implied throughout this Letter. These include
all possible contributions from intermediate states decaying to the mentioned
hadrons via strong or electromagnetic interaction. The $b$-hadron
fragmentation fractions were first measured in $e^{+}e^{-}$ collisions at the
$Z$ resonance by LEP experiments [1, 2, 3, 4] and in ${p}{\overline{p}}$
collisions at $\sqrt{s}=1.8\text{\,Te\kern-1.00006ptV}$ center-of-mass energy
by the CDF experiment [5]. In the absence of contradicting evidence the
fragmentation fractions determined in different collision environments were
considered universal and averaged [6].

More recent measurements have shown that the hadronization fraction ratio
$f_{{{\mathchar 28931\relax}^{0}_{b}}}/f_{d}$ depends strongly on the
$p_{\mathrm{T}}$ and pseudorapidity of the produced $b$ hadron [7, 8, 9].
Evidence has also been seen for a dependence on ${p_{\mathrm{T}}^{{B}}}$ of
the relative ${B}^{0}_{s}$ and ${B}^{0}$ meson production, $f_{s}/f_{d}$ [10].
In combination with changes in the produced $b$-quark spectra it could lead to
modified fragmentation fraction ratios at higher $pp$ collision energies and
therefore affect the branching fraction measurements which rely on
normalization.

This analysis studies the relative ${B}^{0}_{s}$ and ${B}^{+}$ meson
production, $f_{s}/\kern-1.00006ptf_{u}$, dependence on $pp$ collision energy
and on the kinematics of the produced $b$ hadron. Measuring the relative
production is not only important for the studies of underlying QCD;
$f_{s}/\kern-1.00006ptf_{u}$ represents also an essential input and a dominant
source of systematic uncertainty in $B$ branching-fraction measurements
performed in hadron colliders, e.g.
${{B}^{0}_{s}}\\!\rightarrow{\mu^{+}}{\mu^{-}}$ [11, 12].

The analysis is performed on four independent data samples collected with the
LHCb detector at three $pp$ collision energies: at
$\sqrt{s}=7\text{\,Te\kern-1.00006ptV}$ in the year 2011 (corresponding to
$1\text{\,fb}^{-1}$), $8\text{\,Te\kern-1.00006ptV}$ in 2012
($2\text{\,fb}^{-1}$) and at $13\text{\,Te\kern-1.00006ptV}$ in the years 2015
($0.3\text{\,fb}^{-1}$) and 2016 ($1.1\text{\,fb}^{-1}$). The relative
production of ${B}^{0}_{s}$ mesons to ${B}^{+}$ mesons in the detector
acceptance is measured in each sample with the ratio of efficiency-corrected
yields of ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ and
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ decays

$\mathcal{R}\equiv\frac{N({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi)}{N({{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})}\cdot\frac{\epsilon({{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})}{\epsilon({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi)}\propto\frac{f_{s}}{f_{u}},$ (1)

where ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-}$ and $\phi\rightarrow K^{+}K^{-}$. Here $N$
denotes the selected and reconstructed candidate yield and $\epsilon$ the
related efficiency.

The study is further extended to the relative productions as a function of
$B$-meson kinematic variables: momentum (${p^{{B}}}$), transverse momentum
(${p_{\mathrm{T}}^{{B}}}$), longitudinal momentum (${p_{\mathrm{L}}^{{B}}}$),
pseudorapidity (${\eta^{{B}}}$) and rapidity (${y^{{B}}}$).222The longitudinal
momentum component is the momentum component along the beam direction. Due to
the large uncertainty on the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ branching fraction333In Ref. [13] the ratio $\mathcal{R}$ was
converted to an absolute $f_{s}/f_{d}$ value using a theoretical prediction
for the ratio of the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and $B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{\ast 0}$ branching fractions [14]. In this Letter Ref. [14] is not
used due to disputed theoretical uncertainties arising from factorization
assumption. no attempt is made to measure the absolute
$f_{s}/\kern-1.00006ptf_{u}$ value. In the different context of light and
strange hadrons, the ALICE experiment has observed a dependence of their
production ratios on the multiplicity of the event [15, 16, 17]. In this
analysis this dependence is not studied, owing to technical reasons; however
such behavior will be subject of future studies.

The LHCb detector [18, 19] is a single-arm forward spectrometer covering the
(final-state track) pseudorapidity range $2<\eta<5$, largely complementary to
the other LHC experiments. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet, three stations of silicon-strip detectors and straw drift tubes
located downstream of the magnet. Particle identification is provided by two
ring-imaging Cherenkov detectors, an electromagnetic and a hadronic
calorimeter, and a muon system composed of alternating layers of iron and
multi-wire proportional chambers.

The online event selection is performed by a two-stage trigger and relies on
muon candidate tracks. The first level (hardware) trigger decision is based on
information from the muon systems and selects events containing at least one
muon with a large $p_{\mathrm{T}}$ or a pair of muons with a large product of
their transverse momenta ($\sqrt{p_{\mathrm{T}}\cdot
p_{\mathrm{T}}^{\prime}}$). The trigger thresholds vary between $1$ and
$2\text{\,Ge\kern-1.00006ptV\\!/}c$, depending on the data-taking conditions.

The second level (software) trigger reconstructs the full event, looks for
dimuon vertices and requires them to be significantly displaced from any
primary vertex (PV). At least one of the tracks must have
$p_{\mathrm{T}}>1\text{\,Ge\kern-1.00006ptV\\!/}c$ and be inconsistent with
originating from any PV. Only events in which the trigger decision was based
on the muon tracks from the signal candidates are kept. The muon candidates
are required to pass the muon identification criteria [20]. No additional
particle identification is required on the kaon candidates.

Offline, the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ candidates are
reconstructed by combining two oppositely charged muon tracks originating from
the same vertex. The $\phi(1020)$ candidates are reconstructed from the decays
to the $K^{+}K^{-}$ final state. The
${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}$
(${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$) candidates are built by combining the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ candidates with a ${K}^{+}$
($\phi$) candidate. Prompt combinatorial background is suppressed by removing
the events in which the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$
vertex fit $\chi^{2}$, $B$ vertex impact-parameter or
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ vertex distance, indicate
that the decay vertex is either poorly reconstructed or close to the PV. No
further selection is applied on the reconstructed $\phi$ vertex in order to
minimize the differences between the two signal-channel selections. Only
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ ($\phi$) candidates with mass
within $\pm 60\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ ($\pm
10\text{\,Me\kern-1.00006ptV\\!/}c^{2}$) of the known
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ ($\phi$) masses [6] are kept;
these ranges are several times the mass resolutions of about
$16\text{\,Me\kern-1.00006ptV\\!/}c^{2}~{}(3.5\text{\,Me\kern-1.00006ptV\\!/}c^{2})$.

Signal track candidates with momenta
${p>500\text{\,Ge\kern-1.00006ptV\\!/}c}$, transverse momenta
${p_{\mathrm{T}}>40\text{\,Ge\kern-1.00006ptV\\!/}c}$ or pseudorapidity
outside of the range ${2<\eta<4.5}$ are removed. In addition, muon and $B$
transverse momenta are asked to pass
${p_{\mathrm{T}}>250\text{\,Me\kern-1.00006ptV\\!/}c}$ and
${{p_{\mathrm{T}}^{{B}}}>500\text{\,Me\kern-1.00006ptV\\!/}c}$ requirements,
respectively. The selected sample covers the following $B$ meson kinematic
range: ${20<{p^{{B}}}<700\text{\,Ge\kern-1.00006ptV\\!/}c}$,
${20<{p_{\mathrm{L}}^{{B}}}<700\text{\,Ge\kern-1.00006ptV\\!/}c}$,
${0.5<{p_{\mathrm{T}}^{{B}}}<40\text{\,Ge\kern-1.00006ptV\\!/}c}$,
${2.0<{\eta^{{B}}}<6.5}$ and ${2.0<{y^{{B}}}<4.5}$. The ${\eta^{{B}}}$ region
between $2.0$ and $2.5$ is also accessible to the ATLAS and CMS experiments
and thus important for comparison and combination of the results.

Simulated signal events are used to determine the detection efficiencies, to
estimate the background contamination and to model the mass distributions of
the selected candidates. The simulated $pp$ collisions are generated using
Pythia [21] with a specific LHCb configuration [22]. Hadron decays are
described by EvtGen [23] with final-state radiation generated using Photos
[24]. The particle interactions with the detector material and the detector
response are implemented using the Geant4 toolkit [25, 26]. The samples of
simulated signal events are corrected for known differences between data and
simulation [27] in bins of detector occupancy and kinematic variables. When
considering the ${B}^{0}_{s}$ over ${B}^{+}$ distribution ratio, the
consistency between data and simulation before correction corresponded to a
$p$-value of at least 14% in the kinematic variables and exceeding 90% in the
detector occupancy.

The signal yields are obtained by fitting the ${B}^{+}$ and ${B}^{0}_{s}$
candidate mass distributions, $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+})$ and $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}K^{-})$, in the $\pm 100\text{\,Me\kern-1.00006ptV\\!/}c^{2}$
range around the known mass values using independent extended unbinned
maximum-likelihood fits. To improve the mass resolution, the $B$-candidate
masses are computed with the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$
mass constrained to its known value [6].

The mass distributions are described with probability density functions (PDFs)
consisting of signal, combinatorial background and background due to pions or
protons that are wrongly identified as kaons. The signal components are
parameterized by Hypatia functions [28], which consist of hyperbolic cores and
power-law tails on both sides. The values of the parameters that define the
tails are determined from simulation. The combinatorial backgrounds in both
models are described by exponential PDFs. The means and widths of the signal
components and the slopes of the exponentials are unconstrained. The values
obtained in data are larger by 10% or less for the widths, and are consistent
for the means and the other shape parameters. The fits repeated with fixed
tails in the signal shape give consistent yield results to the constrained
fits used by default. The contribution due to misidentified
${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{+}$
decays in the $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+})$
distribution is described using a kernel density estimator technique [29]
applied to simulated events. Its fraction, relative to the signal
contribution, is found to be in agreement with the estimated fraction of
$(3.8\pm 0.1)\%$.

The dominant misidentified background in the
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}K^{-})$ distribution
arises from $B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}\pi^{-}$ decays where a pion is mistakenly reconstructed as a
kaon. The total inclusive
$B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}$
background is a combination of the resonant and nonresonant contributions in
the $K^{+}\pi^{-}$ final state:
$B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{\ast}(892)^{0}$ and
$B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}$.
The PDFs of these components are linked [30], each described by a combination
of two Crystal Ball functions [31] with a common Gaussian mean and tails on
opposite sides. The background component is included in the fit model with
yield fraction defined relative to the signal contribution and Gaussian
constrained to the expected value of ${(4.1\pm 0.5)\%}$, determined on
simulation. Contributions from the decays
$B^{+}_{c}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}K^{-}\pi^{+}$,
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\kern
1.79993pt\overline{\kern-1.79993ptK}}{}^{*0}}$, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK^{-}$,
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ ($\rightarrow$ ${{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{L}}}$)
and $B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}f_{0}(\rightarrow\pi^{+}\pi^{-})$ are considered and found negligible.
The fit results to the
${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}$
and ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ candidates in 2012 data are shown in Fig. 1. Fits to all the
samples are shown in the Supplemental Material (Appendix A).

\begin{overpic}[width=433.62pt,trim=0.0pt 0.0pt 0.0pt 0.0pt]{Fig1_a.pdf}
\put(19.0,50.0){\small(a)} \end{overpic}

\begin{overpic}[width=433.62pt,trim=0.0pt 0.0pt 0.0pt 0.0pt]{Fig1_b.pdf}
\put(19.0,50.0){\small(b)} \end{overpic}

Figure 1: Mass distributions of (a)
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$ and (b)
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$
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
${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{+}$
and cyan triple-dot-dashed line for misidentified the inclusive
$B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}$
contribution.

The signal detection efficiencies include the detector acceptance,
reconstruction efficiencies and the selection efficiencies. The efficiencies
are computed using simulated samples unless stated otherwise. Tracking
efficiency differences in data and simulation are corrected for. The
corrections are applied for each final-state track separately in bins of the
track $p_{\mathrm{T}}$ and $\eta$, and event multiplicity [32].

Trigger efficiencies are determined on data, separately for each data sample
[33]. The trigger decision in every event can be ascribed to the reconstructed
signal candidate and/or the rest of the event. The trigger efficiency is
measured through the overlap of the two categories [34]. The abundant
${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}$
sample is used to build a two-dimensional trigger efficiency map as a function
of the $p_{\mathrm{T}}$ and $p_{\mathrm{L}}$ of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates. The choice of
variables accounts for small differences in the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ kinematic distributions from
${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}$
and ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ decays. The average signal trigger efficiencies are computed by
weighting the map contents with the fractions of simulated events in each bin
and averaging the results, separately for each signal mode. In case of the
results in $B$ meson kinematic bins, the trigger efficiency maps are defined
in bins of the considered kinematic variable and of an independent variable:
$p_{\mathrm{T}}$ of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
candidate for the $f_{s}/\kern-1.00006ptf_{u}$ results as function of
${\eta^{{B}}}$, ${p_{\mathrm{L}}^{{B}}}$ and ${y^{{B}}}$, and the
$p_{\mathrm{L}}$ of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
candidate for results as a function of ${p_{\mathrm{T}}^{{B}}}$.

Identical trigger selection and near-identical reconstruction and offline
selection significantly reduce the uncertainties affecting the efficiency
corrected ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ yield ratio measurement. Due to the similarity of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ kinematic distributions from
${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}$
and ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ decays, the efficiency ratios are close to unity, being about
0.98 for acceptance and selection and 0.99 for the trigger. The systematic
uncertainties associated with acceptance, reconstruction and selection
efficiency arise only from the limited size of simulated samples. The dominant
systematic uncertainties arise from the track-reconstruction efficiency
corrections and the fit. A systematic uncertainty of $0.4\%$ ($0.8\%$) is
assigned, following the procedures in Ref. [35], to the extra kaon track in
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$
decays in 2011 and 2012 (2015 and 2016) samples. For all the samples, the
uncertainty is increased by an additional $1.1\%$ due to the interactions
between the hadrons and detector material [35].

The systematic uncertainty arising from the fit model is propagated to the
fitted signal yields by allowing the parameters to float within Gaussian
constraints with mean and width determined from the simulation. Most of the
signal and misidentified background component shape parameters are constrained
with the remaining (partially correlated) tail parameters fixed to the values
determined from simulation. The effect of fixing or leaving the signal
parameters free has a negligible effect on the yield.

The resonant and nonresonant structure of the
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}K^{-})$ spectrum is
measured in Ref. [36]. The resonant $f_{0}(980)$ meson contribution,
nonresonant $S$-wave contribution and the interference effects are studied on
simulated samples. No attempt is made to separate these contributions from the
signal decays and the uncertainty of the fitted inclusive
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ yield is increased by $0.8\%$, relative to the yield.

The fit models are validated using the fitted PDFs to generate and fit a large
number of simulated pseudoexperiments according to the observed candidate
yields. The pseudoexperiments are generated for the fits on the full samples
as well as for the fits in bins of ${p_{\mathrm{T}}^{{B}}}$ and
${\eta^{{B}}}$. The mass fits in the ${p_{\mathrm{T}}^{{B}}}$ and
${\eta^{{B}}}$ bins do not show a significant bias and no additional
systematic uncertainty is included. The pseudoexperiments for the full samples
show a small yield estimator bias, the largest of which is 20% of the
statistical uncertainty. The uncertainties on these yields are therefore
increased by the same amount to account for this.

The validity of the mass models over the $B$-meson phase space is verified by
comparing the fitted fractions and the model parameters across the samples and
bins. The ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ fit is performed with the
${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{+}$
background shape determined independently in high- and
low-${p_{\mathrm{T}}^{{B}}}$ regions of the simulated decays. The variation in
the observed yield is negligible. The background shapes in regions of
${\eta^{{B}}}$ are very similar. The misidentified
$B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}$
background PDF variation in ${p_{\mathrm{T}}^{{B}}}$ or ${\eta^{{B}}}$ regions
is studied with simulation. The distributions show no evidence for significant
variation and no additional uncertainty is assigned to the fits in bins due to
the assumption of the same fit model.

Table 1: Efficiency-corrected ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ and ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}$ 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.  Year | $\sqrt{s}$ | $\mathcal{R}$ | $\sigma_{\rm{tot}}$ | $\sigma_{\rm{stat}}$ | $\sigma_{\rm{syst}}^{\rm{uncor}}$ | $\sigma^{\rm{cor}}_{\rm{syst}}$ | $\sigma^{\rm{track}}_{\rm{syst}}$ | $\sigma^{\rm{sel}}_{\rm{syst}}$ | $\sigma^{\rm{fit}}_{\rm{syst}}$
---|---|---|---|---|---|---|---|---|---
2011 |  07 TeV | 0.1238 | $0.0024$ | $0.0010$ | $0.0018$ | $0.0012$ | $0.0015$ | $0.0008$ | $0.0013$
2012 |  08 TeV | 0.1270 | $0.0023$ | $0.0007$ | $0.0019$ | $0.0012$ | $0.0016$ | $0.0005$ | $0.0015$
2015 |  13 TeV | 0.1338 | $0.0030$ | $0.0017$ | $0.0022$ | $0.0012$ | $0.0019$ | $0.0004$ | $0.0016$
2016 |  13 TeV | 0.1319 | $0.0024$ | $0.0008$ | $0.0021$ | $0.0007$ | $0.0018$ | $0.0004$ | $0.0012$

The ratios ($\mathcal{R}$) and their detailed uncertainty composition are
shown in Tab. LABEL:tab:ratios. The ratios are fitted as a function of the
$pp$ collision energy with a two-parameter function: $a+k_{s}\sqrt{s}$, as
shown in Fig. 2. The statistical significance of the
$f_{s}/\kern-1.00006ptf_{u}$ dependence on collision energy is estimated by
comparing this fit with that under the null hypothesis $k_{s}=0$. The
$\chi^{2}$ difference between the two cases is used as a test statistic and
its $p$-value is determined from the $\chi^{2}$ distribution with one degree
of freedom [37]. The two-sided significance of the two-parameter fit
($a=0.1159\pm 0.0032$, $k_{s}=(1.27\pm 0.27)\times
10^{-3}\text{\,Te\kern-1.00006ptV}^{-1}$, correlation $\rho=-0.76$) is
$4.8\,\sigma$ with respect to the hypothesis of no energy dependence. The fit
accounts for the correlations between the samples due to the common tracking
and fit uncertainties as described in Appendix A.

Figure 2: Efficiency-corrected
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ 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 TeV
measurements are shifted horizontally for clarity.

The measured double ratios for different collision energies are

$\displaystyle\mathcal{R}_{8\text{\,Te\kern-0.70004ptV}}/\mathcal{R}_{7\text{\,Te\kern-0.70004ptV}}$
$\displaystyle=1.026\pm 0.017,$
$\displaystyle\mathcal{R}_{13\text{\,Te\kern-0.70004ptV}}/\mathcal{R}_{7\text{\,Te\kern-0.70004ptV}}$
$\displaystyle=1.068\pm 0.016,$

with the correlation coefficient $\rho=0.33$ between the two and the
correlated uncertainties accounted for.

In each sample, the efficiency-corrected signal yield ratios are measured in
bins of the $B$-meson kinematic variables
$v\in\\{{p^{{B}}},{p_{\mathrm{T}}^{{B}}},{p_{\mathrm{L}}^{{B}}},{\eta^{{B}}},{y^{{B}}}\\}$
and averaged. On the vertical scale of Fig. 3, the averaged signal-yield
ratios are scaled, assuming $f_{u}=f_{d}$, to match the average $f_{s}/f_{d}$
value measured at $\sqrt{s}=7\text{\,Te\kern-1.00006ptV}$
($f_{s}/f_{d}=0.259$) [38, 10, 39] at the corresponding variable distribution
means; this is for illustrative purpose alone. On the horizontal scale, each
data point is set to the mean value determined from simulation. The
statistical significance of the $f_{s}/\kern-1.00006ptf_{u}$ dependence is
estimated by fitting the $\mathcal{R}$ distributions with a function
$A_{v}\cdot\exp(k_{v}\cdot v)$ under two hypotheses: one where no variation is
allowed and the slope parameter, $k_{v}$, is fixed to zero and one with
$k_{v}$ left free.

The relative ${B}^{0}_{s}$ and ${B}^{+}$ production is observed to depend on
the ${p_{\mathrm{T}}^{{B}}}$ with a significance of $6\,\sigma$ and the fitted
slope parameter is $k_{{p_{\mathrm{T}}^{{B}}}}=-(1.93\pm 0.46)\times
10^{-3}\text{\,Ge\kern-1.00006ptV}^{-1}c$. The strongest variation is measured
for the $13\text{\,Te\kern-1.00006ptV}$ samples: $8.7\,\sigma$,
${k_{{p_{\mathrm{T}}^{{B}}}}=-(4.40\pm 0.67)\times
10^{-3}\text{\,Ge\kern-1.00006ptV}^{-1}c}$, while is not significant
($2.1\,\sigma$ and $1.5\,\sigma$) for the 7 and 8  TeV results obtained
separately; see Appendix A for further details. The variation in
${p_{\mathrm{T}}^{{B}}}$ is further studied in three subregions of
${p_{\mathrm{L}}^{{B}}}$ (${[20,75,125,700]\text{\,Ge\kern-1.00006ptV\\!/}c}$)
and a clear dependence is seen in all the regions. The results for
${p_{\mathrm{T}}^{{B}}}$, ${p_{\mathrm{L}}^{{B}}}$ and ${\eta^{{B}}}$ are
shown in Fig. 3. No evidence is found for significant
$f_{s}/\kern-1.00006ptf_{u}$ variation in ${p^{{B}}}$,
${p_{\mathrm{L}}^{{B}}}$, ${\eta^{{B}}}$ or ${y^{{B}}}$. For the numerical
results in all the studied variables and additional figures see Appendix A.

\begin{overpic}[width=433.62pt,trim=28.45274pt 0.0pt 28.45274pt
0.0pt]{Fig3_a.pdf} \put(16.0,52.0){\small(a)} \end{overpic}

\begin{overpic}[width=433.62pt,trim=28.45274pt 0.0pt 28.45274pt
0.0pt]{Fig3_d.pdf} \put(16.0,52.0){\small(b)} \end{overpic}

\begin{overpic}[width=433.62pt,trim=28.45274pt 0.0pt 28.45274pt
0.0pt]{Fig3_b.pdf} \put(16.0,52.0){\small(c)} \end{overpic}

\begin{overpic}[width=433.62pt,trim=28.45274pt 0.0pt 28.45274pt
0.0pt]{Fig3_c.pdf} \put(16.0,52.0){\small(d)} \end{overpic}

Figure 3: Efficiency-corrected
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ 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 $\pm 1\sigma$ 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.

In conclusion, the ${B}^{0}_{s}$ and ${B}^{+}$ fragmentation fraction ratio
$f_{s}/\kern-1.00006ptf_{u}$ is studied at $7\text{\,Te\kern-1.00006ptV}$,
$8\text{\,Te\kern-1.00006ptV}$, and $13\text{\,Te\kern-1.00006ptV}$ $pp$
collision energies and in different $B$-meson kinematic regions. A
$4.8\,\sigma$ evidence is seen for an $f_{s}/\kern-1.00006ptf_{u}$ dependence
on the collision energy and $f_{s}/\kern-1.00006ptf_{u}$ is observed to depend
on the $B$-meson transverse momentum. The observed ${p_{\mathrm{T}}^{{B}}}$
dependence is compatible with the recent LHCb result on semileptonic modes
[9]. No evidence of $f_{s}/\kern-1.00006ptf_{u}$ variation is seen in
$B$-meson momentum, longitudinal momentum, rapidity or pseudorapidity.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE
(Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC
(United Kingdom); DOE NP and NSF (USA). We acknowledge the computing resources
that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN
(Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and
Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-
GRID (Poland) and OSC (USA). We are indebted to the communities behind the
multiple open-source software packages on which we depend. Individual groups
or members have received support from AvH Foundation (Germany); EPLANET, Marie
Skłodowska-Curie Actions and ERC (European Union); ANR, Labex P2IO and OCEVU,
and Région Auvergne-Rhône-Alpes (France); Key Research Program of Frontier
Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China); RFBR, RSF
and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); the Royal Society
and the Leverhulme Trust (United Kingdom).

## References

  * [1] OPAL collaboration, P. D. Acton et al., _Evidence for the existence of the strange b-flavoured meson $B_{s}^{0}$ in $Z^{0}$ decays_, Phys. Lett. B295 (1992) 357
  * [2] ALEPH collaboration, D. Buskulic et al., _Measurement of the $B_{s}^{0}$ lifetime and production rate with $D_{s}^{-}\ell^{+}$ combinations in $Z$ decays_, Phys. Lett. B361 (1995) 221
  * [3] L3 collaboration, M. Acciarri et al., _Measurements of the $b\overline{b}$ production cross-section and forward-backward asymmetry at centre-of-mass energies above the Z pole at LEP_, Phys. Lett. B485 (2000) 71
  * [4] DELPHI collaboration, J. Abdallah et al., _A Measurement of the branching fractions of the $b$ quark into charged and neutral $b$ hadrons_, Phys. Lett. B576 (2003) 29, arXiv:hep-ex/0311005
  * [5] CDF collaboration, T. Aaltonen et al., _Measurement of ratios of fragmentation fractions for bottom hadrons in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV_, Phys. Rev. D77 (2008) 072003, arXiv:0801.4375
  * [6] Particle Data Group, M. Tanabashi et al., _Review of particle physics_ , Phys. Rev. D98 (2018) 030001
  * [7] CDF collaboration, T. Aaltonen et al., _First measurement of the ratio of branching fractions ${\mathcal{B}}({{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}\mu^{-}\bar{\nu}_{\mu}/{\mathcal{B}}({{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}\pi^{-})$_, Phys. Rev. D79 (2009) 032001, arXiv:0810.3213
  * [8] LHCb collaboration, R. Aaij et al., _Study of the kinematic dependences of ${\mathchar 28931\relax}^{0}_{b}$ production in $p$ $p$ collisions and a measurement of the ${{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}}$ branching fraction_, JHEP 08 (2014) 143, arXiv:1405.6842
  * [9] LHCb collaboration, R. Aaij et al., _Measurement of $b$-hadron fractions in 13 TeV $p$ $p$ collisions_, Phys. Rev. D101 (2019) 031102(R), arXiv:1902.06794
  * [10] LHCb collaboration, R. Aaij et al., _Measurement of the fragmentation fraction ratio $f_{s}/f_{d}$ and its dependence on $B$ meson kinematics_, JHEP 04 (2013) 001, arXiv:1301.5286
  * [11] CMS and LHCb collaborations, V. Khachatryan et al., _Observation of the rare ${{B}^{0}_{s}}\\!\rightarrow{\mu^{+}\mu^{-}}$ decay from the combined analysis of CMS and LHCb data_, Nature 522 (2015) 68, arXiv:1411.4413
  * [12] LHCb collaboration, R. Aaij et al., _Measurement of the ${{B}^{0}_{s}}\\!\rightarrow{\mu^{+}\mu^{-}}$ branching fraction and effective lifetime and search for ${{B}^{0}}\\!\rightarrow{\mu^{+}\mu^{-}}$ decays_, Phys. Rev. Lett. 118 (2017) 191801, arXiv:1703.05747
  * [13] ATLAS collaboration, G. Aad et al., _Determination of the ratio of $b$-quark fragmentation fractions $f_{s}/f_{d}$ in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS detector_, Phys. Rev. Lett. 115 (2015) 262001, arXiv:1507.08925
  * [14] X. Liu, W. Wang, and Y. Xie, _Penguin pollution in $B\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}V$ decays and impact on the extraction of the $B_{s}-\bar{B}_{s}$ mixing phase_, Phys. Rev. D89 (2014) 094010, arXiv:1309.0313
  * [15] ALICE collaboration, J. Adam et al., _Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions_ , Nature Phys. 13 (2017) 535, arXiv:1606.07424
  * [16] ALICE collaboration, S. Acharya et al., _Multiplicity dependence of light-flavor hadron production in pp collisions at $\sqrt{s}$ = 7 TeV_, Phys. Rev. C99 (2019) 024906, arXiv:1807.11321
  * [17] ALICE collaboration, S. Acharya et al., _Multiplicity dependence of (multi-)strange hadron production in proton-proton collisions at $\sqrt{s}$ = 13 TeV_, arXiv:1908.01861
  * [18] LHCb collaboration, A. A. Alves et al., _The LHCb detector at the LHC_ , JINST 3 (2008) S08005
  * [19] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [20] F. Archilli et al., _Performance of the muon identification at LHCb_ , JINST 8 (2013) P10020, arXiv:1306.0249
  * [21] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [22] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [23] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [24] P. Golonka and Z. Was, _PHOTOS Monte Carlo: A precision tool for QED corrections in $Z$ and $W$ decays_, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [25] Geant4 collaboration, S. Agostinelli et al., _Geant4: A simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [26] M. Clemencic et al., _The LHCb simulation application, Gauss: Design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [27] LHCb collaboration, R. Aaij et al., _Measurement of the ${B}^{\pm}$ production cross-section in $p$ $p$ collisions at $\sqrt{s}=$7 and 13 TeV_, JHEP 12 (2017) 026, arXiv:1710.04921
  * [28] D. Martínez Santos and F. Dupertuis, _Mass distributions marginalized over per-event errors_ , Nucl. Instrum. Meth. A764 (2014) 150, arXiv:1312.5000
  * [29] K. S. Cranmer, _Kernel estimation in high-energy physics_ , Comput. Phys. Commun. 136 (2001) 198, arXiv:hep-ex/0011057
  * [30] Belle collaboration, K. Chilikin et al., _Observation of a new charged charmoniumlike state in ${{\kern 1.79993pt\overline{\kern-1.79993ptB}}{}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{K}^{-}{\pi}^{+}$ decays_, Phys. Rev. D90 (2014) 112009
  * [31] T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-prime and Upsilon resonances, PhD thesis, Institute of Nuclear Physics, Krakow, 1986, DESY-F31-86-02
  * [32] LHCb collaboration, R. Aaij et al., _Measurement of the track reconstruction efficiency at LHCb_ , JINST 10 (2015) P02007, arXiv:1408.1251
  * [33] S. Tolk, J. Albrecht, F. Dettori, and A. Pellegrino, _Data driven trigger efficiency determination at LHCb_ , Tech. Rep. LHCb-PUB-2014-039. CERN-LHCb-PUB-2014-039, CERN, Geneva, 2014
  * [34] R. Aaij et al., _The LHCb trigger and its performance in 2011_, JINST 8 (2013) P04022, arXiv:1211.3055
  * [35] LHCb collaboration, R. Aaij et al., _Measurement of the track reconstruction efficiency at LHCb_ , JINST 10 (2015) P02007, arXiv:1408.1251
  * [36] LHCb collaboration, R. Aaij et al., _Amplitude analysis and branching fraction measurement of ${{\kern 1.79993pt\overline{\kern-1.79993ptB}}{}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}}{{K}^{-}}$_, Phys. Rev. D87 (2013) 072004, arXiv:1302.1213
  * [37] S. S. Wilks, _The large-sample distribution of the likelihood ratio for testing composite hypotheses_ , Ann. Math. Stat. 9 (1938) 60
  * [38] LHCb collaboration, R. Aaij et al., _Measurement of $b$ hadron production fractions in 7 TeV $p$ $p$ collisions_, Phys. Rev. D85 (2012) 032008, arXiv:1111.2357
  * [39] LHCb collaboration, _Updated average $f_{s}/f_{d}$ $b$-hadron production fraction ratio for $7\text{\,Te\kern-1.00006ptV}$ $pp$ collisions_, LHCb-CONF-2013-011, 2013

##  Appendix A Supplementary material for LHCb-PAPER-2019-020

###  A.1 Details on the energy variation fit

The four ratios of efficiency corrected
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ and
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$ yields
(Tab. LABEL:tab:ratios) are fitted with a linear function:
$a+k_{s}\cdot\sqrt{s}$. The ratios are correlated due to the common tracking
efficiency systematic uncertainties and due to the common ($0.8\%$) systematic
uncertainty assigned to the fitted
$B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ yield
in order to account for additional resonant and nonresonant contributions. The
following covariance matrix is used to account for the correlations in the
$\chi^{2}$ fit:

$\displaystyle\begin{pmatrix}5.737&3.351&3.948&3.790\\\
3.351&5.471&4.049&3.886\\\ 3.948&4.049&9.219&4.579\\\
3.790&3.886&4.579&5.595\end{pmatrix}\times 10^{-6}.$

###  A.2 Fitted $B$-meson mass distributions

Figure 4: The $B$-meson mass distributions of (left column)
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$ and
(right column) $B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ 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
${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{+}$ in
magenta and the misidentified inclusive
$B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}$
contribution in light blue.

###  A.3 Plotted ratios in bins of ${p^{{B}}}$ and ${y^{{B}}}$

Figure 5: Efficiency-corrected
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ 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 $\pm
1\sigma$ 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.

###  A.4 Numerical and plotted ratios in bins of ${p_{\mathrm{T}}^{{B}}}$ for
${p_{\mathrm{L}}^{{B}}}$ subregions

Table 2: 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.

a) $0\leq{p_{\mathrm{L}}^{{B}}}<75\text{\,Ge\kern-0.80005ptV\\!/}c$
---
Range [$\text{\,Ge\kern-0.80005ptV\\!/}c$ ] | $\mathcal{R}$
$0.5<{p_{\mathrm{T}}^{{B}}}<4$ | $0.124\pm 0.002$
$4<{p_{\mathrm{T}}^{{B}}}<6$ | $0.127\pm 0.003$
$6<{p_{\mathrm{T}}^{{B}}}<8$ | $0.129\pm 0.003$
$8<{p_{\mathrm{T}}^{{B}}}<11$ | $0.125\pm 0.004$
$11<{p_{\mathrm{T}}^{{B}}}<40$ | $0.119\pm 0.006$

b) $75\leq{p_{\mathrm{L}}^{{B}}}<125\text{\,Ge\kern-0.80005ptV\\!/}c$
---
Range [$\text{\,Ge\kern-0.80005ptV\\!/}c$ ] | $\mathcal{R}$
$0.5<{p_{\mathrm{T}}^{{B}}}<4$ | $0.128\pm 0.003$
$4<{p_{\mathrm{T}}^{{B}}}<6$ | $0.132\pm 0.003$
$6<{p_{\mathrm{T}}^{{B}}}<8$ | $0.128\pm 0.003$
$8<{p_{\mathrm{T}}^{{B}}}<11$ | $0.129\pm 0.003$
$11<{p_{\mathrm{T}}^{{B}}}<40$ | $0.119\pm 0.003$

c) $125\leq{p_{\mathrm{L}}^{{B}}}<700\text{\,Ge\kern-0.80005ptV\\!/}c$
---
Range [$\text{\,Ge\kern-0.80005ptV\\!/}c$ ] | $\mathcal{R}$
$0.5<{p_{\mathrm{T}}^{{B}}}<4$ | $0.131\pm 0.004$
$4<{p_{\mathrm{T}}^{{B}}}<6$ | $0.128\pm 0.004$
$6<{p_{\mathrm{T}}^{{B}}}<8$ | $0.127\pm 0.003$
$8<{p_{\mathrm{T}}^{{B}}}<11$ | $0.123\pm 0.003$
$11<{p_{\mathrm{T}}^{{B}}}<40$ | $0.121\pm 0.002$

Figure 6: Efficiency-corrected
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ 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)$\text{\,Ge\kern-0.90005ptV\\!/}c$),
(middle) medium range ([75,125)$\text{\,Ge\kern-0.90005ptV\\!/}c$), and
(bottom) high range ([125,700]$\text{\,Ge\kern-0.90005ptV\\!/}c$). The ratios
are scaled to match the measured $f_{s}/f_{d}$ value (horizontal blue lines,
the $\pm 1\sigma$ 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.

###  A.5 Numerical ratios in bins of ${p^{{B}}}$, ${p_{\mathrm{L}}^{{B}}}$,
${p_{\mathrm{T}}^{{B}}}$, ${\eta^{{B}}}$, and ${y^{{B}}}$

Table 3: The measured efficiency-corrected yield ratio ($\mathcal{R}$) in bins
of the kinematic variables. Uncertainties include both statistical and
systematic sources.

(a) Results as a function of the total $B$-meson momentum.  Range [$\text{\,Ge\kern-0.80005ptV\\!/}c$ ] | $\mathcal{R}$
---|---
$20<{p^{{B}}}<50$ | $0.127\pm 0.002$
$50<{p^{{B}}}<60$ | $0.127\pm 0.003$
$60<{p^{{B}}}<70$ | $0.125\pm 0.003$
$70<{p^{{B}}}<80$ | $0.126\pm 0.003$
$80<{p^{{B}}}<95$ | $0.127\pm 0.002$
$95<{p^{{B}}}<110$ | $0.126\pm 0.002$
$110<{p^{{B}}}<135$ | $0.128\pm 0.003$
$135<{p^{{B}}}<165$ | $0.125\pm 0.003$
$165<{p^{{B}}}<225$ | $0.127\pm 0.003$
$225<{p^{{B}}}<700$ | $0.131\pm 0.003$

(b) Results as a function of the $B$-meson longitudinal momentum. Range [$\text{\,Ge\kern-0.80005ptV\\!/}c$ ] | $\mathcal{R}$
---|---
$20<{p_{\mathrm{L}}^{{B}}}<50$ | $0.126\pm 0.002$
$50<{p_{\mathrm{L}}^{{B}}}<60$ | $0.127\pm 0.003$
$60<{p_{\mathrm{L}}^{{B}}}<70$ | $0.125\pm 0.003$
$70<{p_{\mathrm{L}}^{{B}}}<80$ | $0.127\pm 0.003$
$80<{p_{\mathrm{L}}^{{B}}}<95$ | $0.127\pm 0.002$
$95<{p_{\mathrm{L}}^{{B}}}<110$ | $0.127\pm 0.003$
$110<{p_{\mathrm{L}}^{{B}}}<135$ | $0.127\pm 0.002$
$135<{p_{\mathrm{L}}^{{B}}}<165$ | $0.125\pm 0.003$
$165<{p_{\mathrm{L}}^{{B}}}<225$ | $0.127\pm 0.003$
$225<{p_{\mathrm{L}}^{{B}}}<700$ | $0.130\pm 0.003$

(c) Results as a function of the $B$-meson transverse momentum. Range [$\text{\,Ge\kern-0.80005ptV\\!/}c$ ] | $\mathcal{R}$
---|---
$0.5<{p_{\mathrm{T}}^{{B}}}<2$ | $0.125\pm 0.003$
$2<{p_{\mathrm{T}}^{{B}}}<3$ | $0.127\pm 0.003$
$3<{p_{\mathrm{T}}^{{B}}}<4$ | $0.125\pm 0.003$
$4<{p_{\mathrm{T}}^{{B}}}<5$ | $0.128\pm 0.003$
$5<{p_{\mathrm{T}}^{{B}}}<6$ | $0.128\pm 0.003$
$6<{p_{\mathrm{T}}^{{B}}}<7$ | $0.127\pm 0.003$
$7<{p_{\mathrm{T}}^{{B}}}<8$ | $0.127\pm 0.003$
$8<{p_{\mathrm{T}}^{{B}}}<9$ | $0.126\pm 0.003$
$9<{p_{\mathrm{T}}^{{B}}}<10$ | $0.125\pm 0.003$
$10<{p_{\mathrm{T}}^{{B}}}<11.5$ | $0.125\pm 0.003$
$11.5<{p_{\mathrm{T}}^{{B}}}<14$ | $0.118\pm 0.003$
$14<{p_{\mathrm{T}}^{{B}}}<40$ | $0.120\pm 0.002$

(d) Results as a function of the $B$-meson pseudorapidity. Range | $\mathcal{R}$
---|---
$2.0<{\eta^{{B}}}<2.5$ | $0.127\pm 0.004$
$2.5<{\eta^{{B}}}<2.8$ | $0.131\pm 0.003$
$2.8<{\eta^{{B}}}<3.0$ | $0.129\pm 0.003$
$3.0<{\eta^{{B}}}<3.2$ | $0.130\pm 0.002$
$3.2<{\eta^{{B}}}<3.4$ | $0.126\pm 0.002$
$3.4<{\eta^{{B}}}<3.6$ | $0.125\pm 0.002$
$3.6<{\eta^{{B}}}<3.8$ | $0.127\pm 0.002$
$3.8<{\eta^{{B}}}<4.0$ | $0.128\pm 0.003$
$4.0<{\eta^{{B}}}<4.3$ | $0.129\pm 0.003$
$4.3<{\eta^{{B}}}<6.4$ | $0.130\pm 0.002$

(e) Results as a function of the $B$-meson rapidity. Range | $\mathcal{R}$
---|---
$2.0<{y^{{B}}}<2.5$ | $0.130\pm 0.003$
$2.5<{y^{{B}}}<3.0$ | $0.127\pm 0.002$
$3.0<{y^{{B}}}<3.5$ | $0.126\pm 0.002$
$3.5<{y^{{B}}}<4.0$ | $0.128\pm 0.003$
$4.0<{y^{{B}}}<4.5$ | $0.127\pm 0.005$

###  A.6 Plotted efficiency-corrected yield ratios as a function of ${\Delta
y}$

Given the availability of data at different center-of-mass energies, results
can be compared as a function of the variable

${\Delta y}=y_{\rm{beam}}-y^{B}$

where $y_{\rm{beam}}$ is the rapidity of the incoming proton beam and
${y^{{B}}}$ the $B$-meson rapidity. This variable is typically defined in
association with the transport of the baryon number from the initial to the
final state in $pp\rightarrow NX$ reactions, where $N$ is a generic baryon and
$X$ can be any accompanying process. However, it can be useful also to
understand the hadronization process for mesons.

The results of the efficiency-corrected yield ratios as a function of ${\Delta
y}$ are shown in Fig. 7 as obtained by shifting those as a function of
${y^{{B}}}$ by the corresponding $y_{\rm beam}$. This variable is useful for
comparison with ATLAS and CMS experiments. As an example, LHCb data at
$\sqrt{s}=13\text{\,Te\kern-1.00006ptV}$ (or $y_{\rm{beam}}=10.2$) and
rapidity $y\simeq 2$ could be compared with ATLAS/CMS data at
$\sqrt{s}=7\text{\,Te\kern-1.00006ptV}$ ($y_{\rm{beam}}=9.6$) and rapidity
$y\simeq 1$; a region otherwise unavailable to LHCb at
$\sqrt{s}=7\text{\,Te\kern-1.00006ptV}$.

Figure 7: Efficiency-corrected
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ 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.

###  A.7 Numerical and plotted ratios in bins of ${p_{\mathrm{T}}^{{B}}}$ for
different $pp$ collision energies

Table 4: Efficiency-corrected
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ yield ratios in bins of $B$-meson transverse momentum
${p_{\mathrm{T}}^{{B}}}$, separately for the three $pp$ collision energies.

(a) Results at $\sqrt{s}=7~{}\text{\,Te\kern-0.90005ptV}$ Range [$\text{\,Ge\kern-0.80005ptV\\!/}c$ ] | $\mathcal{R}$
---|---
$0.5<{p_{\mathrm{T}}^{{B}}}<2$ | $0.119\pm 0.003$
$2<{p_{\mathrm{T}}^{{B}}}<3$ | $0.127\pm 0.003$
$3<{p_{\mathrm{T}}^{{B}}}<4$ | $0.120\pm 0.002$
$4<{p_{\mathrm{T}}^{{B}}}<5$ | $0.122\pm 0.002$
$5<{p_{\mathrm{T}}^{{B}}}<6$ | $0.122\pm 0.002$
$6<{p_{\mathrm{T}}^{{B}}}<7$ | $0.128\pm 0.003$
$7<{p_{\mathrm{T}}^{{B}}}<8$ | $0.129\pm 0.003$
$8<{p_{\mathrm{T}}^{{B}}}<9$ | $0.129\pm 0.003$
$9<{p_{\mathrm{T}}^{{B}}}<10$ | $0.115\pm 0.003$
$10<{p_{\mathrm{T}}^{{B}}}<12$ | $0.116\pm 0.003$
$11<{p_{\mathrm{T}}^{{B}}}<14$ | $0.118\pm 0.003$
$14<{p_{\mathrm{T}}^{{B}}}<40$ | $0.117\pm 0.003$

(b) Results at $\sqrt{s}=8~{}\text{\,Te\kern-0.90005ptV}$ Range [$\text{\,Ge\kern-0.80005ptV\\!/}c$ ] | $\mathcal{R}$
---|---
$0.5<{p_{\mathrm{T}}^{{B}}}<2$ | $0.121\pm 0.002$
$2<{p_{\mathrm{T}}^{{B}}}<3$ | $0.121\pm 0.002$
$3<{p_{\mathrm{T}}^{{B}}}<4$ | $0.120\pm 0.002$
$4<{p_{\mathrm{T}}^{{B}}}<5$ | $0.127\pm 0.002$
$5<{p_{\mathrm{T}}^{{B}}}<6$ | $0.125\pm 0.002$
$6<{p_{\mathrm{T}}^{{B}}}<7$ | $0.125\pm 0.002$
$7<{p_{\mathrm{T}}^{{B}}}<8$ | $0.121\pm 0.002$
$8<{p_{\mathrm{T}}^{{B}}}<9$ | $0.122\pm 0.002$
$9<{p_{\mathrm{T}}^{{B}}}<10$ | $0.125\pm 0.002$
$10<{p_{\mathrm{T}}^{{B}}}<12$ | $0.125\pm 0.002$
$11<{p_{\mathrm{T}}^{{B}}}<14$ | $0.119\pm 0.002$
$14<{p_{\mathrm{T}}^{{B}}}<40$ | $0.119\pm 0.002$

(c) Results at $\sqrt{s}=13~{}\text{\,Te\kern-0.90005ptV}$. Range [$\text{\,Ge\kern-0.80005ptV\\!/}c$ ] | $\mathcal{R}$
---|---
$0.5<{p_{\mathrm{T}}^{{B}}}<2$ | $0.133\pm 0.002$
$2<{p_{\mathrm{T}}^{{B}}}<3$ | $0.132\pm 0.002$
$3<{p_{\mathrm{T}}^{{B}}}<4$ | $0.134\pm 0.002$
$4<{p_{\mathrm{T}}^{{B}}}<5$ | $0.132\pm 0.002$
$5<{p_{\mathrm{T}}^{{B}}}<6$ | $0.134\pm 0.002$
$6<{p_{\mathrm{T}}^{{B}}}<7$ | $0.129\pm 0.002$
$7<{p_{\mathrm{T}}^{{B}}}<8$ | $0.131\pm 0.002$
$8<{p_{\mathrm{T}}^{{B}}}<9$ | $0.129\pm 0.002$
$9<{p_{\mathrm{T}}^{{B}}}<10$ | $0.128\pm 0.002$
$10<{p_{\mathrm{T}}^{{B}}}<12$ | $0.128\pm 0.002$
$11<{p_{\mathrm{T}}^{{B}}}<14$ | $0.118\pm 0.002$
$14<{p_{\mathrm{T}}^{{B}}}<40$ | $0.121\pm 0.002$

The statistical significance of the $f_{s}/\kern-1.00006ptf_{u}$ dependence on
${p_{\mathrm{T}}^{{B}}}$ at each $pp$ collision energy is estimated by fitting
the efficiency-corrected
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ yield ratios ($\mathcal{R}$, see Tab.
LABEL:tab:results_fsfds_pt and Fig. 3b of the main text) distributions with a
function
$A_{{p_{\mathrm{T}}^{{B}}}}\cdot\exp(k_{{p_{\mathrm{T}}^{{B}}}}\cdot{p_{\mathrm{T}}^{{B}}})$
under two hypotheses: one where no variation is allowed and the slope
parameter, $k_{{p_{\mathrm{T}}^{{B}}}}$, is fixed to zero and one with
$k_{{p_{\mathrm{T}}^{{B}}}}$ left free. The $\chi^{2}$ difference between the
two cases is used as a test statistic and its $p$-value is determined from the
$\chi^{2}$ distribution with one degree of freedom [37]. The results are
$k_{{p_{\mathrm{T}}^{{B}}}}=-(1.24\pm 0.73)\times
10^{-3}\text{\,Ge\kern-1.00006ptV}^{-1}c$ ($2.1\,\sigma$),
$k_{{p_{\mathrm{T}}^{{B}}}}=-(0.59\pm 0.39)\times
10^{-3}\text{\,Ge\kern-1.00006ptV}^{-1}c$ ($1.5\,\sigma$) and
$k_{{p_{\mathrm{T}}^{{B}}}}=-(4.40\pm 0.67)\times
10^{-3}\text{\,Ge\kern-1.00006ptV}^{-1}c$ ($8.7\,\sigma$) for
$7\text{\,Te\kern-1.00006ptV}$, $8\text{\,Te\kern-1.00006ptV}$ and
$13\text{\,Te\kern-1.00006ptV}$ samples, respectively. The two-sided
significances are given in the brackets.

LHCb collaboration

R. Aaij31, C. Abellán Beteta49, T. Ackernley59, B. Adeva45, M. Adinolfi53, H.
Afsharnia9, C.A. Aidala80, S. Aiola25, Z. Ajaltouni9, S. Akar66, P.
Albicocco22, J. Albrecht14, F. Alessio47, M. Alexander58, A. Alfonso Albero44,
G. Alkhazov37, P. Alvarez Cartelle60, A.A. Alves Jr45, S. Amato2, Y. Amhis11,
L. An21, L. Anderlini21, G. Andreassi48, M. Andreotti20, F. Archilli16, J.
Arnau Romeu10, A. Artamonov43, M. Artuso67, K. Arzymatov41, E. Aslanides10, M.
Atzeni49, B. Audurier26, S. Bachmann16, J.J. Back55, S. Baker60, V.
Balagura11,b, W. Baldini20,47, A. Baranov41, R.J. Barlow61, S. Barsuk11, W.
Barter60, M. Bartolini23,47,h, F. Baryshnikov77, G. Bassi28, V. Batozskaya35,
B. Batsukh67, A. Battig14, A. Bay48, M. Becker14, F. Bedeschi28, I. Bediaga1,
A. Beiter67, L.J. Bel31, V. Belavin41, S. Belin26, N. Beliy5, V. Bellee48, K.
Belous43, I. Belyaev38, G. Bencivenni22, E. Ben-Haim12, S. Benson31, S.
Beranek13, A. Berezhnoy39, R. Bernet49, D. Berninghoff16, H.C. Bernstein67, C.
Bertella47, E. Bertholet12, A. Bertolin27, C. Betancourt49, F. Betti19,e, M.O.
Bettler54, Ia. Bezshyiko49, S. Bhasin53, J. Bhom33, M.S. Bieker14, S.
Bifani52, P. Billoir12, A. Bizzeti21,u, M. Bjørn62, M.P. Blago47, T. Blake55,
F. Blanc48, S. Blusk67, D. Bobulska58, V. Bocci30, O. Boente Garcia45, T.
Boettcher63, A. Boldyrev78, A. Bondar42,x, N. Bondar37, S. Borghi61,47, M.
Borisyak41, M. Borsato16, J.T. Borsuk33, T.J.V. Bowcock59, C. Bozzi20, M.J.
Bradley60, S. Braun16, A. Brea Rodriguez45, M. Brodski47, J. Brodzicka33, A.
Brossa Gonzalo55, D. Brundu26, E. Buchanan53, A. Buonaura49, C. Burr47, A.
Bursche26, J.S. Butter31, J. Buytaert47, W. Byczynski47, S. Cadeddu26, H.
Cai72, R. Calabrese20,g, L. Calero Diaz22, S. Cali22, R. Calladine52, M.
Calvi24,i, M. Calvo Gomez44,m, A. Camboni44, P. Campana22, D.H. Campora
Perez31, L. Capriotti19,e, A. Carbone19,e, G. Carboni29, R. Cardinale23,h, A.
Cardini26, P. Carniti24,i, K. Carvalho Akiba31, A. Casais Vidal45, G. Casse59,
M. Cattaneo47, G. Cavallero47, S. Celani48, R. Cenci28,p, J. Cerasoli10, M.G.
Chapman53, M. Charles12,47, Ph. Charpentier47, G. Chatzikonstantinidis52, M.
Chefdeville8, V. Chekalina41, C. Chen3, S. Chen26, A. Chernov33, S.-G.
Chitic47, V. Chobanova45, M. Chrzaszcz33, A. Chubykin37, P. Ciambrone22, M.F.
Cicala55, X. Cid Vidal45, G. Ciezarek47, F. Cindolo19, P.E.L. Clarke57, M.
Clemencic47, H.V. Cliff54, J. Closier47, J.L. Cobbledick61, V. Coco47, J.A.B.
Coelho11, J. Cogan10, E. Cogneras9, L. Cojocariu36, P. Collins47, T.
Colombo47, A. Comerma-Montells16, A. Contu26, N. Cooke52, G. Coombs58, S.
Coquereau44, G. Corti47, C.M. Costa Sobral55, B. Couturier47, D.C. Craik63, J.
Crkovska66, A. Crocombe55, M. Cruz Torres1, R. Currie57, C.L. Da Silva66, E.
Dall’Occo14, J. Dalseno45,53, C. D’Ambrosio47, A. Danilina38, P. d’Argent16,
A. Davis61, O. De Aguiar Francisco47, K. De Bruyn47, S. De Capua61, M. De
Cian48, J.M. De Miranda1, L. De Paula2, M. De Serio18,d, P. De Simone22, J.A.
de Vries31, C.T. Dean66, W. Dean80, D. Decamp8, L. Del Buono12, B. Delaney54,
H.-P. Dembinski15, M. Demmer14, A. Dendek34, V. Denysenko49, D. Derkach78, O.
Deschamps9, F. Desse11, F. Dettori26,f, B. Dey7, A. Di Canto47, P. Di Nezza22,
S. Didenko77, H. Dijkstra47, V. Dobishuk51, F. Dordei26, M. Dorigo28,y, A.C.
dos Reis1, L. Douglas58, A. Dovbnya50, K. Dreimanis59, M.W. Dudek33, L.
Dufour47, G. Dujany12, P. Durante47, J.M. Durham66, D. Dutta61, R.
Dzhelyadin43,†, M. Dziewiecki16, A. Dziurda33, A. Dzyuba37, S. Easo56, U.
Egede69, V. Egorychev38, S. Eidelman42,x, S. Eisenhardt57, R. Ekelhof14, S.
Ek-In48, L. Eklund58, S. Ely67, A. Ene36, E. Epple66, S. Escher13, S. Esen31,
T. Evans47, A. Falabella19, J. Fan3, N. Farley52, S. Farry59, D. Fazzini11, P.
Fedin38, M. Féo47, P. Fernandez Declara47, A. Fernandez Prieto45, F.
Ferrari19,e, L. Ferreira Lopes48, F. Ferreira Rodrigues2, S. Ferreres Sole31,
M. Ferrillo49, M. Ferro-Luzzi47, S. Filippov40, R.A. Fini18, M. Fiorini20,g,
M. Firlej34, K.M. Fischer62, C. Fitzpatrick47, T. Fiutowski34, F. Fleuret11,b,
M. Fontana47, F. Fontanelli23,h, R. Forty47, V. Franco Lima59, M. Franco
Sevilla65, M. Frank47, C. Frei47, D.A. Friday58, J. Fu25,q, M. Fuehring14, W.
Funk47, E. Gabriel57, A. Gallas Torreira45, D. Galli19,e, S. Gallorini27, S.
Gambetta57, Y. Gan3, M. Gandelman2, P. Gandini25, Y. Gao4, L.M. Garcia
Martin46, J. García Pardiñas49, B. Garcia Plana45, F.A. Garcia Rosales11, J.
Garra Tico54, L. Garrido44, D. Gascon44, C. Gaspar47, D. Gerick16, E.
Gersabeck61, M. Gersabeck61, T. Gershon55, D. Gerstel10, Ph. Ghez8, V.
Gibson54, A. Gioventù45, O.G. Girard48, P. Gironella Gironell44, L. Giubega36,
C. Giugliano20, K. Gizdov57, V.V. Gligorov12, C. Göbel70, D. Golubkov38, A.
Golutvin60,77, A. Gomes1,a, P. Gorbounov38,6, I.V. Gorelov39, C. Gotti24,i, E.
Govorkova31, J.P. Grabowski16, R. Graciani Diaz44, T. Grammatico12, L.A.
Granado Cardoso47, E. Graugés44, E. Graverini48, G. Graziani21, A. Grecu36, R.
Greim31, P. Griffith20, L. Grillo61, L. Gruber47, B.R. Gruberg Cazon62, C.
Gu3, E. Gushchin40, A. Guth13, Yu. Guz43,47, T. Gys47, T. Hadavizadeh62, G.
Haefeli48, C. Haen47, S.C. Haines54, P.M. Hamilton65, Q. Han7, X. Han16, T.H.
Hancock62, S. Hansmann-Menzemer16, N. Harnew62, T. Harrison59, R. Hart31, C.
Hasse47, M. Hatch47, J. He5, M. Hecker60, K. Heijhoff31, K. Heinicke14, A.
Heister14, A.M. Hennequin47, K. Hennessy59, L. Henry46, J. Heuel13, A.
Hicheur68, D. Hill62, M. Hilton61, P.H. Hopchev48, J. Hu16, W. Hu7, W. Huang5,
W. Hulsbergen31, T. Humair60, R.J. Hunter55, M. Hushchyn78, D. Hutchcroft59,
D. Hynds31, P. Ibis14, M. Idzik34, P. Ilten52, A. Inglessi37, A. Inyakin43, K.
Ivshin37, R. Jacobsson47, S. Jakobsen47, J. Jalocha62, E. Jans31, B.K.
Jashal46, A. Jawahery65, V. Jevtic14, F. Jiang3, M. John62, D. Johnson47, C.R.
Jones54, B. Jost47, N. Jurik62, S. Kandybei50, M. Karacson47, J.M. Kariuki53,
N. Kazeev78, M. Kecke16, F. Keizer54,54, M. Kelsey67, M. Kenzie54, T. Ketel32,
B. Khanji47, A. Kharisova79, K.E. Kim67, T. Kirn13, V.S. Kirsebom48, S.
Klaver22, K. Klimaszewski35, S. Koliiev51, A. Kondybayeva77, A.
Konoplyannikov38, P. Kopciewicz34, R. Kopecna16, P. Koppenburg31, I.
Kostiuk31,51, O. Kot51, S. Kotriakhova37, L. Kravchuk40, R.D. Krawczyk47, M.
Kreps55, F. Kress60, S. Kretzschmar13, P. Krokovny42,x, W. Krupa34, W.
Krzemien35, W. Kucewicz33,l, M. Kucharczyk33, V. Kudryavtsev42,x, H.S.
Kuindersma31, G.J. Kunde66, T. Kvaratskheliya38, D. Lacarrere47, G.
Lafferty61, A. Lai26, D. Lancierini49, J.J. Lane61, G. Lanfranchi22, C.
Langenbruch13, T. Latham55, F. Lazzari28,v, C. Lazzeroni52, R. Le Gac10, R.
Lefèvre9, A. Leflat39, O. Leroy10, T. Lesiak33, B. Leverington16, H. Li71, X.
Li66, Y. Li6, Z. Li67, X. Liang67, R. Lindner47, V. Lisovskyi14, G. Liu71, X.
Liu3, D. Loh55, A. Loi26, J. Lomba Castro45, I. Longstaff58, J.H. Lopes2, G.
Loustau49, G.H. Lovell54, Y. Lu6, D. Lucchesi27,o, M. Lucio Martinez31, Y.
Luo3, A. Lupato27, E. Luppi20,g, O. Lupton55, A. Lusiani28, X. Lyu5, S.
Maccolini19,e, F. Machefert11, F. Maciuc36, V. Macko48, P. Mackowiak14, S.
Maddrell-Mander53, L.R. Madhan Mohan53, O. Maev37,47, A. Maevskiy78, D.
Maisuzenko37, M.W. Majewski34, S. Malde62, B. Malecki47, A. Malinin76, T.
Maltsev42,x, H. Malygina16, G. Manca26,f, G. Mancinelli10, R. Manera
Escalero44, D. Manuzzi19,e, D. Marangotto25,q, J. Maratas9,w, J.F. Marchand8,
U. Marconi19, S. Mariani21, C. Marin Benito11, M. Marinangeli48, P. Marino48,
J. Marks16, P.J. Marshall59, G. Martellotti30, L. Martinazzoli47, M.
Martinelli24, D. Martinez Santos45, F. Martinez Vidal46, A. Massafferri1, M.
Materok13, R. Matev47, A. Mathad49, Z. Mathe47, V. Matiunin38, C. Matteuzzi24,
K.R. Mattioli80, A. Mauri49, E. Maurice11,b, M. McCann60, L. Mcconnell17, A.
McNab61, R. McNulty17, J.V. Mead59, B. Meadows64, C. Meaux10, G. Meier14, N.
Meinert74, D. Melnychuk35, S. Meloni24,i, M. Merk31, A. Merli25, M.
Mikhasenko47, D.A. Milanes73, E. Millard55, M.-N. Minard8, O. Mineev38, L.
Minzoni20,g, S.E. Mitchell57, B. Mitreska61, D.S. Mitzel47, A. Mödden14, A.
Mogini12, R.D. Moise60, T. Mombächer14, I.A. Monroy73, S. Monteil9, M.
Morandin27, G. Morello22, M.J. Morello28,t, J. Moron34, A.B. Morris10, A.G.
Morris55, R. Mountain67, H. Mu3, F. Muheim57, M. Mukherjee7, M. Mulder31, D.
Müller47, K. Müller49, V. Müller14, C.H. Murphy62, D. Murray61, P. Muzzetto26,
P. Naik53, T. Nakada48, R. Nandakumar56, A. Nandi62, T. Nanut48, I. Nasteva2,
M. Needham57, N. Neri25,q, S. Neubert16, N. Neufeld47, R. Newcombe60, T.D.
Nguyen48, C. Nguyen-Mau48,n, E.M. Niel11, S. Nieswand13, N. Nikitin39, N.S.
Nolte47, C. Nunez80, A. Oblakowska-Mucha34, V. Obraztsov43, S. Ogilvy58, D.P.
O’Hanlon19, R. Oldeman26,f, C.J.G. Onderwater75, J. D. Osborn80, A.
Ossowska33, J.M. Otalora Goicochea2, T. Ovsiannikova38, P. Owen49, A.
Oyanguren46, P.R. Pais48, T. Pajero28,t, A. Palano18, M. Palutan22, G.
Panshin79, A. Papanestis56, M. Pappagallo57, L.L. Pappalardo20,g, C.
Pappenheimer64, W. Parker65, C. Parkes61, G. Passaleva21,47, A. Pastore18, M.
Patel60, C. Patrignani19,e, A. Pearce47, A. Pellegrino31, M. Pepe Altarelli47,
S. Perazzini19, D. Pereima38, P. Perret9, L. Pescatore48, K. Petridis53, A.
Petrolini23,h, A. Petrov76, S. Petrucci57, M. Petruzzo25,q, B. Pietrzyk8, G.
Pietrzyk48, M. Pili62, D. Pinci30, J. Pinzino47, F. Pisani47, A. Piucci16, V.
Placinta36, S. Playfer57, J. Plews52, M. Plo Casasus45, F. Polci12, M. Poli
Lener22, M. Poliakova67, A. Poluektov10, N. Polukhina77,c, I. Polyakov67, E.
Polycarpo2, G.J. Pomery53, S. Ponce47, A. Popov43, D. Popov52, S.
Poslavskii43, K. Prasanth33, L. Promberger47, C. Prouve45, V. Pugatch51, A.
Puig Navarro49, H. Pullen62, G. Punzi28,p, W. Qian5, J. Qin5, R. Quagliani12,
B. Quintana9, N.V. Raab17, R.I. Rabadan Trejo10, B. Rachwal34, J.H.
Rademacker53, M. Rama28, M. Ramos Pernas45, M.S. Rangel2, F. Ratnikov41,78, G.
Raven32, M. Reboud8, F. Redi48, F. Reiss12, C. Remon Alepuz46, Z. Ren3, V.
Renaudin62, S. Ricciardi56, S. Richards53, K. Rinnert59, P. Robbe11, A.
Robert12, A.B. Rodrigues48, E. Rodrigues64, J.A. Rodriguez Lopez73, M.
Roehrken47, S. Roiser47, A. Rollings62, V. Romanovskiy43, M. Romero Lamas45,
A. Romero Vidal45, J.D. Roth80, M. Rotondo22, M.S. Rudolph67, T. Ruf47, J.
Ruiz Vidal46, J. Ryzka34, J.J. Saborido Silva45, N. Sagidova37, B. Saitta26,f,
C. Sanchez Gras31, C. Sanchez Mayordomo46, R. Santacesaria30, C. Santamarina
Rios45, M. Santimaria22, E. Santovetti29,j, G. Sarpis61, A. Sarti30, C.
Satriano30,s, A. Satta29, M. Saur5, D. Savrina38,39, L.G. Scantlebury Smead62,
S. Schael13, M. Schellenberg14, M. Schiller58, H. Schindler47, M.
Schmelling15, T. Schmelzer14, B. Schmidt47, O. Schneider48, A. Schopper47,
H.F. Schreiner64, M. Schubiger31, S. Schulte48, M.H. Schune11, R. Schwemmer47,
B. Sciascia22, A. Sciubba30,k, S. Sellam68, A. Semennikov38, A. Sergi52,47, N.
Serra49, J. Serrano10, L. Sestini27, A. Seuthe14, P. Seyfert47, D.M.
Shangase80, M. Shapkin43, L. Shchutska48, T. Shears59, L. Shekhtman42,x, V.
Shevchenko76,77, E. Shmanin77, J.D. Shupperd67, B.G. Siddi20, R. Silva
Coutinho49, L. Silva de Oliveira2, G. Simi27,o, S. Simone18,d, I. Skiba20, N.
Skidmore16, T. Skwarnicki67, M.W. Slater52, J.G. Smeaton54, A. Smetkina38, E.
Smith13, I.T. Smith57, M. Smith60, A. Snoch31, M. Soares19, L. Soares Lavra1,
M.D. Sokoloff64, F.J.P. Soler58, B. Souza De Paula2, B. Spaan14, E. Spadaro
Norella25,q, P. Spradlin58, F. Stagni47, M. Stahl64, S. Stahl47, P. Stefko48,
S. Stefkova60, O. Steinkamp49, S. Stemmle16, O. Stenyakin43, M. Stepanova37,
H. Stevens14, S. Stone67, S. Stracka28, M.E. Stramaglia48, M. Straticiuc36, S.
Strokov79, J. Sun3, L. Sun72, Y. Sun65, P. Svihra61, K. Swientek34, A.
Szabelski35, T. Szumlak34, M. Szymanski5, S. Taneja61, Z. Tang3, T. Tekampe14,
G. Tellarini20, F. Teubert47, E. Thomas47, K.A. Thomson59, M.J. Tilley60, V.
Tisserand9, S. T’Jampens8, M. Tobin6, S. Tolk47, L. Tomassetti20,g, D.
Tonelli28, D. Torres Machado1, D.Y. Tou12, E. Tournefier8, M. Traill58, M.T.
Tran48, C. Trippl48, A. Trisovic54, A. Tsaregorodtsev10, G. Tuci28,47,p, A.
Tully48, N. Tuning31, A. Ukleja35, A. Usachov11, A. Ustyuzhanin41,78, U.
Uwer16, A. Vagner79, V. Vagnoni19, A. Valassi47, G. Valenti19, M. van
Beuzekom31, H. Van Hecke66, E. van Herwijnen47, C.B. Van Hulse17, M. van
Veghel75, R. Vazquez Gomez44, P. Vazquez Regueiro45, C. Vázquez Sierra31, S.
Vecchi20, J.J. Velthuis53, M. Veltri21,r, A. Venkateswaran67, M. Vernet9, M.
Veronesi31, M. Vesterinen55, J.V. Viana Barbosa47, D. Vieira5, M. Vieites
Diaz48, H. Viemann74, X. Vilasis-Cardona44,m, A. Vitkovskiy31, V. Volkov39, A.
Vollhardt49, D. Vom Bruch12, A. Vorobyev37, V. Vorobyev42,x, N. Voropaev37, R.
Waldi74, J. Walsh28, J. Wang3, J. Wang72, J. Wang6, M. Wang3, Y. Wang7, Z.
Wang49, D.R. Ward54, H.M. Wark59, N.K. Watson52, D. Websdale60, A. Weiden49,
C. Weisser63, B.D.C. Westhenry53, D.J. White61, M. Whitehead13, D. Wiedner14,
G. Wilkinson62, M. Wilkinson67, I. Williams54, M. Williams63, M.R.J.
Williams61, T. Williams52, F.F. Wilson56, M. Winn11, W. Wislicki35, M.
Witek33, L. Witola16, G. Wormser11, S.A. Wotton54, H. Wu67, K. Wyllie47, Z.
Xiang5, D. Xiao7, Y. Xie7, H. Xing71, A. Xu3, L. Xu3, M. Xu7, Q. Xu5, Z. Xu8,
Z. Xu3, Z. Yang3, Z. Yang65, Y. Yao67, L.E. Yeomans59, H. Yin7, J. Yu7,aa, X.
Yuan67, O. Yushchenko43, K.A. Zarebski52, M. Zavertyaev15,c, M. Zdybal33, M.
Zeng3, D. Zhang7, L. Zhang3, S. Zhang3, W.C. Zhang3,z, Y. Zhang47, A.
Zhelezov16, Y. Zheng5, X. Zhou5, Y. Zhou5, X. Zhu3, V. Zhukov13,39, J.B.
Zonneveld57, S. Zucchelli19,e.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4School of Physics State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing, China
5University of Chinese Academy of Sciences, Beijing, China
6Institute Of High Energy Physics (IHEP), Beijing, China
7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei,
China
8Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
9Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
10Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
11LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
12LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
13I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
14Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
15Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
16Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
17School of Physics, University College Dublin, Dublin, Ireland
18INFN Sezione di Bari, Bari, Italy
19INFN Sezione di Bologna, Bologna, Italy
20INFN Sezione di Ferrara, Ferrara, Italy
21INFN Sezione di Firenze, Firenze, Italy
22INFN Laboratori Nazionali di Frascati, Frascati, Italy
23INFN Sezione di Genova, Genova, Italy
24INFN Sezione di Milano-Bicocca, Milano, Italy
25INFN Sezione di Milano, Milano, Italy
26INFN Sezione di Cagliari, Monserrato, Italy
27INFN Sezione di Padova, Padova, Italy
28INFN Sezione di Pisa, Pisa, Italy
29INFN Sezione di Roma Tor Vergata, Roma, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
32Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
33Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35National Center for Nuclear Research (NCBJ), Warsaw, Poland
36Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
37Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
38Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia, Moscow, Russia
39Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
40Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
41Yandex School of Data Analysis, Moscow, Russia
42Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
43Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
44ICCUB, Universitat de Barcelona, Barcelona, Spain
45Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
46Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
47European Organization for Nuclear Research (CERN), Geneva, Switzerland
48Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
49Physik-Institut, Universität Zürich, Zürich, Switzerland
50NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
51Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
52University of Birmingham, Birmingham, United Kingdom
53H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
54Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
55Department of Physics, University of Warwick, Coventry, United Kingdom
56STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
57School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
58School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
59Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
60Imperial College London, London, United Kingdom
61Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
62Department of Physics, University of Oxford, Oxford, United Kingdom
63Massachusetts Institute of Technology, Cambridge, MA, United States
64University of Cincinnati, Cincinnati, OH, United States
65University of Maryland, College Park, MD, United States
66Los Alamos National Laboratory (LANL), Los Alamos, United States
67Syracuse University, Syracuse, NY, United States
68Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria,
associated to 2
69School Of Physics And Astronomy Monash University, Melbourne, Australia,
associated to 55
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71South China Normal University, Guangzhou, China, associated to 3
72School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
73Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 12
74Institut für Physik, Universität Rostock, Rostock, Germany, associated to 16
75Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 31
76National Research Centre Kurchatov Institute, Moscow, Russia, associated to
38
77National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 38
78National Research University Higher School of Economics, Moscow, Russia,
associated to 41
79National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
38
80University of Michigan, Ann Arbor, United States, associated to 67

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Vietnam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vUniversità di Siena, Siena, Italy
wMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
xNovosibirsk State University, Novosibirsk, Russia
ySezione INFN di Trieste, Trieste, Italy
zSchool of Physics and Information Technology, Shaanxi Normal University
(SNNU), Xi’an, China
aaPhysics and Micro Electronic College, Hunan University, Changsha City, China
†Deceased