EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2019-016 LHCb-PAPER-2018-050 February 18, 2019

Measurement of $b$-hadron fractions in $13\text{\,Te\kern-2.07413ptV}$ $pp$
collisions

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

The production fractions of ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ hadrons, normalized to the sum of ${{B}^{-}}$ and
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ fractions, are measured
in $13\text{\,Te\kern-1.00006ptV}$ $pp$ collisions using data collected by the
LHCb experiment, corresponding to an integrated luminosity of
1.67$\text{\,fb}^{-1}$. These ratios, averaged over the $b$-hadron transverse
momenta from 4 to 25 GeV and pseudorapidity from 2 to 5, are $0.122\pm 0.006$
for ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$, and $0.259\pm
0.018$ for ${\mathchar 28931\relax}^{0}_{b}$, where the uncertainties arise
from both statistical and systematic sources. The ${\mathchar
28931\relax}^{0}_{b}$ ratio depends strongly on transverse momentum, while the
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ ratio shows a mild
dependence. Neither ratio shows variations with pseudorapidity. The
measurements are made using semileptonic decays to minimize theoretical
uncertainties. In addition, the ratio of ${D}^{+}$ to ${D}^{0}$ mesons
produced in the sum of ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$
and ${{B}^{-}}$ semileptonic decays is determined as $0.359\pm 0.006\pm
0.009$, where the uncertainties are statistical and systematic.

To be published in Physical Review D Rapid Communications

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

Knowledge of the fragmentation fractions of ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ ($f_{s}$) and ${\mathchar
28931\relax}^{0}_{b}$ ($f_{{{\mathchar 28931\relax}^{0}_{b}}}$) hadrons is
essential for determining absolute branching fractions (${\cal{B}}$) of decays
of these hadrons at the LHC, allowing measurements, for example, of
${\cal{B}}({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow\mu^{+}\mu^{-})$
[1] and the future evaluation of $|V_{cb}|$ from ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}\mu^{-}\overline{\nu}_{\mu}$ decays [2].111Mention of a
particular decay mode implies the use of the charge-conjugate one as well.
Once these fractions are determined, measurements of absolute branching
fractions of ${{B}^{-}}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mesons performed at
$e^{+}e^{-}$ colliders operating at the $\mathchar 28935\relax(4S)$ resonance
can be used to determine the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ branching fractions [3].

In this Letter we measure the ratios $f_{s}/(f_{u}+f_{d})$ and $f_{{{\mathchar
28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$, where the denominator is the sum of
${{B}^{-}}$ and ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$
contributions, in the LHCb acceptance of pseudorapidity $2<\eta<5$ and
transverse momentum $4<p_{\mathrm{T}}<25\text{\,Ge\kern-1.00006ptV}$,222We use
natural units where $c=\hbar=1$. in 13 TeV $pp$ collisions. These ratios can
depend on $p_{\mathrm{T}}$ and $\eta$; therefore, we perform the analysis
using two-dimensional binning.

Much of the analysis method adopted in this study is an evolution of our
previous $b$-hadron fraction measurements for 7 TeV $pp$ collisions[4]. We use
the inclusive semileptonic decays $H_{b}\rightarrow
H_{c}X\mu^{-}\overline{\nu}_{\mu}$, where $H_{b}$ indicates a $b$ hadron,
$H_{c}$ a charm hadron, and $X$ possible additional particles. Each of the
different $H_{c}$ plus muon final states can originate from the decay of
different $b$ hadrons. Semileptonic decays of ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ mesons usually result in a
mixture of $D^{0}$ and $D^{+}$ mesons, while $B^{-}$ mesons decay
predominantly into $D^{0}$ mesons with a smaller admixture of $D^{+}$ mesons.
Both include a tiny component of ${{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}}$ meson pairs. Similarly, ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ mesons decay predominantly
into $D_{s}^{+}$ mesons, but can also decay into $D^{0}K^{+}$ and
$D^{+}{{K}^{0}}$ meson pairs; this is expected if the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ meson decays into an
excited $D_{s}^{+}$ state that is heavy enough to decay into a $DK$ pair. We
measure this contribution using $D^{0}K^{+}X\mu^{-}\overline{\nu}_{\mu}$
events. Finally, ${{\mathchar 28931\relax}^{0}_{b}}$ baryons decay
semileptonically mostly into ${{\mathchar 28931\relax}^{+}_{c}}$ final states,
but can also decay into $D^{0}p$ and $D^{+}n$ pairs. We ignore the
contributions of $b\rightarrow u$ decays that comprise approximately 1% of
semileptonic $b$-hadron decays, and contribute almost equally to all
$b$-hadron species. The detailed equations relating these yields to the final
results are given in Ref. [4] and in the Supplemental material.

The theoretical basis for this measurement is the near equality of
semileptonic widths, $\Gamma_{\rm SL}$, for all $b$-hadron species [5] whose
differences are predicted to precisions of about 1%. The values we use for the
individual $H_{b}$ semileptonic branching fractions (${\cal{B}}_{\rm SL}$) are
listed in Table 1. The $H_{c}$ decay modes used and their branching fractions
are given in Table 2.

The ratio of ${D}^{+}$ to ${D}^{0}$ meson production in the sum of
semileptonic ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ and
${{B}^{-}}$ decays, ${f_{+}}/{f_{0}}$, is used to check the analysis method.
This result can be related to models of the hadronic final states in
${{{B}^{-}}}$ and ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$
semileptonic decays [6].

The data sample corresponds to 1.67$\text{\,fb}^{-1}$ of integrated luminosity
obtained with the LHCb detector in 13 TeV $pp$ collisions during 2016. The
LHCb detector [7, 8] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector elements that are particularly
relevant to this analysis are: a silicon-strip vertex detector surrounding the
$pp$ interaction region that allows $c$ and $b$ hadrons to be identified from
their characteristically long flight distance from the primary vertex (PV); a
tracking system that provides a measurement of the momentum, $p$, of charged
particles, two ring-imaging Cherenkov detectors that are able to discriminate
between different species of charged hadrons, and a muon detection system.

The online event selection is performed by a trigger [9] which consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage, which applies a full event reconstruction. At
the hardware trigger stage, events are required to have a muon with large
$p_{\mathrm{T}}$ or a hadron, photon or electron with high transverse energy
in the calorimeters. For hadrons, the transverse energy threshold is 3.5 GeV.
The software trigger requires a two-, three- or four-track secondary vertex
with a significant displacement from any primary $pp$ interaction vertex. At
least one charged particle must have
$p_{\mathrm{T}}>1.6\text{\,Ge\kern-1.00006ptV}$ and be inconsistent with
originating from a PV. A multivariate algorithm [10] is used for the
identification of secondary vertices consistent with the decay of a $b$
hadron.

Simulation is required to model the effects of the detector acceptance and the
imposed selection requirements. Here $pp$ collisions are generated using
Pythia [11, *Sjostrand:2006za] with a specific LHCb configuration [13]. Decays
of unstable particles are described by EvtGen [14], in which final-state
radiation is generated using Photos [15]. The interaction of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [16, *Agostinelli:2002hh] as described in Ref. [18].

Table 1: Branching fractions of semileptonic $b$-hadron decays from direct measurements for ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ and ${{B}^{-}}$ mesons, ($\left<B\right>\equiv\left<{{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}+B^{-}\right>$), and derived for ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ and ${\mathchar 28931\relax}^{0}_{b}$ hadrons based on the equality of semileptonic widths and the lifetime ratios [3, 5]. Corrections to $\Gamma_{\rm SL}$ for ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ $(-1.0\pm 0.5)$% and ${\mathchar 28931\relax}^{0}_{b}$ $(3.0\pm 1.5)$% are applied [5]. Correlations in the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ and ${{B}^{-}}$ branching fraction measurements have been taken into account. See Ref. [19] for more information. Particle |  $\tau$ (ps) |  ${\cal{B}}_{\rm SL}$ (%) |  ${\cal{B}_{\rm SL}}$ (%)
---|---|---|---
| measured | measured | used
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ | $1.520\pm 0.004$ | $10.30\pm 0.19$ | $10.30\pm 0.19$
$B^{-}$ | $1.638\pm 0.004$ | $11.08\pm 0.20$ | $11.08\pm 0.20$
$\left<B\right>$ |  | $10.70\pm 0.19$ | $10.70\pm 0.19$
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ | $1.526\pm 0.015$ |  | $10.24\pm 0.21$
${{\mathchar 28931\relax}^{0}_{b}}$ | $1.470\pm 0.010$ |  | $10.26\pm 0.25$
Table 2: Charm-hadron branching fractions for the decay modes used in this analysis. Note, the ${\mathchar 28931\relax}^{+}_{c}$ branching fraction has been significantly improved since the previous analysis.  Decay |  ${\cal{B}}$ (%) |  Source
---|---|---
$D^{0}\rightarrow K^{-}\pi^{+}$ | $3.93\pm 0.05$ | PDG average [3]
$D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ | $9.22\pm 0.17$ | CLEO-c [20]
$D_{s}^{+}\rightarrow K^{-}K^{+}\pi^{+}$ | $5.44\pm 0.18$ | PDG average [3]
${{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+}$ | $6.23\pm 0.33$ | From Refs. [21, 22]

Selection criteria are applied to muons and $H_{c}$ decay particles. The
transverse momentum of each hadron must be greater than 0.3 GeV, and that of
the muon larger than 1.3 GeV. Each track cannot point to any PV, implemented
by requiring $\chi^{2}_{\text{IP}}>9$ with respect to any PV, where
$\chi^{2}_{\text{IP}}$ is defined as the difference in the vertex-fit
$\chi^{2}$ of a given PV reconstructed with and without the track under
consideration being included. All final state particles are required to be
positively identified using information from the RICH detectors (PID).
Particles from $H_{c}$ decay candidates must have a good fit to a common
vertex with $\chi^{2}$/ndof $<9$, where ndof is the number of degrees of
freedom. They must also be well separated from the nearest PV, with the flight
distance divided by its uncertainty greater than 5.

Candidate $b$ hadrons are formed by combining $H_{c}$ and muon candidates
originating from a common vertex with $\chi^{2}$/ndof $<9$ and an
$H_{c}\mu^{-}$ invariant mass, $m_{H_{c}\mu^{-}}$, in the range 3.0–5.0 GeV
for $D^{0}$ and $D^{+}$, 3.1–5.1 GeV for ${D}^{+}_{s}$ and 3.3–5.3 GeV for
${\mathchar 28931\relax}^{+}_{c}$ candidates. In addition, we define $m_{\rm
corr}\equiv\sqrt{m_{H_{c}\mu}^{2}+p_{\perp}^{2}}+p_{\perp}$, where $p_{\perp}$
is the magnitude of the combination’s momentum component transverse to the
$b$-hadron flight direction; we require that $m_{\rm corr}>4.2$ or
$4.5\text{\,Ge\kern-1.00006ptV}$ for ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ or ${\mathchar
28931\relax}^{0}_{b}$ candidates, respectively. For the
${{D}^{+}_{s}}\rightarrow K^{+}K^{-}\pi^{+}$ decay mode, vetoes are employed
to remove backgrounds from real $D^{+}$ or ${\mathchar 28931\relax}^{+}_{c}$
decays where the particle assignments are incorrect.

Background from prompt $H_{c}$ production at the PV needs to be considered. We
use the natural logarithm of the $H_{c}$ impact parameter, IP, with respect to
the PV in units of mm. Requiring ln(IP/mm)$>-3$ is found to reduce the prompt
component to be below 0.1%, while preserving 97% of all signals. This
restriction allows us to perform fits only to the $H_{c}$ candidate mass
spectra to find the $b$-hadron decay yields.

Figure 1: Fit to the mass spectra of the $H_{c}$ candidates of the selected
$H_{b}$ decays: (a) $D^{0}$, (b) $D^{+}$, (c) $D_{s}^{+}$ mesons, and (d) the
${\mathchar 28931\relax}^{+}_{c}$ baryon. The data are shown as black points
with error bars. The signal component is shown as the dashed (green) line and
the combinatorial background component is shown as the dashed (red) line. The
solid (blue) line shows all components added together.

The $H_{c}$ candidates mass distributions integrated over
$p_{\mathrm{T}}(H_{b})$ and $\eta$ are shown in Fig. 1. They consist of a
prominent peak resulting from signal, and a small contribution due to
combinatorial background from random combinations of particles that pass the
selection. They are fit with a signal component comprised of two Gaussian
functions, and a combinatorial background component modeled as a linear
function. The total signal yields for $D^{0}X\mu^{-}\overline{\nu}_{\mu}$,
$D^{+}X\mu^{-}\overline{\nu}_{\mu}$, $D_{s}^{+}X\mu^{-}\overline{\nu}_{\mu}$
and ${{\mathchar 28931\relax}^{+}_{c}}\mu^{-}X\overline{\nu}_{\mu}$ are 13 775
000, 4 282 700, 845 300, and 1 753 600, respectively.

Background contributions to the $b$-hadron candidates include hadrons faking
muons, false combinations of charm hadrons and muons from the two $b$ hadrons
in the event, as well as real muons and charm hadrons from
$B\rightarrow{D}{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}}X$ decays,
where one of the $D$ mesons decays into a muon. All the backgrounds are
evaluated in two-dimensional $\eta$ and $p_{\mathrm{T}}$ intervals. The first
two backgrounds are evaluated using events where the $H_{c}$ is combined with
a muon of the wrong-sign (e.g. $D^{0}\mu^{+}$), forbidden in a semileptonic
$b$-hadron decay. The wrong-sign backgrounds are $<1$% for each $H_{c}$
species. The background from $B\rightarrow D{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}}X$ decays is determined by simulating
a mixture of these decays using their measured branching fractions [3]. The
only decay mode significantly affected is ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}_{s}}X\mu^{-}\overline{\nu}_{\mu}$
with contributions varying from 0.1% for $D^{0}D_{s}^{-}X$ to 1.8% for
${{D}^{+}_{s}}D_{s}^{-}X$ due to the large
${{D}^{+}_{s}}\rightarrow\mu^{+}\nu$ decay rate. The total $B\rightarrow
D{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}}X$ background is $(5.8\pm
0.9)\%$.

The dominant component in ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ semileptonic decays is
${{D}^{+}_{s}}X\mu^{-}\overline{\nu}_{\mu}$, where $X$ contains possible
additional hadrons. However, the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ meson also can decay into
$D^{0}K^{+}$ or $D^{+}K^{0}$ instead of ${D}^{+}_{s}$, so we must add this
component to the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$
rate and subtract it from the $f_{u}+f_{d}$ fraction. Similarly, in
${\mathchar 28931\relax}^{0}_{b}$ semileptonic decays we find a $D^{0}pX$
component. The selection criteria for these final states are similar to those
for the $D^{0}X\mu^{-}\overline{\nu}_{\mu}$ and ${{\mathchar
28931\relax}^{+}_{c}}X\mu^{-}\overline{\nu}_{\mu}$ final states described
above with the addition of a kaon or proton with
$p_{\mathrm{T}}>300\text{\,Me\kern-1.00006ptV}$ that has been positively
identified. A veto is also applied to reject $D^{*+}\rightarrow\pi^{+}D^{0}$
decays where the pion mimics a kaon or a proton.

These samples contain background, resonant and nonresonant decays. Separation
of these components is achieved by using both right-sign ($H_{c}$ with
$\mu^{-}$) and wrong-sign ($H_{c}$ with $\mu^{+}$) candidates. In addition,
the logarithm of the difference between the vertex $\chi^{2}$ formed by the
added hadron track and the $D\mu$ system and the vertex $\chi^{2}$ of the
$D\mu$ system, ${\rm ln}(\Delta\chi^{2}_{\rm V})$, provides separation between
combinatorial background and nonresonant semileptonic decays. True resonant
and nonresonant ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{0}}{{K}^{+}}\mu^{-}\overline{\nu}_{\mu}$
or ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{D}^{0}}p\mu^{-}\overline{\nu}_{\mu}$ decays
peak in the ${\rm ln}(\Delta\chi^{2}_{\rm V})$ distribution at a value of
unity while the background is smooth and rises at higher values as the added
track is generally not associated with the ${{D}^{0}}{\mu^{-}}$ vertex. To
distinguish signal from background we define $m(D^{0}h)_{C}\equiv
m(D^{0}h)-m(D^{0})+m(D^{0})_{\rm PDG}$, and perform two-dimensional fits to
the $m(D^{0}h)_{C}$ and ${\rm ln}(\Delta\chi^{2}_{\rm V})$ distributions,
where $h=K^{+}(p)$ for right-sign ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ (${\mathchar
28931\relax}^{0}_{b}$) decays.

Figure 2:  Projections of the two-dimensional fits to the (a)
$m(D^{0}K^{\pm})_{C}$ and (c) $m(D^{0}\kern
0.20004pt\shortstack{{(\rule[2.15277pt]{8.50006pt}{0.51212pt})} \\\ [-.7ex]
$\kern-0.20004ptp$}{})_{C}$ mass distributions and (b, d) ${\rm
ln}(\Delta\chi^{2}_{\rm V})$ for (top)
${{D}^{0}}K^{\pm}X\mu^{-}\overline{\nu}_{\mu}$ candidates, and (bottom) for
${{D}^{0}}\kern
0.20004pt\shortstack{{(\rule[2.15277pt]{8.50006pt}{0.51212pt})} \\\ [-.7ex]
$\kern-0.20004ptp$}{}X\overline{\nu}_{\mu}$ candidates. The curves show
projections of the 2D fit. The dashed (red) curves show the $D_{s1}^{+}$ and
$D_{s2}^{*+}$ resonant components in (a) and (b), and ${{\mathchar
28931\relax}^{+}_{c}}(2860)$, ${{\mathchar 28931\relax}^{+}_{c}}(2880)$ and
${{\mathchar 28931\relax}^{+}_{c}}(2940)$ resonant components in (c) and (d).
The long-dashed-dotted (green) curves show the nonresonant component, the
dotted (black) curves are the background components, whose shapes are
determined from wrong-sign combinations, and the solid (blue) curve shows all
components added together.

The wrong-sign shapes are used to model the backgrounds. The resonant
structures are modeled with relativistic Breit–Wigner functions convoluted
with Gaussians to take into account the experimental resolution, except for
the narrow $D_{s1}(2536)^{+}$ which is modeled with the sum of two Gaussians
with a fixed mean. The nonresonant shape for the ${\rm ln}(\Delta\chi^{2}_{\rm
V})$ distribution is taken as the same as the resonant one. Figure 2 shows the
data and result of the fits for ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ candidates.

For the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ case, we
find $22~{}\\!610\pm 210$ $D_{s1}(2536)^{+}$, $14~{}\\!290\pm 260$
$D_{s2}^{*}(2573)^{+}$, and $38~{}\\!140\pm 460$ nonresonant decays,
confirming the existence of both the $D_{s1}^{+}$ [23, 24] and $D_{s2}^{*+}$
[24] particles in semileptonic ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ decays with substantially
more data, and showing the existence of the nonresonant component. To account
for the unmeasured $D^{+}K^{0}$ channel we take different mixtures of $D^{*}$
and $D$ final states for the different resonant and nonresonant components.
The $D_{s1}^{+}$ decays dominantly into $D^{*}$, while the $D_{s2}^{*+}$
decays dominantly into $D$ mesons [3]. For the nonresonant part we assume
equal $D^{*}$ and $D$ yields.

In the ${\mathchar 28931\relax}^{0}_{b}$ case, we find $6120\pm 460$
${{\mathchar 28931\relax}^{+}_{c}}(2860)$, $2200\pm 200$ ${{\mathchar
28931\relax}^{+}_{c}}(2880)$, $1200\pm 260$ ${{\mathchar
28931\relax}^{+}_{c}}(2940)$, and $29~{}\\!770\pm 690$ nonresonant events. The
decay rate into $D^{0}p$ is assumed to be equal to that into $D^{+}n$ using
isospin conservation. All decays with an extra hadron have lower detection
efficiencies than the sample without.

Efficiencies for all the samples are determined using data in two-dimensional
$p_{\mathrm{T}}$ and $\eta$ bins. Trigger efficiencies are determined using a
sample of $B^{-}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{-}$, with ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{+}}{\mu^{-}}$ decays where only one muon track is
positively identified, in conjunction with viewing the effects of combinations
of different triggers [25]. This sample is also used to determine muon
identification efficiencies. Decays of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons to muons reconstructed using partial information from the
tracking system, e.g. eliminating the vertex locator information, are also
used to determine tracking efficiencies using data and to correct the
simulation. Finally, the PID efficiencies are evaluated using kaons and pions
from $D^{*+}\rightarrow\pi^{+}D^{0}$ decays, with $D^{0}\rightarrow
K^{-}\pi^{+}$, and protons from $\mathchar 28931\relax\rightarrow p\pi^{-}$
and ${{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+}$ decays [26].
In the measurement of $b$-hadron fraction ratios many of the efficiencies
cancel and we are left with only residual effects to which we assign
systematic uncertainties.

The $b$-hadron $\eta$ and $p_{\mathrm{T}}$, $p_{\mathrm{T}}(H_{b})$, must be
known because the $b$ fractions can depend on production kinematics. While
$\eta$ can be evaluated directly using the measured primary and secondary $b$
vertices, the value of $p_{\mathrm{T}}(H_{b})$ must be determined to account
for the missing neutrino plus extra particles. The correction factor $k$ is
given by the ratio of the average reconstructed to true
$p_{\mathrm{T}}(H_{b})$ as a function of $m(H_{c}\mu^{-})$ and is determined
using simulation. It varies from 0.75 for $m(H_{c}\mu^{-})$ equals 3 GeV to
unity at $m(H_{c}\mu^{-})=m(H_{b})$.

Figure 3: The ratios $f_{s}/(f_{u}+f_{d})$ and $f_{{{\mathchar
28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$ in bins of $p_{\mathrm{T}}(H_{b})$. The
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ data are indicated
by solid circles, while the ${\mathchar 28931\relax}^{0}_{b}$ by triangles.
The smaller (black) error bars show the combined bin-by-bin statistical and
systematic uncertainties, and the larger (blue) ones show the global
systematics added in quadrature. The fits to the data are shown as the solid
(green) bands, whose widths represents the $\pm 1\sigma$ uncertainty limits on
the fit shapes, and the dashed (black) lines give the total uncertainty on the
fit results including the global scale uncertainty. In the highest two
$p_{\mathrm{T}}$ bins the points have been displaced from the center of the
bin.

The distribution of $f_{s}/(f_{u}+f_{d})$ as a function of
$p_{\mathrm{T}}(H_{b})$ is shown in Fig. 3. We perform a linear $\chi^{2}$ fit
incorporating a full covariance matrix which takes into account the bin-by-bin
correlations introduced from the kaon kinematics, and PID and tracking
systematic uncertainties. The factor $A$ in Eq. 1 incorporates the global
systematic uncertainties described later, which are independent of
$p_{\mathrm{T}}(H_{b})$. The resulting function is

$\frac{f_{s}}{f_{u}+f_{d}}(p_{\mathrm{T}})=A\left[p_{1}+p_{2}\times\left(p_{\mathrm{T}}-\langle
p_{\mathrm{T}}\rangle\right)\right],$ (1)

where $p_{\mathrm{T}}$ here refers to $p_{\mathrm{T}}(H_{b})$, $A=1\pm 0.043$,
$p_{1}=0.119\pm 0.001$, $p_{2}=(-0.91\pm 0.25)\cdot 10^{-3}~{}\\!{\rm
GeV}^{-1}$, and $\langle
p_{\mathrm{T}}\rangle=10.1\text{\,Ge\kern-1.00006ptV}$. The correlation
coefficient between the fit parameters is 0.20. After integrating over
$p_{\mathrm{T}}(H_{b})$, no $\eta$ dependence is observed (see the
Supplemental material).

We determine an average value for $f_{s}/(f_{u}+f_{d})$ by dividing the yields
of ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ semileptonic
decays by the sum of ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$
and ${{{B}^{-}}}$ semileptonic yields, which are all efficiency-corrected,
between the limits of $p_{\mathrm{T}}(H_{b})$ of 4 and 25 GeV and $\eta$ of 2
and 5, resulting in

$\frac{f_{s}}{f_{u}+f_{d}}=0.122\pm 0.006,$

where the uncertainty contains both statistical and systematic components,
with the latter being dominant, and discussed subsequently. The total relative
uncertainty is 4.8%.

Figure 3 also shows the ${\mathchar 28931\relax}^{0}_{b}$ fraction as a
function of $p_{\mathrm{T}}(H_{b})$ demonstrating a large $p_{\mathrm{T}}$
dependence. The distribution in $\eta$ is flat. We perform a similar fit as in
the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ fraction case,
using

$\frac{f_{{{\mathchar
28931\relax}^{0}_{b}}}}{f_{u}+f_{d}}(p_{\mathrm{T}})=A\left[p_{1}+\exp\left(p_{2}+p_{3}\times
p_{\mathrm{T}}\right)\right],\\\ $ (2)

where $p_{\mathrm{T}}$ here refers to $p_{\mathrm{T}}(H_{b})$, $A=1\pm 0.061$,
$p_{1}=(7.93\pm 1.41)\cdot 10^{-2}$, $p_{2}=-1.022\pm 0.047$, and
$p_{3}=-0.107\pm 0.002~{}\\!{\rm GeV}^{-1}$. The correlation coefficients
among the fit parameters are 0.40 $(\rho_{12})$, –0.95 $(\rho_{13})$, and
–0.63 $(\rho_{23})$.

The average value for $f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$ is
determined using the same method as in the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ case. The result is

$\frac{f_{{{\mathchar 28931\relax}^{0}_{b}}}}{f_{u}+f_{d}}=0.259\pm 0.018,$

where the dominant uncertainty is systematic, and the statistical uncertainty
is included. The overall uncertainty is 6.9%.

As a systematic check of the analysis method, and a useful measurement to test
the knowledge of known semileptonic branching fractions and extrapolations
used to saturate the unknown portion of the inclusive hadron spectrum, we
measure the ratio of the $D^{0}X\mu^{-}\overline{\nu}_{\mu}$ to
$D^{+}X\mu^{-}\overline{\nu}_{\mu}$ corrected yields $f_{+}/f_{0}$. We
subtract the small contributions from ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ decays, and a very small contribution from
$B\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}}\mu^{-}X$ decays has been taken into
account [27], as in all the fractions measured above.

Assuming $f_{u}$ equals $f_{d}$, Ref. [6] estimates the fraction of $D^{+}\mu$
with respect to $D^{0}\mu$ modes in the sum of ${{{B}^{-}}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ decays as $0.387\pm 0.012\pm
0.026$. The first uncertainty comes from the uncertainties on known
measurements. The second uncertainty comes from the different extrapolations
from excited $D$ mesons used to saturate the remaining portion of the
inclusive rate.

The $f_{+}/f_{0}$ ratio must be independent of $\eta$ and $p_{\mathrm{T}}$. To
derive an overall value for $f_{+}/f_{0}$, the $p_{\mathrm{T}}(H_{b})$
distribution is fit to a constant. Only the PID and tracking systematic
uncertainties on the second pion in the $D^{+}$ decay need be considered.
Performing a $\chi^{2}$ fit using the full covariance matrix we find
$f_{+}/f_{0}=0.359\pm 0.006\pm 0.009$, where the first uncertainty is from
bin-by-bin statistical and systematic uncertainties, including correlations,
and the second is systematic. The $\chi^{2}$/ndof is 0.63, in agreement with a
flat spectrum. The measurement is consistent with the prediction and places
some constraints on the $D^{**}$ content of semileptonic $B$ decays [6].

The dominant global systematic uncertainties are listed in Table 3. Simulation
uncertainties are due to the modeling of excited charm states for the
$f_{s}/(f_{u}+f_{d})$ determination and the weighting required for the
$f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$ ratio, due to
differences between the simulated and measured $p_{\mathrm{T}}$ spectra.
Background uncertainties arise from $D{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}}X$ final states with uncertain
branching fractions. Cross-feed uncertainties come from errors on efficiency
estimates and the assumed $D^{*}$ to $D$ mixtures. Other smaller uncertainties
depend on $p_{\mathrm{T}}(H_{b})$ and include tracking (0.2–1.8)%, particle
identification (0.4–3.0)%, trigger (0.3–3.9)% and $k$-factor (0.2–1.8)%.

Table 3: Global systematic uncertainties. The $D^{0}$ and $D^{+}$ branching fraction uncertainties are scaled by the fraction of each decay, $f_{0}$ and $f_{+}$ for $f_{s}/(f_{u}+f_{d})$ and $f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$ uncertainties.  Source | Value (%)
---|---
| $f_{s}/(f_{u}+f_{d})$ | $f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$ | $f_{+}/f_{0}$
Simulation | 1.7 | 2.4 | –
Backgrounds | 0.9 | 0.3 | –
Cross-feeds | 1.2 | 0.4 | 0.2
$\mathcal{B}$($D^{0}\rightarrow K^{-}\pi^{+}$) | 1.0 | 1.0 | 1.3
$\mathcal{B}$($D^{+}\rightarrow K^{+}\pi^{-}\pi^{-}$) | 0.6 | 0.6 | 1.8
$\mathcal{B}$($D^{+}_{s}\rightarrow K^{+}K^{-}\pi^{+}$) | 3.3 | – | –
$\mathcal{B}$(${{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{+}\pi^{-}$) | – | 5.3 | –
Measured lifetime ratio | 1.2 | 0.7 | –
$\Gamma_{SL}$ correction | 0.5 | 1.5 | –
Total | 4.3 | 6.1 | 2.2

In conclusion, we measure the ratios of ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ production to the sum of ${{B}^{-}}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ to be $p_{\mathrm{T}}(H_{b})$
dependent (see Eqs. 1 and 2). The averages in the ranges
$4<p_{\mathrm{T}}(H_{b})<25\text{\,Ge\kern-1.00006ptV}$, and $2<\eta<5$ are
$f_{s}/(f_{u}+f_{d})=0.122\pm 0.006$, and $f_{{{\mathchar
28931\relax}^{0}_{b}}}/(f_{u}+f_{d})=0.259\pm 0.018$, respectively. Using 7
TeV data, LHCb determined $f_{s}/(f_{u}+f_{d})=0.1295\pm 0.0075$ with a
$p_{\mathrm{T}}(H_{b})$ slope larger than, but consistent with these 13 TeV
results [28]; no dependence on $\eta$ was observed. For the ${{\mathchar
28931\relax}^{0}_{b}}$ baryon, the fraction ratio is consistent with the 7 TeV
measurements after taking into account the different $p_{\mathrm{T}}(H_{b})$
ranges used [29, 30, 4]. We observe no rapidity dependence over a similar
$p_{\mathrm{T}}(H_{b})$ range as in Ref. [30].

These results are crucial for determining absolute branching fractions of
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ hadron decays in LHC experiments. We also determine the
ratio of $D^{0}$ to $D^{+}$ mesons produced in the sum of ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ and ${{B}^{-}}$ semileptonic
decays as $f_{+}/f_{0}=0.359\pm 0.006\pm 0.009$.

## 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); 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); Laboratory Directed Research and
Development program of LANL (USA).

##  1 Supplemental material

###  1.1 Relationships between raw $H_{c}\mu^{-}X$ measured yields and
corrected yields

The corrected yields for ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ or $B^{-}$ mesons decaying
into $D^{0}\mu^{-}\overline{\nu}_{\mu}X$ or
$D^{+}\mu^{-}\overline{\nu}_{\mu}X$, $n_{\rm corr}$, can be expressed in terms
of the measured yields, $n$, as

$\displaystyle n_{\rm corr}(B\rightarrow{{D}^{0}}{\mu^{-}})$
$\displaystyle=\frac{1}{{\cal{B}}({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}})\epsilon(B\rightarrow{{D}^{0}})}\times$
(3)
$\displaystyle\left[n({{D}^{0}}\mu^{-})-n({{D}^{0}}{{K}^{+}}{\mu^{-}})\frac{\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{0}})}{\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{0}}{{K}^{+}})}-n({{D}^{0}}p{\mu^{-}})\frac{\epsilon({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{D}^{0}})}{\epsilon({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{D}^{0}}p)}\right],$

where we use the shorthand $n(D{\mu^{-}})\equiv
n(DX\mu^{-}\overline{\nu}_{\mu})$. An analogous abbreviation $\epsilon$ is
used for the total trigger and detection efficiencies. For example, the ratio
$\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
D^{0}K^{+})/\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow D^{0})$ gives
the relative efficiency to reconstruct a charged kaon in semimuonic ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ decays producing a
${{D}^{0}}$ meson. The second term in this equation accounts for the
${{D}^{0}}{\mu^{-}}$ pairs originating from a ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ decay, such as ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{0}}{{K}^{+}}{\mu^{-}}$,
while the third term accounts for the ${{D}^{0}}{\mu^{-}}$ pairs originating
from ${{\mathchar 28931\relax}^{0}_{b}}$ semileptonic decays. These components
are determined from the study of the final states
${{D}^{0}}{{K}^{+}}{\mu^{-}}$ and ${{D}^{0}}p{\mu^{-}}$respectively. The
branching fraction ${\cal B}({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}})$
appears because this decay mode is used in this study. Similarly

$\displaystyle n_{\rm corr}(B\rightarrow{{D}^{+}}{\mu^{-}})$ $\displaystyle=$
$\displaystyle\frac{1}{\epsilon(B\rightarrow{{D}^{+}})}\left[\frac{n({{D}^{+}}{\mu^{-}})}{{\cal{B}}({{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}})}\right.$
(4)
$\displaystyle\left.-\frac{n({{D}^{0}}{{K}^{+}}{\mu^{-}})}{{\cal{B}}({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}})}\frac{\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}})}{\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{0}}{{K}^{+}})}\right.$
$\displaystyle\left.-\frac{n({{D}^{0}}p{\mu^{-}})}{{\cal{B}}({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}})}\frac{\epsilon({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{D}^{+}})}{\epsilon({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{D}^{0}}p)}\right].$

Both the ${{D}^{0}}X\mu^{-}\overline{\nu}_{\mu}$ and the
${{D}^{+}}X\mu^{-}\overline{\nu}_{\mu}$ final states contain small components
of cross-feed from ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ decays to
${{D}^{0}}K^{+}X\mu^{-}\overline{\nu}_{\mu}$ and to
$D^{+}{{K}^{0}}X\mu^{-}\overline{\nu}_{\mu}$, and from ${{\mathchar
28931\relax}^{0}_{b}}$ decays to ${{D}^{0}}pX\mu^{-}\overline{\nu}_{\mu}$ and
to $D^{+}nX\mu^{-}\overline{\nu}_{\mu}$. Here we use isospin symmetry and
infer the contributions by ${{D}^{+}}{\mu^{-}}$ pairs originating from a
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ decay, such as
${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}}{{K}^{0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}$
from the ${{D}^{0}}{{K}^{+}}{\mu^{-}}$ final states, and the contributions
from ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{D}^{+}}n{\mu^{-}}{{\overline{\nu}}_{\mu}}$
from the ${{D}^{0}}p{\mu^{-}}$ yields.

The number of ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}_{s}}X\mu^{-}\overline{\nu}_{\mu}$
decays in the final state is given by

$\displaystyle n_{\rm corr}({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}_{s}}\mu^{-})$
$\displaystyle=$ $\displaystyle\frac{n({{D}^{+}_{s}}\mu^{-})}{{\cal
B}({{D}^{+}_{s}}\rightarrow K^{+}K^{-}\pi^{+})\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}_{s}}\mu^{-})}$
(5) $\displaystyle-N({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}+B^{-}){\cal
B}(B\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}}^{0})\frac{\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}}^{0}\mu^{-})}{\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}_{s}}\mu^{-})}.$

In addition, the ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$
meson decays semileptonically into $DKX\mu^{-}\overline{\nu}_{\mu}$, and thus
we need to add to Eq. 5 the term

$n_{\rm corr}({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
DK\mu^{-})=\kappa\frac{n({{D}^{0}}K^{+}\mu^{-})}{{\cal B}({{D}^{0}}\rightarrow
K^{-}\pi^{+})\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
D^{0}K^{+}\mu^{-})},$ (6)

where $\kappa$ accounts for the unmeasured ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
D^{+}KX\mu^{-}\overline{\nu}_{\mu}$ semileptonic decays. The correction
$\kappa$ is evaluated using the known decay modes of the $D_{s1}(2536)^{+}$
and $D^{*}_{s2}(2573)^{+}$ states and assuming that the nonresonant component
of the hadronic mass spectrum decays in equal portions into $D$ or ${{D}^{*}}$
final states. The last term in Eq. 5 accounts for
${{D}^{+}_{s}}KX\mu^{-}\overline{\nu}_{\mu}$ final states originating from
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ or $B^{-}$
semileptonic decays, and $N({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}+B^{-})$ indicates the total
number of ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ and $B^{-}$
produced. We derive this correction using the PDG value for the branching
fraction ${\cal B}(B^{-}\rightarrow D_{s}^{(*)+}K^{-}\mu^{-}\nu)=(6.1\pm
1.0)\times 10^{-4}$, and assuming the same rate for ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ decays using isospin
invariance [3].

The equation for the ratio $f_{s}/(f_{u}+f_{d})$ is

$\displaystyle\frac{f_{s}}{f_{u}+f_{d}}=\frac{n_{\rm corr}({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
D\mu^{-})}{n_{\rm corr}(B\rightarrow D^{0}\mu^{-})+n_{\rm corr}(B\rightarrow
D^{+}\mu^{-})}\frac{\tau_{B^{-}}+\tau_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}}}{2\tau_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}_{s}}}}(1-\xi_{s})$
$\displaystyle-\frac{\mathcal{B}(B\rightarrow D_{s}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}}\mu^{-})}{\left<\mathcal{B}_{\rm
SL}\right>}\frac{\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}\rightarrow
D_{s}^{+})}{\epsilon({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow D_{s}^{+})},$
(7)

where ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
D\mu$ represents ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$
semileptonic decays to a charmed hadron, given by the sum of the contributions
shown in Eqs. 5 and 6, and the symbols $\tau_{B_{i}}$ indicate the $B_{i}$
hadron lifetimes, that are all well measured [3]. We use the average ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ lifetime, $1.526\pm 0.015$
ps. This equation assumes equality of the semileptonic widths of all the
$b$-hadron species. This is a reliable assumption, as corrections in HQET
arise only to order 1/$m_{b}^{2}$ and the SU(3) breaking correction is quite
small, $(-1.0\pm 0.5)\%$ [5]. The parameter $\xi_{s}$ accounts for this small
adjustment. The second term is the subtraction of the
$B^{-,0}\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}}X\mu^{-}\overline{\nu}_{\mu}$
component that is reconstructed in the signal sample as described in Eq. 5.
The $\mathcal{B}_{\rm SL}$ term in the denominator is the semileptonic
branching fraction of the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ derived using the equality
of the semileptonic widths and the measured lifetime of the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$, listed in Table 1.

The ${{\mathchar 28931\relax}^{0}_{b}}$ corrected yield is derived in an
analogous manner

$n_{\rm corr}({{\mathchar 28931\relax}^{0}_{b}}\rightarrow
H_{c}\mu^{-})=\frac{n({{\mathchar
28931\relax}^{+}_{c}}{\mu^{-}})}{{\cal{B}}({{\mathchar
28931\relax}^{+}_{c}}\rightarrow p{{K}^{-}}{{\pi}^{+}})\epsilon({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}})}+2\frac{n({{D}^{0}}p{\mu^{-}})}{{\cal{B}}({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}})\epsilon({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{D}^{0}}p)},$ (8)

where $H_{c}$ represents a generic charmed hadron. The second term includes
the cross-feed channel and the factor of two accounts for the isospin
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow D^{+}n{\mu^{-}}$ decay. The
${{\mathchar 28931\relax}^{0}_{b}}$ fraction is written as

$\frac{f_{{{\mathchar 28931\relax}^{0}_{b}}}}{f_{u}+f_{d}}=\frac{n_{\rm
corr}({{\mathchar 28931\relax}^{0}_{b}}\rightarrow H_{c}\mu^{-})}{n_{\rm
corr}(B\rightarrow{{D}^{0}}\mu^{-})+n_{\rm
corr}(B\rightarrow{{D}^{+}}\mu^{-})}\frac{\tau_{{{{B}^{-}}}}+\tau_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}}}{2\tau_{{{\mathchar
28931\relax}^{0}_{b}}}}(1-\xi_{{{\mathchar 28931\relax}^{0}_{b}}}).$ (9)

While we assume near equality of the semileptonic widths of different $b$
hadrons, we apply a small adjustment $\xi_{{{\mathchar
28931\relax}^{0}_{b}}}=(3.0\pm 1.5)$%, to account for the chromomagnetic
correction, affecting $b$-flavored mesons but not $b$ baryons [5]. The
uncertainty is evaluated with conservative assumptions for all the parameters
of the heavy quark expansion.

###  1.2 Table of $b$-fractions versus $p_{\mathrm{T}}(H_{b})$

Table 4: Values of $f_{s}/(f_{u}+f_{d})$ and $f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$ in each $p_{\mathrm{T}}(H_{b})$ bin. The first uncertainty is statistical and incorporates both the uncertainties due to the data sample size and the finite amount of simulated events, while the second is the overall systematic uncertainty, including global and bin-dependent systematic uncertainties.  $p_{\mathrm{T}}(H_{b})[\\!\text{\,Ge\kern-1.00006ptV}]$ | $f_{s}/(f_{u}+f_{d})$ | $f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$
---|---|---
4–5 | $0.125\pm 0.001\pm 0.007$ | $0.324\pm 0.001\pm 0.025$
5–6 | $0.125\pm 0.001\pm 0.007$ | $0.281\pm 0.001\pm 0.018$
6–7 | $0.122\pm 0.001\pm 0.006$ | $0.257\pm 0.001\pm 0.017$
7–8 | $0.125\pm 0.001\pm 0.006$ | $0.245\pm 0.001\pm 0.017$
8–9 | $0.116\pm 0.001\pm 0.006$ | $0.227\pm 0.001\pm 0.015$
9–10 | $0.120\pm 0.001\pm 0.006$ | $0.210\pm 0.001\pm 0.015$
10–11 | $0.121\pm 0.001\pm 0.006$ | $0.194\pm 0.001\pm 0.013$
11–12 | $0.116\pm 0.001\pm 0.006$ | $0.191\pm 0.001\pm 0.014$
12–13 | $0.116\pm 0.001\pm 0.006$ | $0.172\pm 0.001\pm 0.013$
13–14 | $0.122\pm 0.001\pm 0.007$ | $0.159\pm 0.001\pm 0.012$
14–16 | $0.112\pm 0.001\pm 0.006$ | $0.165\pm 0.001\pm 0.012$
16–18 | $0.107\pm 0.001\pm 0.006$ | $0.136\pm 0.001\pm 0.010$
18–20 | $0.115\pm 0.001\pm 0.008$ | $0.126\pm 0.001\pm 0.010$
20–25 | $0.111\pm 0.001\pm 0.007$ | $0.109\pm 0.001\pm 0.009$

###  1.3 Fraction ratios as functions of $\eta$

Figure 4 shows measurements of the fraction ratios $f_{s}/(f_{u}+f_{d})$ and
$f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$ as functions of $\eta$,
integrated over $p_{\mathrm{T}}$. No $\eta$ dependence is visible with the
current data sample.

Figure 4: Measurement of the fraction ratios (a) $f_{s}/(f_{u}+f_{d})$ and (b)
$f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$ as functions of $\eta$
integrated over $p_{\mathrm{T}}$.

###  1.4 Correlation matrices for the fits to $f_{s}/(f_{u}+f_{d})$ and
$f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$

Table 5 shows the covariance matrix among the different
$p_{\mathrm{T}}(H_{b})$ bins for $f_{s}/(f_{u}+f_{d})$, while Table 6 shows
the covariance matrix among the different $p_{\mathrm{T}}(H_{b})$ bins for
$f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$.

Table 5: Covariance matrix for $f_{s}/(f_{u}+f_{d})$ in $p_{\mathrm{T}}(H_{b})$ [GeV] bins; it accounts for statistical and bin-dependent systematic uncertainties, but not the global systematic uncertainties.  $p_{\mathrm{T}}(H_{b})$ | 4–5 | 5–6 | 6–7 | 7–8 | 8–9 | 9–10 | 10–11 | 11–12 | 12–13 | 13–14 | 14–16 | 16–18 | 18–20 | 20–25
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
4–5 | 2.30E-05 | 3.80E-06 | 1.84E-06 | 1.53E-06 | 9.28E-07 | 1.54E-06 | 1.77E-06 | 9.05E-07 | 7.47E-07 | 6.99E-07 | 6.46E-07 | 6.84E-07 | 5.47E-07 | 5.55E-07
5–6 | 3.80E-06 | 1.96E-05 | 2.37E-06 | 2.02E-06 | 1.23E-06 | 2.05E-06 | 2.36E-06 | 1.22E-06 | 1.04E-06 | 9.64E-07 | 8.94E-07 | 9.85E-07 | 8.04E-07 | 8.00E-07
6–7 | 1.84E-06 | 2.37E-06 | 1.10E-05 | 1.08E-06 | 6.71E-07 | 1.14E-06 | 1.32E-06 | 6.94E-07 | 5.83E-07 | 5.46E-07 | 5.18E-07 | 5.60E-07 | 4.67E-07 | 4.89E-07
7–8 | 1.53E-06 | 2.02E-06 | 1.08E-06 | 1.08E-05 | 6.46E-07 | 1.10E-06 | 1.27E-06 | 6.75E-07 | 5.73E-07 | 5.43E-07 | 5.06E-07 | 5.48E-07 | 4.80E-07 | 4.86E-07
8–9 | 9.28E-07 | 1.23E-06 | 6.71E-07 | 6.46E-07 | 8.73E-06 | 7.75E-07 | 9.09E-07 | 5.07E-07 | 4.26E-07 | 4.04E-07 | 3.79E-07 | 4.16E-07 | 3.77E-07 | 3.88E-07
9–10 | 1.54E-06 | 2.05E-06 | 1.14E-06 | 1.10E-06 | 7.75E-07 | 1.09E-05 | 1.66E-06 | 9.39E-07 | 8.03E-07 | 7.62E-07 | 7.24E-07 | 7.77E-07 | 7.01E-07 | 7.34E-07
10–11 | 1.77E-06 | 2.36E-06 | 1.32E-06 | 1.27E-06 | 9.09E-07 | 1.66E-06 | 1.33E-05 | 1.13E-06 | 9.90E-07 | 9.33E-07 | 9.37E-07 | 1.00E-06 | 9.03E-07 | 9.58E-07
11–12 | 9.05E-07 | 1.22E-06 | 6.94E-07 | 6.75E-07 | 5.07E-07 | 9.39E-07 | 1.13E-06 | 1.33E-05 | 5.94E-07 | 5.64E-07 | 5.74E-07 | 6.24E-07 | 5.73E-07 | 6.17E-07
12–13 | 7.47E-07 | 1.04E-06 | 5.83E-07 | 5.73E-07 | 4.26E-07 | 8.03E-07 | 9.90E-07 | 5.94E-07 | 1.60E-05 | 5.42E-07 | 5.62E-07 | 6.33E-07 | 5.73E-07 | 6.08E-07
13–14 | 6.99E-07 | 9.64E-07 | 5.46E-07 | 5.43E-07 | 4.04E-07 | 7.62E-07 | 9.33E-07 | 5.64E-07 | 5.42E-07 | 2.31E-05 | 5.31E-07 | 6.33E-07 | 5.98E-07 | 6.13E-07
14–16 | 6.46E-07 | 8.94E-07 | 5.18E-07 | 5.06E-07 | 3.79E-07 | 7.24E-07 | 9.37E-07 | 5.74E-07 | 5.62E-07 | 5.31E-07 | 1.32E-05 | 7.11E-07 | 6.66E-07 | 7.27E-07
16–18 | 6.84E-07 | 9.85E-07 | 5.60E-07 | 5.48E-07 | 4.16E-07 | 7.77E-07 | 1.00E-06 | 6.24E-07 | 6.33E-07 | 6.33E-07 | 7.11E-07 | 1.96E-05 | 8.08E-07 | 9.33E-07
18–20 | 5.47E-07 | 8.04E-07 | 4.67E-07 | 4.80E-07 | 3.77E-07 | 7.01E-07 | 9.03E-07 | 5.73E-07 | 5.73E-07 | 5.98E-07 | 6.66E-07 | 8.08E-07 | 3.71E-05 | 9.58E-07
20–25 | 5.55E-07 | 8.00E-07 | 4.89E-07 | 4.86E-07 | 3.88E-07 | 7.34E-07 | 9.58E-07 | 6.17E-07 | 6.08E-07 | 6.13E-07 | 7.27E-07 | 9.33E-07 | 9.58E-07 | 2.93E-05

Table 6: Covariance matrix for $f_{{{\mathchar 28931\relax}^{0}_{b}}}/(f_{u}+f_{d})$ in $p_{\mathrm{T}}(H_{b})$ [GeV] bins; it accounts for statistical and bin-dependent systematic uncertainties, but not the global systematic uncertainties.  $p_{\mathrm{T}}(H_{b})$ | 4–5 | 5–6 | 6–7 | 7–8 | 8–9 | 9–10 | 10–11 | 11–12 | 12–13 | 13–14 | 14–16 | 16–18 | 18–20 | 20–25
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
4–5 | 2.40E-4 | 3.21E-5 | 2.08E-5 | 5.03E-5 | 3.36E-5 | 4.21E-5 | 1.60E-5 | 3.50E-5 | 2.47E-5 | 1.30E-5 | 6.20E-6 | 3.10E-6 | 2.60E-6 | 3.46E-6
5–6 | 3.21E-5 | 4.34E-5 | 5.05E-6 | 1.30E-5 | 8.90E-6 | 1.12E-5 | 4.47E-6 | 9.65E-6 | 7.12E-6 | 3.73E-6 | 1.80E-6 | 9.11E-7 | 7.82E-7 | 1.12E-6
6–7 | 2.08E-5 | 5.05E-6 | 2.99E-5 | 9.39E-6 | 6.55E-6 | 8.41E-6 | 3.35E-6 | 7.43E-6 | 5.44E-6 | 2.86E-6 | 1.43E-6 | 7.04E-7 | 6.25E-7 | 8.96E-7
7–8 | 5.03E-5 | 1.30E-5 | 9.39E-6 | 5.32E-5 | 1.97E-5 | 2.56E-5 | 1.05E-5 | 2.26E-5 | 1.72E-5 | 9.14E-6 | 4.53E-6 | 2.33E-6 | 2.04E-6 | 3.01E-6
8–9 | 3.36E-5 | 8.90E-6 | 6.55E-6 | 1.97E-5 | 3.96E-5 | 2.10E-5 | 8.88E-6 | 1.95E-5 | 1.47E-5 | 7.91E-6 | 3.91E-6 | 2.03E-6 | 1.75E-6 | 2.75E-6
9–10 | 4.21E-5 | 1.12E-5 | 8.41E-6 | 2.56E-5 | 2.10E-5 | 5.44E-5 | 1.27E-5 | 2.81E-5 | 2.14E-5 | 1.21E-5 | 5.88E-6 | 3.11E-6 | 2.69E-6 | 4.44E-6
10–11 | 1.60E-5 | 4.47E-6 | 3.35E-6 | 1.05E-5 | 8.88E-6 | 1.27E-5 | 3.03E-5 | 1.33E-5 | 1.10E-5 | 6.15E-6 | 3.07E-6 | 1.67E-6 | 1.43E-6 | 2.48E-6
11–12 | 3.50E-5 | 9.65E-6 | 7.43E-6 | 2.26E-5 | 1.95E-5 | 2.81E-5 | 1.33E-5 | 6.41E-5 | 2.54E-5 | 1.42E-5 | 7.23E-6 | 3.98E-6 | 3.44E-6 | 5.86E-6
12–13 | 2.47E-5 | 7.12E-6 | 5.44E-6 | 1.72E-5 | 1.47E-5 | 2.14E-5 | 1.10E-5 | 2.54E-5 | 5.71E-5 | 1.36E-5 | 6.78E-6 | 3.85E-6 | 3.41E-6 | 6.10E-6
13–14 | 1.30E-5 | 3.73E-6 | 2.86E-6 | 9.14E-6 | 7.90E-6 | 1.21E-5 | 6.15E-6 | 1.42E-5 | 1.36E-5 | 4.37E-5 | 4.23E-6 | 2.47E-6 | 7.22E-6 | 3.88E-6
14–16 | 6.20E-6 | 1.80E-6 | 1.43E-6 | 4.53E-6 | 3.91E-6 | 5.88E-6 | 3.07E-6 | 7.23E-6 | 6.78E-6 | 4.23E-6 | 3.01E-5 | 1.35E-6 | 1.21E-6 | 2.24E-6
16–18 | 3.10E-6 | 9.11E-7 | 7.04E-7 | 2.33E-6 | 2.03E-6 | 3.11E-6 | 1.67E-6 | 3.98E-6 | 3.85E-6 | 2.47E-6 | 1.35E-6 | 3.17E-5 | 8.03E-7 | 1.54E-6
18–20 | 2.61E-6 | 7.82E-7 | 6.25E-7 | 2.04E-6 | 1.75E-6 | 2.67E-6 | 1.43E-6 | 3.44E-6 | 3.41E-6 | 2.22E-6 | 1.21E-6 | 8.03E-7 | 4.21E-5 | 1.62E-6
20–25 | 3.46E-6 | 1.12E-6 | 8.97E-7 | 3.01E-6 | 2.75E-6 | 4.44E-6 | 2.48E-6 | 5.83E-6 | 6.10E-6 | 3.88E-6 | 2.24E-6 | 1.54E-6 | 1.62E-6 | 3.09E-5

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LHCb Collaboration

R. Aaij29, C. Abellán Beteta46, B. Adeva43, M. Adinolfi50, C.A. Aidala77, Z.
Ajaltouni7, S. Akar61, P. Albicocco20, J. Albrecht12, F. Alessio44, M.
Alexander55, A. Alfonso Albero42, G. Alkhazov35, P. Alvarez Cartelle57, A.A.
Alves Jr43, S. Amato2, S. Amerio25, Y. Amhis9, L. An19, L. Anderlini19, G.
Andreassi45, M. Andreotti18, J.E. Andrews62, F. Archilli29, J. Arnau Romeu8,
A. Artamonov41, M. Artuso63, K. Arzymatov39, E. Aslanides8, M. Atzeni46, B.
Audurier24, S. Bachmann14, J.J. Back52, S. Baker57, V. Balagura9,b, W.
Baldini18, A. Baranov39, R.J. Barlow58, G.C. Barrand9, S. Barsuk9, W.
Barter57, M. Bartolini21, F. Baryshnikov73, V. Batozskaya33, B. Batsukh63, A.
Battig12, V. Battista45, A. Bay45, J. Beddow55, F. Bedeschi26, I. Bediaga1, A.
Beiter63, L.J. Bel29, S. Belin24, N. Beliy4, V. Bellee45, N. Belloli22,i, K.
Belous41, I. Belyaev36, G. Bencivenni20, E. Ben-Haim10, S. Benson29, S.
Beranek11, A. Berezhnoy37, R. Bernet46, D. Berninghoff14, E. Bertholet10, A.
Bertolin25, C. Betancourt46, F. Betti17,44, M.O. Bettler51, Ia. Bezshyiko46,
S. Bhasin50, J. Bhom31, M.S. Bieker12, S. Bifani49, P. Billoir10, A.
Birnkraut12, A. Bizzeti19,u, M. Bjørn59, M.P. Blago44, T. Blake52, F. Blanc45,
S. Blusk63, D. Bobulska55, V. Bocci28, O. Boente Garcia43, T. Boettcher60, A.
Bondar40,x, N. Bondar35, S. Borghi58,44, M. Borisyak39, M. Borsato14, M.
Boubdir11, T.J.V. Bowcock56, C. Bozzi18,44, S. Braun14, M. Brodski44, J.
Brodzicka31, A. Brossa Gonzalo52, D. Brundu24,44, E. Buchanan50, A.
Buonaura46, C. Burr58, A. Bursche24, J. Buytaert44, W. Byczynski44, S.
Cadeddu24, H. Cai67, R. Calabrese18,g, R. Calladine49, M. Calvi22,i, M. Calvo
Gomez42,m, A. Camboni42,m, P. Campana20, D.H. Campora Perez44, L.
Capriotti17,e, A. Carbone17,e, G. Carboni27, R. Cardinale21, A. Cardini24, P.
Carniti22,i, K. Carvalho Akiba2, G. Casse56, M. Cattaneo44, G. Cavallero21, R.
Cenci26,p, D. Chamont9, M.G. Chapman50, M. Charles10, Ph. Charpentier44, G.
Chatzikonstantinidis49, M. Chefdeville6, V. Chekalina39, C. Chen3, S. Chen24,
S.-G. Chitic44, V. Chobanova43, M. Chrzaszcz44, A. Chubykin35, P. Ciambrone20,
X. Cid Vidal43, G. Ciezarek44, F. Cindolo17, P.E.L. Clarke54, M. Clemencic44,
H.V. Cliff51, J. Closier44, V. Coco44, J.A.B. Coelho9, J. Cogan8, E.
Cogneras7, L. Cojocariu34, P. Collins44, T. Colombo44, A. Comerma-Montells14,
A. Contu24, G. Coombs44, S. Coquereau42, G. Corti44, M. Corvo18,g, C.M. Costa
Sobral52, B. Couturier44, G.A. Cowan54, D.C. Craik60, A. Crocombe52, M. Cruz
Torres1, R. Currie54, F. Da Cunha Marinho2, C.L. Da Silva78, E. Dall’Occo29,
J. Dalseno43,v, C. D’Ambrosio44, A. Danilina36, P. d’Argent14, A. Davis58, O.
De Aguiar Francisco44, K. De Bruyn44, S. De Capua58, M. De Cian45, J.M. De
Miranda1, L. De Paula2, M. De Serio16,d, P. De Simone20, J.A. de Vries29, C.T.
Dean55, W. Dean77, D. Decamp6, L. Del Buono10, B. Delaney51, H.-P.
Dembinski13, M. Demmer12, A. Dendek32, D. Derkach74, O. Deschamps7, F. Desse9,
F. Dettori56, B. Dey68, A. Di Canto44, P. Di Nezza20, S. Didenko73, H.
Dijkstra44, F. Dordei24, M. Dorigo44,y, A.C. dos Reis1, A. Dosil Suárez43, L.
Douglas55, A. Dovbnya47, K. Dreimanis56, L. Dufour29, G. Dujany10, P.
Durante44, J.M. Durham78, D. Dutta58, R. Dzhelyadin41,†, M. Dziewiecki14, A.
Dziurda31, A. Dzyuba35, S. Easo53, U. Egede57, V. Egorychev36, S.
Eidelman40,x, S. Eisenhardt54, U. Eitschberger12, R. Ekelhof12, L. Eklund55,
S. Ely63, A. Ene34, S. Escher11, S. Esen29, T. Evans61, A. Falabella17, C.
Färber44, N. Farley49, S. Farry56, D. Fazzini22,44,i, M. Féo44, P. Fernandez
Declara44, A. Fernandez Prieto43, F. Ferrari17,e, L. Ferreira Lopes45, F.
Ferreira Rodrigues2, M. Ferro-Luzzi44, S. Filippov38, R.A. Fini16, M.
Fiorini18,g, M. Firlej32, C. Fitzpatrick45, T. Fiutowski32, F. Fleuret9,b, M.
Fontana44, F. Fontanelli21,h, R. Forty44, V. Franco Lima56, M. Frank44, C.
Frei44, J. Fu23,q, W. Funk44, E. Gabriel54, A. Gallas Torreira43, D.
Galli17,e, S. Gallorini25, S. Gambetta54, Y. Gan3, M. Gandelman2, P.
Gandini23, Y. Gao3, L.M. Garcia Martin76, J. García Pardiñas46, B. Garcia
Plana43, J. Garra Tico51, L. Garrido42, D. Gascon42, C. Gaspar44, G. Gazzoni7,
D. Gerick14, E. Gersabeck58, M. Gersabeck58, T. Gershon52, D. Gerstel8, Ph.
Ghez6, V. Gibson51, O.G. Girard45, P. Gironella Gironell42, L. Giubega34, K.
Gizdov54, V.V. Gligorov10, C. Göbel65, D. Golubkov36, A. Golutvin57,73, A.
Gomes1,a, I.V. Gorelov37, C. Gotti22,i, E. Govorkova29, J.P. Grabowski14, R.
Graciani Diaz42, L.A. Granado Cardoso44, E. Graugés42, E. Graverini46, G.
Graziani19, A. Grecu34, R. Greim29, P. Griffith24, L. Grillo58, L. Gruber44,
B.R. Gruberg Cazon59, O. Grünberg70, C. Gu3, E. Gushchin38, A. Guth11, Yu.
Guz41,44, T. Gys44, T. Hadavizadeh59, C. Hadjivasiliou7, G. Haefeli45, C.
Haen44, S.C. Haines51, B. Hamilton62, X. Han14, T.H. Hancock59, S. Hansmann-
Menzemer14, N. Harnew59, T. Harrison56, C. Hasse44, M. Hatch44, J. He4, M.
Hecker57, K. Heinicke12, A. Heister12, K. Hennessy56, L. Henry76, M. Heß70, J.
Heuel11, A. Hicheur64, R. Hidalgo Charman58, D. Hill59, M. Hilton58, P.H.
Hopchev45, J. Hu14, W. Hu68, W. Huang4, Z.C. Huard61, W. Hulsbergen29, T.
Humair57, M. Hushchyn74, D. Hutchcroft56, D. Hynds29, P. Ibis12, M. Idzik32,
P. Ilten49, A. Inglessi35, A. Inyakin41, K. Ivshin35, R. Jacobsson44, S.
Jakobsen44, J. Jalocha59, E. Jans29, B.K. Jashal76, A. Jawahery62, F. Jiang3,
M. John59, D. Johnson44, C.R. Jones51, C. Joram44, B. Jost44, N. Jurik59, S.
Kandybei47, M. Karacson44, J.M. Kariuki50, S. Karodia55, N. Kazeev74, M.
Kecke14, F. Keizer51, M. Kelsey63, M. Kenzie51, T. Ketel30, E. Khairullin39,
B. Khanji44, C. Khurewathanakul45, K.E. Kim63, T. Kirn11, V.S. Kirsebom45, S.
Klaver20, K. Klimaszewski33, T. Klimkovich13, S. Koliiev48, M. Kolpin14, R.
Kopecna14, P. Koppenburg29, I. Kostiuk29,48, S. Kotriakhova35, M. Kozeiha7, L.
Kravchuk38, M. Kreps52, F. Kress57, P. Krokovny40,x, W. Krupa32, W.
Krzemien33, W. Kucewicz31,l, M. Kucharczyk31, V. Kudryavtsev40,x, A.K.
Kuonen45, T. Kvaratskheliya36,44, D. Lacarrere44, G. Lafferty58, A. Lai24, D.
Lancierini46, G. Lanfranchi20, C. Langenbruch11, T. Latham52, C. Lazzeroni49,
R. Le Gac8, R. Lefèvre7, A. Leflat37, F. Lemaitre44, O. Leroy8, T. Lesiak31,
B. Leverington14, P.-R. Li4,ab, Y. Li5, Z. Li63, X. Liang63, T.
Likhomanenko72, R. Lindner44, F. Lionetto46, V. Lisovskyi9, G. Liu66, X. Liu3,
D. Loh52, A. Loi24, I. Longstaff55, J.H. Lopes2, G. Loustau46, G.H. Lovell51,
D. Lucchesi25,o, M. Lucio Martinez43, Y. Luo3, A. Lupato25, E. Luppi18,g, O.
Lupton44, A. Lusiani26, X. Lyu4, F. Machefert9, F. Maciuc34, V. Macko45, P.
Mackowiak12, S. Maddrell-Mander50, O. Maev35,44, K. Maguire58, D.
Maisuzenko35, M.W. Majewski32, S. Malde59, B. Malecki44, A. Malinin72, T.
Maltsev40,x, H. Malygina14, G. Manca24,f, G. Mancinelli8, D. Marangotto23,q,
J. Maratas7,w, J.F. Marchand6, U. Marconi17, C. Marin Benito9, M.
Marinangeli45, P. Marino45, J. Marks14, P.J. Marshall56, G. Martellotti28, M.
Martinelli44, D. Martinez Santos43, F. Martinez Vidal76, A. Massafferri1, M.
Materok11, R. Matev44, A. Mathad52, Z. Mathe44, C. Matteuzzi22, K.R.
Mattioli77, A. Mauri46, E. Maurice9,b, B. Maurin45, M. McCann57,44, A.
McNab58, R. McNulty15, J.V. Mead56, B. Meadows61, C. Meaux8, N. Meinert70, D.
Melnychuk33, M. Merk29, A. Merli23,q, E. Michielin25, D.A. Milanes69, E.
Millard52, M.-N. Minard6, L. Minzoni18,g, D.S. Mitzel14, A. Mödden12, A.
Mogini10, R.D. Moise57, T. Mombächer12, I.A. Monroy69, S. Monteil7, M.
Morandin25, G. Morello20, M.J. Morello26,t, O. Morgunova72, J. Moron32, A.B.
Morris8, R. Mountain63, F. Muheim54, M. Mukherjee68, M. Mulder29, D. Müller44,
J. Müller12, K. Müller46, V. Müller12, C.H. Murphy59, D. Murray58, P. Naik50,
T. Nakada45, R. Nandakumar53, A. Nandi59, T. Nanut45, I. Nasteva2, M.
Needham54, N. Neri23,q, S. Neubert14, N. Neufeld44, R. Newcombe57, T.D.
Nguyen45, C. Nguyen-Mau45,n, S. Nieswand11, R. Niet12, N. Nikitin37, A.
Nogay72, N.S. Nolte44, A. Oblakowska-Mucha32, V. Obraztsov41, S. Ogilvy55,
D.P. O’Hanlon17, R. Oldeman24,f, C.J.G. Onderwater71, A. Ossowska31, J.M.
Otalora Goicochea2, T. Ovsiannikova36, P. Owen46, A. Oyanguren76, P.R. Pais45,
T. Pajero26,t, A. Palano16, M. Palutan20, G. Panshin75, A. Papanestis53, M.
Pappagallo54, L.L. Pappalardo18,g, W. Parker62, C. Parkes58,44, G.
Passaleva19,44, A. Pastore16, M. Patel57, C. Patrignani17,e, A. Pearce44, A.
Pellegrino29, G. Penso28, M. Pepe Altarelli44, S. Perazzini44, D. Pereima36,
P. Perret7, L. Pescatore45, K. Petridis50, A. Petrolini21,h, A. Petrov72, S.
Petrucci54, M. Petruzzo23,q, B. Pietrzyk6, G. Pietrzyk45, M. Pikies31, M.
Pili59, D. Pinci28, J. Pinzino44, F. Pisani44, A. Piucci14, V. Placinta34, S.
Playfer54, J. Plews49, M. Plo Casasus43, F. Polci10, M. Poli Lener20, A.
Poluektov8, N. Polukhina73,c, I. Polyakov63, E. Polycarpo2, G.J. Pomery50, S.
Ponce44, A. Popov41, D. Popov49,13, S. Poslavskii41, E. Price50, J.
Prisciandaro43, C. Prouve43, V. Pugatch48, A. Puig Navarro46, H. Pullen59, G.
Punzi26,p, W. Qian4, J. Qin4, R. Quagliani10, B. Quintana7, N.V. Raab15, B.
Rachwal32, J.H. Rademacker50, M. Rama26, M. Ramos Pernas43, M.S. Rangel2, F.
Ratnikov39,74, G. Raven30, M. Ravonel Salzgeber44, M. Reboud6, F. Redi45, S.
Reichert12, F. Reiss10, C. Remon Alepuz76, Z. Ren3, V. Renaudin59, S.
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Rodrigues45, E. Rodrigues61, J.A. Rodriguez Lopez69, M. Roehrken44, S.
Roiser44, A. Rollings59, V. Romanovskiy41, A. Romero Vidal43, J.D. Roth77, M.
Rotondo20, M.S. Rudolph63, T. Ruf44, J. Ruiz Vidal76, J.J. Saborido Silva43,
N. Sagidova35, B. Saitta24,f, V. Salustino Guimaraes65, C. Sanchez Gras29, C.
Sanchez Mayordomo76, B. Sanmartin Sedes43, R. Santacesaria28, C. Santamarina
Rios43, M. Santimaria20,44, E. Santovetti27,j, G. Sarpis58, A. Sarti20,k, C.
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Schellenberg12, M. Schiller55, H. Schindler44, M. Schmelling13, T.
Schmelzer12, B. Schmidt44, O. Schneider45, A. Schopper44, H.F. Schreiner61, M.
Schubiger45, S. Schulte45, M.H. Schune9, R. Schwemmer44, B. Sciascia20, A.
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L. Shekhtman40,x, V. Shevchenko72, E. Shmanin73, B.G. Siddi18, R. Silva
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S. Zucchelli17,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
4University of Chinese Academy of Sciences, Beijing, China
5Institute Of High Energy Physics (ihep), Beijing, China
6Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
7Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
8Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
9LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
10LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
11I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
12Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
13Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
14Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
15School of Physics, University College Dublin, Dublin, Ireland
16INFN Sezione di Bari, Bari, Italy
17INFN Sezione di Bologna, Bologna, Italy
18INFN Sezione di Ferrara, Ferrara, Italy
19INFN Sezione di Firenze, Firenze, Italy
20INFN Laboratori Nazionali di Frascati, Frascati, Italy
21INFN Sezione di Genova, Genova, Italy
22INFN Sezione di Milano-Bicocca, Milano, Italy
23INFN Sezione di Milano, Milano, Italy
24INFN Sezione di Cagliari, Monserrato, Italy
25INFN Sezione di Padova, Padova, Italy
26INFN Sezione di Pisa, Pisa, Italy
27INFN Sezione di Roma Tor Vergata, Roma, Italy
28INFN Sezione di Roma La Sapienza, Roma, Italy
29Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
30Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
31Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
32AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
33National Center for Nuclear Research (NCBJ), Warsaw, Poland
34Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
35Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
36Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
37Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
38Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
39Yandex School of Data Analysis, Moscow, Russia
40Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
41Institute for High Energy Physics (IHEP), Protvino, Russia
42ICCUB, Universitat de Barcelona, Barcelona, Spain
43Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
44European Organization for Nuclear Research (CERN), Geneva, Switzerland
45Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
46Physik-Institut, Universität Zürich, Zürich, Switzerland
47NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
48Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
49University of Birmingham, Birmingham, United Kingdom
50H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
51Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
52Department of Physics, University of Warwick, Coventry, United Kingdom
53STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
54School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
55School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
56Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
57Imperial College London, London, United Kingdom
58School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
59Department of Physics, University of Oxford, Oxford, United Kingdom
60Massachusetts Institute of Technology, Cambridge, MA, United States
61University of Cincinnati, Cincinnati, OH, United States
62University of Maryland, College Park, MD, United States
63Syracuse University, Syracuse, NY, United States
64Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria,
associated to 2
65Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
66South China Normal University, Guangzhou, China, associated to 3
67School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
68Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
69Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 10
70Institut für Physik, Universität Rostock, Rostock, Germany, associated to 14
71Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 29
72National Research Centre Kurchatov Institute, Moscow, Russia, associated to
36
73National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 36
74National Research University Higher School of Economics, Moscow, Russia,
associated to 39
75National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
36
76Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 42
77University of Michigan, Ann Arbor, United States, associated to 63
78Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 63

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
vH.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
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
abLanzhou University, Lanzhou, China
†Deceased