EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2018-190 LHCb-PAPER-2018-024 3 June, 2019

Measurement of the relative
${{{B}^{-}}\\!\rightarrow{{D}^{0}}/{{D}^{*0}}/{D^{**0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}}$
branching fractions using ${B}^{-}$ mesons from ${\kern
3.73305pt\overline{\kern-3.73305ptB}{}}{}_{s2}^{*0}$ decays

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

The decay of the narrow resonance ${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}}\\!\rightarrow{{B}^{-}}{{K}^{+}}}$
can be used to determine the ${B}^{-}$ momentum in partially reconstructed
decays without any assumptions on the decay products of the ${B}^{-}$ meson.
This technique is employed for the first time to distinguish contributions
from ${D}^{0}$, ${D}^{*0}$, and higher-mass charmed states ($D^{**0}$) in
semileptonic ${B}^{-}$ decays by using the missing-mass distribution. The
measurement is performed using a data sample corresponding to an integrated
luminosity of $3.0\mbox{\,fb}^{-1}$ collected with the LHCb detector in $pp$
collisions at center-of-mass energies of 7 and
8$\mathrm{\,Te\kern-1.00006ptV}$. The resulting branching fractions relative
to the inclusive
${{{B}^{-}}\\!\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}}$ are

$\displaystyle
f_{{{D}^{0}}}={\mathcal{B}}\quantity({{B}^{-}}\rightarrow{{D}^{0}}{\mu^{-}}{{\overline{\nu}}_{\mu}})/{\mathcal{B}}\quantity({{B}^{-}}\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}})$
$\displaystyle=0.25\pm 0.06,$ $\displaystyle
f_{{D^{**0}}}={\mathcal{B}}\quantity({{B}^{-}}\rightarrow\quantity({D^{**0}}\rightarrow{{D}^{0}}X){\mu^{-}}{{\overline{\nu}}_{\mu}})/{\mathcal{B}}\quantity({{B}^{-}}\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}})$
$\displaystyle=0.21\pm 0.07,$

with $f_{{D}^{*0}}=1-f_{{D}^{0}}-f_{D^{**0}}$ making up the remainder.

Published in Phys. Rev. D99 (2019) 092009

© 2024 CERN on behalf of the LHCb collaboration. CC-BY-4.0 licence.

##  1 Introduction

The composition of the inclusive bottom-to-charm semileptonic rate is not
fully understood. Measurements of the exclusive branching fractions for
${{B}\\!\rightarrow D\ell\nu}$ and ${{B}\\!\rightarrow{{D}^{*}}\ell\nu}$ and
corresponding decays with up to two additional charged pions [1] do not
saturate the total ${b\\!\rightarrow c}$ semileptonic rate as determined from
analysis of the charged lepton’s kinematic moments [2, 3, 4]. One way to
resolve this inclusive–exclusive gap is to make measurements of relative rates
between different final states.

Semileptonic decays with excited charm states act as important backgrounds
both to the exclusive decay channels ${B\\!\rightarrow D\ell\nu}$ and
${B\\!\rightarrow{{D}^{*}}\ell\nu}$ and for the study of semileptonic
${b\\!\rightarrow u}$ transitions. For example, understanding these
backgrounds is essential for experimental tests of lepton flavor universality
studied by comparing the rates of tauonic and muonic $b$-hadron decays, _e.g._
$R(D^{(*)})\equiv{\mathcal{B}}\quantity({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}\\!\rightarrow
D^{(*)}{\tau^{-}}{{\overline{\nu}}_{\tau}}})/{\mathcal{B}}\quantity({{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}\\!\rightarrow
D^{(*)}{\mu^{-}}{{\overline{\nu}}_{\mu}}})$ [5, 6, 7, 8, 9, 10, 11].111The
inclusion of charge-conjugate processes is implied throughout.

The largest contributions of excited charm states besides the
$D^{*}(2007)^{0}$ or $D^{*}(2010)^{+}$ mesons come from the orbitally excited
$L=1$ states $D_{0}^{*}\quantity(2400)$, $D_{1}\quantity(2420)$,
$D_{1}\quantity(2430)$, and $D_{2}^{*}\quantity(2460)$, which have been
individually measured [1]. We use the collective term $D^{**}$ to refer to
these as well as other resonances such as radially excited $D$ mesons, and to
nonresonant contributions with additional pions.

The contribution of excited states to the total semileptonic rate can be
studied using $B$ decays in which the $B$ momentum is known. This allows one
to calculate the mass of the undetected or “missing” part of the decay, and
thus separate different excited $D$ states. In this paper we employ for the
first time the technique described in Ref. [12] to accomplish this
reconstruction in
${{{B}^{-}}\\!\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}}$ decays,
where $X$ refers to any number of additional particles, without assumptions
about the decay products of the ${B}^{-}$ meson. There are three narrow peaks
in the ${{B}^{-}}{{K}^{+}}$ mass distribution just above the mass threshold
from decays of the orbitally excited $L=1$ ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}_{s}^{**}$ mesons [13, 14, 15]. We
focus on the decay ${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}}\\!\rightarrow{{B}^{-}}{{K}^{+}}}$,
which forms a narrow peak approximately
$67\text{\,}\mathrm{Me\kern-1.00006ptV}$ above the threshold,222Natural units
with $c=1$ are used throughout. and has the largest yield of any observed
excited ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ state. By
tagging ${B}^{-}$ mesons produced from the decay of these excited ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ mesons, the ${B}^{-}$
energy can be determined up to a quadratic ambiguity using the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ and ${B}^{-}$ decay
vertices and by imposing mass constraints for the ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ mesons. Since only
approximately 1% of ${B}^{-}$ mesons originate from a ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ decay, this method
requires a large data set.

We determine the relative branching fractions of ${B}^{-}$ to ${D}^{0}$,
${D}^{*0}$, and $D^{**0}$, referred to as $f_{{D}^{0}}$, $f_{{D}^{*0}}$, and
$f_{D^{**0}}$ respectively, in the
${{{B}^{-}}\\!\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}}$ channel
by fitting the distribution of the missing mass for ${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}}\\!\rightarrow{{B}^{-}}{{K}^{+}}}$
candidates. A similar set of fractions (along with their ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ counterparts), where the charge
of the final state $D$ meson is not specified, has been measured previously at
the BaBar experiment [16]. From the derivations in Ref. [17], we expect based
on previous branching fraction measurements

$\displaystyle f_{{{D}^{0}}}$
$\displaystyle={\mathcal{B}}\quantity({{B}^{-}}\rightarrow{{D}^{0}}{\mu^{-}}{{\overline{\nu}}_{\mu}})/{\mathcal{B}}\quantity({{B}^{-}}\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}})$
$\displaystyle=0.235\pm 0.011^{+0.018}_{-0.012},$ $\displaystyle
f_{{{D}^{*0}}}$
$\displaystyle={\mathcal{B}}\quantity({{B}^{-}}\rightarrow{{D}^{*0}}{\mu^{-}}{{\overline{\nu}}_{\mu}})/{\mathcal{B}}\quantity({{B}^{-}}\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}})$
$\displaystyle=0.564\pm 0.017^{+0.042}_{-0.028},$ $\displaystyle
f_{{D^{**0}}}$
$\displaystyle={\mathcal{B}}\quantity({{B}^{-}}\rightarrow\quantity({D^{**0}}\rightarrow{{D}^{0}}X){\mu^{-}}{{\overline{\nu}}_{\mu}})/{\mathcal{B}}\quantity({{B}^{-}}\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}})$
$\displaystyle=0.201\pm 0.020^{+0.039}_{-0.060},$

where the first uncertainty is experimental and the second gives an envelope
of different extrapolation hypotheses to explain the inclusive–exclusive gap.
Precise measurements of the relative branching fractions can distinguish
between the hypotheses. Higher values in the $D^{**0}$ envelope (20% or more)
would point towards a scenario in which there is a large contribution of
unmeasured excited charm states. Lower fractions, closer to 14%, would suggest
that the currently measured exclusive decays correctly describe the makeup of
the total rate, and the inclusive–exclusive gap is due to other systematic
effects.

A description of the data samples and selections used in this paper may be
found in Sect. 2. Afterwards we discuss the missing mass reconstruction and
related variables in Sect. 3. Along with the signal ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ decays, a large fraction
of background decays are also selected. Yields and missing mass shapes must be
determined for each of the background categories as described in Sect. 4. The
most important background source is semileptonic decays of ${B}^{-}$ and
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mesons with the same
final state as the signal that do not originate from ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ decays. After accounting
for other sources of background in Sect. 4.1, we estimate the yield and shape
of this source in Sect. 4.2. The relative branching fractions are determined
using a template fit to the missing mass distribution as described in Sect. 5.
The systematic uncertainties included in the fit are then described in Sect.
6. The final result is presented in Sect. 7.

##  2 Data sample and selection

The LHCb detector [18, 19] 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 includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region [20], a large-area silicon-strip detector located upstream
of a dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes [21] placed
downstream of the magnet. The tracking system provides a measurement of
momentum, $p$, of charged particles with a relative uncertainty that varies
from 0.5% at low momentum to 1.0% at 200$\mathrm{\,Ge\kern-1.00006ptV}$. The
minimum distance of a track to a primary vertex (PV), the impact parameter
(IP), is measured with a resolution of
$(15+29/p_{\mathrm{T}}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$ is the
component of the momentum transverse to the beam, in
$\mathrm{\,Ge\kern-1.00006ptV}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
[22]. Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers
[23]. The online event selection is performed by a trigger [24], 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.

We use data samples collected in 2011 and 2012, at center-of-mass energies of
$7\text{\,}\mathrm{Te\kern-1.00006ptV}$ and
$8\text{\,}\mathrm{Te\kern-1.00006ptV}$ respectively, corresponding to an
integrated luminosity of 3.0$\mbox{\,fb}^{-1}$. All ${B}^{-}$ candidates are
selected from ${{D}^{0}}{\mu^{-}}$ combinations, with
${{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}}$. The final-state particles are
formed from high-quality tracks required to be inconsistent with being
produced at any primary collision vertex in the event. Loose particle-
identification requirements are also applied to these tracks. The ${{K}^{-}}$
and ${{\pi}^{+}}$ candidates must form a high-quality vertex, and their
combined mass must lie in the range
$18401890\text{\,}\mathrm{Me\kern-1.00006ptV}$. The muon from the
${{D}^{0}}{\mu^{-}}$ candidate is required to pass the hardware trigger, which
requires a transverse momentum of
$p_{\mathrm{T}}>$1.48\text{\,}\mathrm{Ge\kern-1.00006ptV}$$ in the
$7\text{\,}\mathrm{Te\kern-1.00006ptV}$ data or
$p_{\mathrm{T}}>$1.76\text{\,}\mathrm{Ge\kern-1.00006ptV}$$ in the
$8\text{\,}\mathrm{Te\kern-1.00006ptV}$ data. The software trigger requires a
two-, three- or four-track secondary vertex with a significant displacement
from any primary $pp$ interaction vertex, consistent with coming from a $b$
hadron. The ${{D}^{0}}{\mu^{-}}$ vertex must be of high quality, and well
separated from the primary vertex.

After selecting ${B}^{-}$ candidates, we add candidate kaons consistent with
originating from the primary vertex, referred to as prompt, to form the
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ candidates. To
reduce background from misidentified pions from the primary interaction, we
impose strong particle-identification requirements. The selection requirements
for the prompt kaons are optimized using the fully reconstructed decay
${{{B}^{-}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{-}}}$. Signal decays produce a ${{B}^{-}}{{K}^{+}}$ pair; in
addition to this opposite-sign kaon (OS$K$) data sample, we also use
${{B}^{-}}{{K}^{-}}$ same-sign kaon (SS$K$) combinations to help estimate
backgrounds from data.

Samples of simulated ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ events are used to model
the ${{{B}^{-}}\\!\rightarrow{{D}^{0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}}$,
${{{B}^{-}}\\!\rightarrow{{D}^{*0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}}$, and
${{{B}^{-}}\\!\rightarrow{D^{**0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}}$ signal
components. For the $D^{**0}$ component, the simulation includes contributions
from the four $L=1$ $D$ mesons as well as a small contributions of nonresonant
$D^{(*)}\pi$ decays. In the simulation, $pp$ collisions are generated using
Pythia [25, *Sjostrand:2007gs] with a specific LHCb configuration [27]. Decays
of hadronic particles are described by EvtGen [28], in which final-state
radiation is generated using Photos [29]. The interaction of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [30, *Agostinelli:2002hh] as described in Ref. [32].

##  3 Reconstruction of the $\boldsymbol{{{B}^{-}}}$ meson momentum

We find the energy of the ${B}^{-}$ meson by using its flight direction from
the primary vertex to the secondary ${{D}^{0}}{\mu^{-}}$ vertex; a diagram of
the decay topology is shown in Fig. 1. Applying mass constraints for the
${B}^{-}$ meson mass, $m_{B}$, and the hypothesized parent particle mass,
$m_{BK}$, leaves a quadratic equation for the ${B}^{-}$ meson energy, $E_{B}$,
derived in Appendix A.

Figure 1: Decay topology for the
${{{B}^{-}}\\!\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}}$ signal
decays. A ${\kern 1.61993pt\overline{\kern-1.61993ptB}{}}{}_{s2}^{*0}$ meson
decays at the primary vertex position, producing a ${B}^{-}$ meson and a
${K}^{+}$ meson. The angle in the laboratory frame between the ${K}^{+}$ and
${B}^{-}$ directions is defined as $\theta$. The ${B}^{-}$ meson then decays
semileptonically to a ${D}^{0}$ meson and a muon, accompanied by an undetected
neutrino and potentially other particles, referred to collectively as $X$.

In carrying out the analysis we use two different quantities related to this
calculation. The first is the minimum mass of the ${{B}^{-}}{{K}^{\pm}}$ pair.
For a particular ${B}^{-}$ vertex and kaon track, there is a minimum $m_{BK}$
mass hypothesis for which the ${B}^{-}$ energy solutions are real. At this
value, the discriminant of the quadratic equation is zero. This minimum mass
value is given by

$m_{\mathrm{min}}=\sqrt{m_{B}^{2}+m_{K}^{2}+2m_{B}\sqrt{p_{K}^{2}\sin^{2}\theta+m_{K}^{2}}},$
(1)

where $p_{K}$ is the kaon momentum in the laboratory frame, $m_{K}$ is the
kaon mass, and $\theta$ is the angle between the kaon direction and the
direction from the primary to the secondary vertex. The distribution of the
difference between $m_{\mathrm{min}}$ and the $m_{B}+m_{K}$ threshold, $\Delta
m_{\mathrm{min}}=m_{\mathrm{min}}-m_{B}-m_{K}$, shown in Fig. 2 for both the
OS$K$ and SS$K$ data samples, has excesses corresponding to the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s1}^{0}$ states even for decays
that are not fully reconstructed. We use these distributions in a control
region of $0<\Delta
m_{\mathrm{min}}<$220\text{\,}\mathrm{Me\kern-1.00006ptV}$$ to constrain the
total amount of ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$
decays and non-${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$
background contributions in our selection, as described in more detail in
Sect. 4.

Figure 2:  Distribution of the minimum mass difference for
${{B}^{-}}{{K}^{+}}$ (OS$K$) candidates and ${{B}^{-}}{{K}^{-}}$ (SS$K$)
candidates. For OS$K$ combinations, peaks for the ${\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}_{s2}^{*0}$ and ${\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}_{s1}^{0}$ states are visible. The
contribution of decays in which a kaon from a $b$-hadron decay is chosen as
prompt produces the sharp increase near zero. The SS$K$ sample is used for
background estimation.

Decays of ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s1}^{0}$ mesons
and background candidates where a secondary kaon is misidentified as coming
from the primary interaction have small values of $\Delta m_{\mathrm{min}}$;
the latter produces the increase near zero seen in Fig. 2. To remove these, we
define our signal region for the missing mass fit as $30<\Delta
m_{\mathrm{min}}<$67\text{\,}\mathrm{Me\kern-1.00006ptV}$$.

The second quantity is the missing mass, assuming the particles result from
the decay of a ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$
meson (imposing $m_{BK}=m_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}_{s2}^{*0}}}$). The energy of the
${B}^{-}$ meson, $E_{B}$, is calculated as follows:

$\displaystyle E_{B}$
$\displaystyle=\frac{\Delta^{2}}{2E_{K}}\frac{1}{1-\quantity(p_{K}/E_{K})^{2}\cos^{2}\theta}\quantity[1\pm\sqrt{d}],$
(2) where $\displaystyle\Delta^{2}$ $\displaystyle=m_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}_{s2}^{*0}}}^{2}-m_{B}^{2}-m_{K}^{2},$
(3) and $\displaystyle d$
$\displaystyle=\frac{p_{K}^{2}}{E_{K}^{2}}\cos^{2}\theta-\frac{4m_{B}^{2}p_{K}^{2}\cos^{2}\theta}{\Delta^{4}}\quantity(1-\frac{p_{K}^{2}}{E_{K}^{2}}\cos^{2}\theta).$
(4)

Once $E_{B}$ has been determined, we calculate the missing mass squared

$m_{\mathrm{miss}}^{2}=(p_{B}-p_{\mathrm{vis}})^{2},$ (5)

where $p_{B}$ is the four momentum calculated from $E_{B}$ and the ${B}^{-}$
direction, and $p_{\mathrm{vis}}$ is the four momentum of the
${{D}^{0}}{\mu^{-}}$ combination. We require real solutions for Eq. 2. This
keeps only candidates with $m_{\mathrm{min}}$ less than the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ mass; candidates with
$\Delta m_{\mathrm{min}}>m_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}_{s2}^{*0}}}-m_{B}-m_{K}$, which is
approximately $67\text{\,}\mathrm{Me\kern-1.00006ptV}$, produce imaginary
solutions. The $m_{\mathrm{miss}}^{2}$ variable is then used to perform the
final fit to determine the relative branching fractions.

We keep only the physical solutions for $E_{B}$ which are greater than the sum
of the energies of the reconstructed decay products. Based on simulation,
approximately 75% of signal candidates have a physical solution. For
candidates with two physical solutions, the one with lower energy is correct
90% of the time. Only the lower energy solution is used for these candidates.
The difference $\Delta m_{\mathrm{miss}}^{2}$ between the reconstructed
missing-mass squared and the corresponding true values for different classes
of solutions are shown in Fig. 3. When $E_{B}$ is correctly reconstructed, the
full-width at half maximum of the $\Delta m_{\mathrm{miss}}^{2}$ distribution
is approximately $0.4\text{\,}{\mathrm{Ge\kern-1.00006ptV}}^{2}$ and is
consistent among the signal channels. The resulting $m_{\mathrm{miss}}^{2}$
distributions for the signal decays to be used in the fit are shown in Fig. 4.

Figure 3: The difference $\Delta m_{\mathrm{miss}}^{2}$ between the
reconstructed missing mass squared and the corresponding true values for the
(top left)
${{{B}^{-}}\\!\rightarrow{{D}^{0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}}$ channel,
(top right) the
${{{B}^{-}}\\!\rightarrow{{D}^{*0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}}$
channel, and (bottom) the
${{{B}^{-}}\\!\rightarrow{D^{**0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}}$ channel.
The contributions from events in which there is only one physical solution, in
which there are two and the chosen lower energy solution is correct, or in
which the incorrect solution is chosen are shown. Figure 4:  The missing mass
shapes from simulation for the signal samples are shown. The bands around the
points represent the systematic uncertainties on the form factors in the
simulation and the branching fractions for different contributions to the
$D^{**0}$ channel.

##  4 Background estimation

The backgrounds to the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ signal candidates come
from a number of different sources. For each of these sources, we estimate the
overall yield as well as the missing-mass shapes. The most important sources
are semileptonic decays of ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mesons not originating from a
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ or ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s1}^{0}$ decay, which represent 83%
of the total number of selected candidates.

The overall estimated background in the $m_{\mathrm{miss}}^{2}$ distribution
is shown in Fig. 5. We make this estimation by first considering a number of
smaller contributions not from semileptonic decays of ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mesons:

  * •

misreconstructed backgrounds consisting of

    * –

non-${D}^{0}$ backgrounds,

    * –

${{D}^{0}}{\mu^{-}}$ combinations not from the same $b$-hadron decay,

    * –

backgrounds with a hadron misidentified as the muon;

  * •

${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ semileptonic decays to final states including a
${D}^{0}$ meson.

Together, these backgrounds total 8% of all selected candidates. We estimate
their yield and shape in both the $m_{\mathrm{miss}}^{2}$ and the $\Delta
m_{\mathrm{min}}$ variables as described in Sect. 4.1. These can then be
accounted for in both the distributions of the OS$K$ and SS$K$ data samples.
We then estimate the semileptonic ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ backgrounds as described in
Sect. 4.2. The expectation for the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ contribution is subtracted from
the remaining SS$K$ sample, producing an estimate for the shape of the
${B}^{-}$ contribution in that sample. These two distributions are then
extrapolated to the OS$K$ sample to produce the background estimation. The
difference between this estimation and the full OS$K$ yield is composed of
signal decays.

Figure 5: Missing-mass distribution for data and estimated background
contributions in the (left) same-sign kaon sample and (right) opposite-sign
sample. The other background decays include contributions from
misreconstructed backgrounds, and semileptonic decays of ${\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ mesons. The remainder of the SS$K$ sample not from
${\kern 1.61993pt\overline{\kern-1.61993ptB}{}}{}^{0}$ or other background
decays is used to define the background contribution from ${B}^{-}$
semileptonic decays. This is then extrapolated to the OS$K$ sample, where the
remainder is composed of signal. The background distributions are stacked.

###  4.1 Backgrounds not from semileptonic decays of $\boldsymbol{{{B}^{-}}}$
and $\boldsymbol{{{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}}$
mesons

Misreconstructed backgrounds are estimated using data-driven techniques. The
yields and $\Delta m_{\mathrm{min}}$ and $m_{\mathrm{miss}}^{2}$ shapes of
backgrounds without a ${D}^{0}$ meson are estimated using sidebands around the
${D}^{0}$ mass peak. The sideband ranges chosen are from
$17901830\text{\,}\mathrm{Me\kern-1.00006ptV}$ and from
$19001940\text{\,}\mathrm{Me\kern-1.00006ptV}$. The difference of the
$m_{\mathrm{miss}}^{2}$ shape between the left and right sidebands is
negligible. Approximately 3% of the selected candidates come from this
background.

Combinations of ${{D}^{0}}{\mu^{-}}$ not coming from a single $b$-hadron decay
are estimated using a wrong-sign (${{D}^{0}}{\mu^{+}}$) control sample,
assuming that the doubly Cabbibo-suppressed contribution from
${{{D}^{0}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}}$ is negligible. Along with this
estimation, the contributions from misidentified muons to both the signal and
wrong-sign samples are estimated using a control sample with particle-
identification requirements that remove true muons. We then weight this sample
using-particle identification efficiencies derived from calibration samples
[33] to estimate the misidentified muon contamination. Together these two
sources make up less than 1% of selected candidates.

We use a combination of data and simulation to estimate backgrounds from
${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\\!\rightarrow{{D}^{0}}K^{+}X{\mu^{-}}{{\overline{\nu}}_{\mu}}}$,
${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\\!\rightarrow{{D}^{0}}K^{0}X{\mu^{-}}{{\overline{\nu}}_{\mu}}}$,
and ${{{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{{D}^{0}}pX{\mu^{-}}{{\overline{\nu}}_{\mu}}}$
decays. In data, additional candidates identified as kaons or protons, which
are inconsistent with being produced at any primary collision vertex, are
combined with the ${{D}^{0}}{\mu^{-}}$ candidates. This is done for both
right- (${{D}^{0}}{{K}^{+}}$ or ${{D}^{0}}p$) and wrong-sign
(${{D}^{0}}{{K}^{-}}$ or ${{D}^{0}}{\overline{p}}$) combinations. The wrong-
sign combinations are used to model the combinatorial background in this
selection. Using a-two dimensional fit to the ${{D}^{0}}K$ or ${{D}^{0}}p$
mass and the track impact parameter with respect to the ${{D}^{0}}{\mu^{-}}$
vertex, we determine the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ yields.

For the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ case, the
resulting yield is corrected for efficiency, and for modes with neutral kaons,
using simulation. We take the shape of the contribution in $\Delta
m_{\mathrm{min}}$ from simulation. There is an important contribution at low
$\Delta m_{\mathrm{min}}$ where the kaon from the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ decay points back to the
primary vertex and is selected as the prompt kaon. This contribution is not
present in the data control sample because of the requirement for the
additional kaon to be inconsistent with any primary vertex. The final cut on
$\Delta m_{\mathrm{min}}$ does, however, remove this component from the signal
region. The simulated samples well reproduce the shape of the $\Delta
m_{\mathrm{min}}$ distribution measured using the
${{D}^{0}}{{K}^{+}}X{\mu^{-}}$ selection.

Since the simulation does not reproduce well the shape in
$m_{\mathrm{miss}}^{2}$ for the ${{D}^{0}}{{K}^{+}}X{\mu^{-}}$ control sample,
the shape of the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$
contribution to the main $m_{\mathrm{miss}}^{2}$ fit is instead derived from
the control sample. We obtain it by taking the difference in the right- and
wrong-sign kaon $m_{\mathrm{miss}}^{2}$ distributions, scaling the wrong-sign
yield to match the combinatorial contribution found by the two dimensional fit
described above. The ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ contribution to the final
selection is 3%, with a relative normalization uncertainty of 10%. For the
${\mathchar 28931\relax}^{0}_{b}$ case, the contribution is less than 1%. The
shapes in both $\Delta m_{\mathrm{min}}$ and $m_{\mathrm{miss}}^{2}$ are taken
from the control sample, and scaled based on the efficiency in simulation. The
relative uncertainty on the normalization of this contribution is 20%. The
$\Delta m_{\mathrm{min}}$ distribution for the sum of these backgrounds is
shown in Fig. 6.

Figure 6: Distribution of the minimum mass difference for (left)
${{B}^{-}}{{K}^{+}}$ opposite-sign candidates and (right) ${{B}^{-}}{{K}^{-}}$
same-sign candidates. All candidates are compared to the estimated background
from other sources besides decays of a ${B}^{-}$ or ${\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}^{0}$ meson to
${{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}$. The remaining non-peaking part
of the distributions is made up of ${B}^{-}$ and ${\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}^{0}$ semileptonic decays that do not
come from an excited ${\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}^{0}_{s}$ state.

###  4.2 Backgrounds from semileptonic decays of $\boldsymbol{{{B}^{-}}}$ and
$\boldsymbol{{{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}}$ mesons

We first estimate the number of candidates in the OS$K$ signal region that do
not come from ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$
decays. This is done with a fit to the $\Delta m_{\mathrm{min}}$ distribution
in the control region after subtracting the backgrounds described in Sect.
4.1. The fit is done for three bins of prompt kaon $p_{\mathrm{T}}$ to account
for the different spectra of the SS$K$ and OS$K$ samples:
$0.5<p_{\mathrm{T}}<$1.25\text{\,}\mathrm{Ge\kern-1.00006ptV}$$,
$1.25<p_{\mathrm{T}}<$2\text{\,}\mathrm{Ge\kern-1.00006ptV}$$, and
$p_{\mathrm{T}}>$2\text{\,}\mathrm{Ge\kern-1.00006ptV}$$. The $\Delta
m_{\mathrm{min}}$ shapes for ${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}}\\!\rightarrow{{B}^{-}}{{K}^{+}}}$
signals as well as ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s1}^{0}$
and ${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}}\\!\rightarrow{B}^{*-}{{K}^{+}}}$,
with ${{B}^{*-}\\!\rightarrow{{B}^{-}}\gamma}$, backgrounds are taken from
simulation. We model the background contribution using a fifth-order
polynomial; the high order allows the fit to account for additional
backgrounds peaking near $\Delta m_{\mathrm{min}}=0$.

In an alternative approach, the SS$K$ sample is scaled to model the background
in the OS$K$ sample. The scaling is based on a linear fit to the ratio between
OS$K$ and SS$K$ samples in the region $\Delta
m_{\mathrm{min}}>$100\text{\,}\mathrm{Me\kern-1.00006ptV}$$, where the signal
contribution is negligible. The $\Delta m_{\mathrm{min}}$ distributions,
showing the results of these two methods of background estimation, are shown
in Fig. 7. We use the difference of the two methods to estimate the systematic
uncertainty on the background yield.

Figure 7: Fits to the opposite-sign and same-sign kaon
$m_{\mathrm{min}}-m_{B}-m_{K}$ distributions with non-${B}^{-}$ and ${\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}^{0}$ backgrounds subtracted, and the
resulting estimations of the non-${\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}_{s2}^{*0}$ and ${\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}_{s1}^{0}$ contributions. The fits
are done separately in three bins of the prompt kaon $p_{\mathrm{T}}$: (top
left) $0.5<p_{\mathrm{T}}<1.25\mathrm{\,Ge\kern-0.90005ptV}$, (top right)
$1.25<p_{\mathrm{T}}<2\mathrm{\,Ge\kern-0.90005ptV}$, and (bottom)
$p_{\mathrm{T}}>2\mathrm{\,Ge\kern-0.90005ptV}$. The dashed line shows the
background estimation using a fit to the full OS$K$ distribution with signal
templates from simulation and a fifth-order polynomial for the background. The
points estimate the background using a linear extrapolation of the OS$K$ to
SS$K$ ratio in the region
$m_{\mathrm{min}}-m_{B}-m_{K}>100\mathrm{\,Me\kern-0.90005ptV}$.

The two methods constrain the yield of non-${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ decays as a function of
$\Delta m_{\mathrm{min}}$, however the missing-mass shape in the OS$K$ channel
must still be determined. For each type of background decay, the missing-mass
distribution is the same in the OS$K$ and SS$K$ samples for a particular value
of $\Delta m_{\mathrm{min}}$. This equivalence is tested using fully
reconstructed ${{{B}^{-}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{-}}}$ decays. However, since the missing mass also depends on the
decay products, the distributions are different for ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays. The fraction of this
background coming from ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$
decays is also different in the SS$K$ and OS$K$ samples.

We use the SS$K$ shape to model the background contribution in the OS$K$
sample, considering ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays separately. This is done
by estimating first the contribution of ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays to both the OS$K$ and
SS$K$ channels. The remainder of the SS$K$ channel is used to model the shape
of the ${B}^{-}$ contribution. The normalization of the ${B}^{-}$ background
in the OS$K$ channel is then derived from the overall non-${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ contribution with that
from ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mesons removed.

To estimate the fractional contribution from ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays in SS$K$ sample, we use
the expected fraction resulting in the final state
${{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}$ based on measured branching
fractions [17]. The overlap with this measurement is removed by considering
separately the ratio of contributions to the final state from ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ and ${B}^{-}$ decays for the
${{B}\\!\rightarrow D^{*(*)}{\mu^{-}}{{\overline{\nu}}_{\mu}}}$ channels,
$r_{D^{*(*)}}$, with ${D^{*(*)}\\!\rightarrow{{D}^{0}}X}$. These ratios are
combined with the measured fractions $f_{{{D}^{*0}}}$ and $f_{{D^{**0}}}$. We
assume equal production of ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ and ${B}^{-}$ mesons. The
fraction of ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays in
the SS$K$ sample, $f_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}}$, is thus given by

$\displaystyle\frac{1}{f_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}}}$
$\displaystyle=\frac{{\mathcal{B}}\quantity({{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\\!\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}})+{\mathcal{B}}\quantity({{{B}^{-}}\\!\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}})}{{\mathcal{B}}\quantity({{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\\!\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}})}$
$\displaystyle=1+\quantity[\frac{{\mathcal{B}}\quantity({{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\\!\rightarrow{{D}^{*+}}{\mu^{-}}{{\overline{\nu}}_{\mu}}}){\mathcal{B}}\quantity({{{D}^{*+}}\\!\rightarrow{{D}^{0}}X})+{\mathcal{B}}\quantity({{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\\!\rightarrow
D^{**+}{\mu^{-}}{{\overline{\nu}}_{\mu}}}){\mathcal{B}}\quantity({D^{**+}\\!\rightarrow{{D}^{0}}X})}{{\mathcal{B}}\quantity({{{B}^{-}}\\!\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}})}]^{-1}$
$\displaystyle=1+\quantity[r_{{{D}^{*}}}f_{D^{*0}}+r_{D^{**}}f_{D^{**0}}]^{-1}$
$\displaystyle=1+\quantity[(0.591\pm 0.024)f_{D^{*0}}+(1.00\pm
0.23)f_{D^{**0}}]^{-1}.$ (6)

The uncertainty on $r_{{{D}^{*}}}$ comes chiefly from experimental
uncertainty, while the dominant uncertainty on $r_{D^{**}}$ comes from
extrapolation to the unmeasured parts of the semileptonic width. The
uncertainty is taken as one standard deviation of the full extrapolation
envelope assuming a uniform distribution. Using the central values of the
expectations for $f_{{{D}^{*0}}}$ and $f_{{D^{**0}}}$ given in Sect. 1, the
central value for $f_{{\kern 1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}$
is 35%; variations within the uncertainties change it by approximately 2%. We
then combine this value of $f_{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}$ with an efficiency correction
from simulation which depends on the lifetime difference between ${B}^{-}$ and
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mesons.

The contribution from ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$
mesons is studied similarly to the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ backgrounds, by attaching an additional candidate
identified as a pion to the ${{D}^{0}}{\mu^{-}}$ candidates. We fit the
${{D}^{0}}\pi^{\pm}$ mass distributions, including peaking contributions from
${D}^{*+}$, $D_{1}$, and $D_{2}^{*}$ mesons on top of a smooth distribution.
The normalizations of the peaks from the decay ${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\\!\rightarrow\quantity({D_{2}^{*+}\\!\rightarrow{{D}^{0}}{{\pi}^{+}}}){\mu^{-}}{{\overline{\nu}}_{\mu}}}$
and the partially reconstructed decays ${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\\!\rightarrow\quantity({D_{1}^{+}\\!\rightarrow{{D}^{*0}}{{\pi}^{+}}}){\mu^{-}}{{\overline{\nu}}_{\mu}}}$
and ${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\\!\rightarrow\quantity({D_{2}^{*+}\\!\rightarrow{{D}^{*0}}{{\pi}^{+}}}){\mu^{-}}{{\overline{\nu}}_{\mu}}}$
show that there are more ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ candidates in the OS$K$ sample
than there are in the SS$K$ sample. This is verified using fully reconstructed
${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*}}\quantity(892)^{0}}$ decays.
Combining the ratios in the two channels, we find there is a 10% larger
contribution of ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays
in the OS$K$ sample.

While the decays in the resonance peaks are dominated by either a ${B}^{-}$ or
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ initial state, the
other contributions to the ${{D}^{0}}\pi^{\pm}$ distributions are more
difficult to disentangle. The combinatorial background is expected to be
symmetric in ${{D}^{0}}{{\pi}^{+}}{\mu^{-}}$ and
${{D}^{0}}{{\pi}^{-}}{\mu^{-}}$, while ${B}^{-}$ decays produce
${{D}^{0}}{{\pi}^{+}}{{\pi}^{-}}{\mu^{-}}$ which also contribute equally to
both distributions. We therefore derive the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ missing-mass shape by
subtracting the ${{D}^{0}}{{\pi}^{-}}{\mu^{-}}$ shape from the
${{D}^{0}}{{\pi}^{+}}{\mu^{-}}$ shape. Each shape is corrected for the
efficiency to reconstruct the additional pion based on simulation. The
resulting distribution is validated using a simulated mixture of ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays.

We determine the total background shape from ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays in the OS$K$ sample by
first removing the expected ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ contribution from the initial
SS$K$ sample’s $m_{\mathrm{miss}}^{2}$ distribution. This is then scaled up by
10% to estimate the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$
contribution to the OS$K$ sample. The remainder of the SS$K$ sample, composed
of ${B}^{-}$ decays, is scaled up so that when it is added to the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ estimate, the total number of
background candidates in the OS$K$ sample is equal to the result of the
$\Delta m_{\mathrm{min}}$ fit. We accomplish this procedure using an event-by-
event weighting that accounts for the background yield as a function of
$\Delta m_{\mathrm{min}}$.

Contributions not from semileptonic decays of ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mesons that are subtracted from
the SS$K$ sample (${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$
and ${\mathchar 28931\relax}^{0}_{b}$ contributions, combinatorial, and
misidentified muons) are also weighted in the same manner before being
subtracted to produce the final background template.

###  4.3 Backgrounds from $\boldsymbol{{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}}}$ and
$\boldsymbol{{{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s1}^{0}}}$
decays

The final class of backgrounds are ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s}^{**0}$ decays that produce a
${B}^{-}$ meson with a ${{D}^{0}}{\mu^{-}}X$ final state that is not a
semileptonic channel of interest. The $m_{\mathrm{miss}}^{2}$ shapes for
semitauonic
${{{B}^{-}}\\!\rightarrow{{D}^{0}}X\quantity({{\tau^{-}}\\!\rightarrow{\mu^{-}}{{\overline{\nu}}_{\mu}}{{\nu}_{\tau}}}){{\overline{\nu}}_{\tau}}}$
decays and ${B}^{-}$ decays involving two charm mesons are estimated from
simulation, and are included in the final fit. Contributions from ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s1}^{0}$ or ${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}}\\!\rightarrow
B^{*-}{{K}^{+}}}$, where ${B^{*-}\\!\rightarrow{{B}^{-}}\gamma}$, are
negligible after the requirement on the $\Delta m_{\mathrm{min}}$ variable.

##  5 Fit description

The fractions of interest, $f_{{D}^{0}}$ and $f_{D^{**0}}$, are determined
from a binned-template, maximum-likelihood fit to the missing-mass
distribution of the OS$K$ sample. The signal fraction $f_{{{D}^{*0}}}$ is
given by the remainder, $1-f_{{{D}^{0}}}-f_{D^{**0}}$. To control statistical
fluctuations in the templates for the missing-mass tails, which are important
for determining the $D^{**0}$ content, a variable bin size is used for the
template fit. The sum of the templates is allowed to vary bin-by-bin based on
the combined statistical uncertainty of all templates. This variation is
included using a single nuisance parameter for each bin that is constrained by
the statistical uncertainty. It is dominated by the uncertainty of the SS$K$
sample used to create the combined ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ background template. The effect
of these uncertainty parameters is determined analytically using the
Barlow–Beeston method [34]. Unless otherwise specified, we account for
systematic uncertainties using nuisance parameters that are free to vary in
the fit; these parameters are allowed to vary around their central values with
a Gaussian constraint based on their uncertainty.

In total, the fit contains three signal and eight background templates:
background from semileptonic ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays not from a ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ decay, non-${D}^{0}$
backgrounds, ${{D}^{0}}{\mu^{-}}$ combinations not from the same $b$-hadron
decay, backgrounds with a hadron misidentified as the muon, ${B}^{0}_{s}$,
${\mathchar 28931\relax}^{0}_{b}$, ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ decays with a semitauonic
${B}^{-}$ decay, and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ decays with a ${B}^{-}$
decay to two charm mesons. There are 18 free parameters in the fit, not
including the nuisance parameters for the template statistical uncertainties.

The three templates describing the signal are obtained from
simulation—exclusive ${D}^{0}$, exclusive ${D}^{*0}$, and the sum of all
$D^{**0}$ modes; these are shown in Fig. 4. We also correct for the relative
reconstruction and selection efficiencies between these samples, which are
taken from simulation. Relative to the ${D}^{*0}$ mode, the efficiency of the
${D}^{0}$ mode is 92% and that of the $D^{**0}$ mode is 68%. In addition to
the two signal fractions of interest, three more free parameters govern the
shape changes from the variations of the form factors, and one parameter gives
the overall signal yield.

The template describing the ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ backgrounds not coming from a
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ meson is
extrapolated from the SS$K$ sample as described in Sect. 4. Four free
parameters describe the systematic variations of the normalization as a
function of $\Delta m_{\mathrm{min}}$. In the fit, the parameters
$r_{{{D}^{*}}}$ and $r_{D^{**}}$ and the fractions $f_{{D}^{0}}$ and
$f_{D^{**0}}$ are used to calculate $f_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}}$ for the current evaluation of
the fit function. This variation is constrained by the uncertainties of
$r_{{{D}^{*}}}$ and $r_{D^{**}}$. The current value of $f_{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}$ is combined with a set of
templates that vary $f_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}}$ by ${}\pm 1\%$ to extrapolate
from the nominal value and produce the estimated background shape for this
evaluation. An additional uncertainty in this template comes from the
$m_{\mathrm{miss}}^{2}$ shape of the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ component, which is controlled
by one parameter.

The normalizations of the contributions from ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ decays, ${\mathchar
28931\relax}^{0}_{b}$ decays, and decays involving misidentified muons are
also allowed to vary. The data-driven background shapes for fake and
combinatorial muons, and for ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ and ${\mathchar
28931\relax}^{0}_{b}$ decays are described in Sect. 4.

The templates for the contribution of semitauonic decays of ${B}^{-}$ mesons
from ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ are obtained
from simulation. We determine the normalization relative to the semimuonic
modes by deriving an effective ratio of semitauonic to semimuonic decays,
$R\quantity({{D}^{0}}X)$, using the Standard Model values [35, 36, 37] and the
expected fractions of ${D}^{0}$, ${D}^{*0}$, and $D^{**0}$,

$R\quantity({{D}^{0}}X)=R\quantity(D)f_{{D}^{0}}+R\quantity(D^{*})f_{{D}^{*0}}+R\quantity(D^{**})f_{D^{**0}},$
(7)

where $R\quantity(D)$ is the ratio ${\mathcal{B}}\quantity({{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}\\!\rightarrow
D{\tau^{-}}{{\overline{\nu}}_{\tau}}})/{\mathcal{B}}\quantity({{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}\\!\rightarrow
D{\mu^{-}}{{\overline{\nu}}_{\mu}}})$, and $R(D^{*})$ and $R(D^{**})$ are the
corresponding ratios in the other decay channels. This is combined with the
$\tau\rightarrow\mu X$ branching fraction [38] and the relative efficiency to
reconstruct $\tau$ decays taken from simulation. The expected contribution is
$\quantity(1.5\pm 0.3)\%$ of the selected ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ decays. The uncertainty
is dominated by the difference of the Standard Model expectations and the
world-average measured values of $R(D)$ and $R(D^{*})$ [1], which we take as a
systematic uncertainty.

The other backgrounds coming from ${{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}}\\!\rightarrow{{B}^{-}}{{K}^{+}}}$
decays are ${B}^{-}$ mesons decaying to double-charm states of various types.
A simulated sample composed of many different decays producing
${{D}^{0}}{\mu^{-}}$ final states is used to determine the shape of this
component. The normalization of the resulting missing-mass template is
expected to be about 1% of ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ decays based on branching
fractions, but is left unconstrained in the fit.

##  6 Systematic uncertainties

Each of the signal components has systematic uncertainties associated to its
shape. The systematic uncertainty on the ${D}^{0}$ and ${D}^{*0}$ components
is estimated based on uncertainties in the form-factor parameters. We reweight
our simulated samples using the Caprini–Lellouch–Neubert (CLN) expansion
formalism [39], with the uncertainties on the parameters taken from HFLAV [1].
This produces negligible changes in the missing mass template shapes compared
to the other uncertainties in this analysis.

The uncertainty on the relative signal efficiencies is approximately 2%. We
obtain the associated systematic uncertainty by repeating the fit with
different efficiency values obtained by varying the efficiencies by their
uncertainties.

For the $D^{**0}$ template, in addition to a large variation in the form-
factor distribution based on results from Ref. [37], we create an alternative
template with different branching fractions for the various resonant and
nonresonant decay modes. The most important difference is the inclusion of a
larger fraction of higher mass, nonresonant $D^{(*)}\pi$ and $D^{(*)}\pi\pi$
decays, where the pions may be of any allowed charge combination. This shape
is fixed in the template fit; a second fit with the alternative template is
used to estimate the systematic uncertainty from this shape. During this
second fit, the signal efficiency of the $D^{**0}$ component is also adjusted
along with the template. This uncertainty leads to the bands shown in Fig. 4.

For background contributions not from ${B}^{-}$ or ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ semileptonic decays, we include
individual uncertainties on their normalizations. Systematic variations in the
shapes are dominated by the statistical bin-by-bin statistical uncertainty.

We consider a number of systematic uncertainties on the ${B}^{-}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ contributions. The uncertainty
due to the overall normalization comes from two sources. The statistical
uncertainties in the polynomial background function of the $\Delta
m_{\mathrm{min}}$ fit are used to modify the template. This corresponds to an
uncertainty of less than 1% on the yield in each prompt kaon $p_{\mathrm{T}}$
bin. We also use the alternative extrapolation using the $\Delta
m_{\mathrm{min}}$ ratio to provide an alternative normalization, giving an
uncertainty of approximately 2%. Both of these uncertainties produce only
small changes in the templates. The uncertainties in $r_{{{D}^{*}}}$ and
$r_{D^{**}}$ give the uncertainty on the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ fraction. The uncertainty in
the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$
$m_{\mathrm{miss}}^{2}$ shape is estimated from the uncertainty in the
efficiency from simulation to reconstruct the pion in the
${{D}^{0}}\pi^{\pm}{\mu^{-}}$ combination.

An estimated breakdown of the total statistical and systematic uncertainty is
given in Table 1. The largest source of uncertainty is the statistical
uncertainty from the extrapolated SS$K$ data sample. The uncertainty in the
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ $m_{\mathrm{miss}}^{2}$
shape is also important because of its effect on the high
$m_{\mathrm{miss}}^{2}$ tail. Most systematic uncertainties are included in
the fit with constrained nuisance parameters. The only source for which the
fit result has a significantly smaller uncertainty than the initial constraint
is the normalization of the non-${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ background from the
$\Delta m_{\mathrm{min}}$ extrapolation. For the final result, the total
uncertainty is taken from the best fit, with the fixed systematic
uncertainties for the relative signal efficiencies and the $D^{**0}$ branching
fractions from added in quadrature.

Table 1: Estimates of the breakdown of the total uncertainty. All estimates are done by repeating the fit with systematic nuisance parameters fixed to their best fit values. The statistical uncertainty of the OS$K$ sample is estimated from the uncertainty on the signal fractions with the template statistical nuisance parameters fixed to their best fit values. The template statistical uncertainty is added in by allowing only the statistical nuisance parameters to vary. The effect of each floating systematic uncertainty is estimated by refitting with its systematic nuisance parameter shifted by the uncertainty found by the best fit and taking the difference in the signal fractions as the uncertainty. The total uncertainty is taken from the best fit, with the fixed systematic uncertainties added in quadrature. Source of uncertainty | $f_{{D}^{0}}$ | $f_{D^{**0}}$
---|---|---
Statistical |  OS$K$ sample | $0.025$ | $0.027$
Templates | $0.047$ | $0.052$
Floating syst. | Signal form-factors | $0.006$ | $0.004$
Non-${B}^{-}$, ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ backgrounds | $0.004$ | $0.004$
${B}^{-}$, ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ background normalization | $0.003$ | $0.015$
|  ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ fraction and $m_{\mathrm{miss}}^{2}$ shape | $0.004$ | $0.030$
Fixed syst. |  $D^{**0}$ branching fractions | $0.025$ | $0.044$
Relative signal efficiency | $0.003$ | $0.003$
Total uncertainty | 0.056 | $+0.070$
$-0.074$

##  7 Results and conclusions

The result of the template fit is shown in Fig. 8. We find the parameters of
interest

$\displaystyle f_{{{D}^{0}}}$ $\displaystyle=0.25\pm 0.06,$ $\displaystyle
f_{{D^{**0}}}$ $\displaystyle=0.21\pm 0.07,$

where the uncertainty is the total due to statistical and systematic
uncertainties. Contours for the 68.3% and 95.5% confidence intervals for the
nominal fit are shown in Fig. 9. From the conditional covariance of the two
parameters of interest combined with the fit result using alternate $D^{**0}$
branching fractions, the correlation coefficient of the two parameters is
$\rho=-0.38$, which is dominated by the change in the alternate branching-
fraction fit. The fraction $f_{{{D}^{*0}}}$ is equal to
$1-f_{{{D}^{0}}}-f_{{D^{**0}}}=0.54\pm 0.07$, but this cannot be taken as an
independent determination.

Figure 8: Template fit to the missing-mass distribution. The nuisance
parameters used to quantify the template statistical uncertainties are set to
their nominal values. The full distribution (left) is shown, comparing the
background to the sum of the signal templates. The background-subtracted
distribution (right) is compared to the breakdown of the signal components.
The statistical uncertainty in the background templates is represented as the
shaded band around the fit. In the pull distribution, the statistical
uncertainty of the background templates is added to the statistical
uncertainty of the data points. Figure 9: Contours for 68.3% and 95.5%
confidence intervals for the fractions of
${{{B}^{-}}\\!\rightarrow{{D}^{0}}X{\mu^{-}}{{\overline{\nu}}_{\mu}}}$ into
the exclusive
${{{B}^{-}}\\!\rightarrow{{D}^{0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}}$ channel
and the higher excited
${{{B}^{-}}\\!\rightarrow\left({{D^{**0}}\\!\rightarrow{{D}^{0}}X}\right){\mu^{-}}{{\overline{\nu}}_{\mu}}}$
channels. The alternate fit using different branching fractions for different
$D^{**0}$ states is not included.

The results are compatible with expectations based on previous exclusive
measurements [17]. Because of the uncertainty on the $D^{**0}$ component, the
results do not yet favor a particular explanation for the exclusive–inclusive
gap.

We have demonstrated that the reconstruction of the momentum of ${B}^{-}$
decays with missing particles using ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}_{s2}^{*0}$ decays is a viable method
at the LHCb experiment. This technique requires much larger data sets than
measurements with inclusive ${B}^{-}$ selections, but measuring the missing
mass provides important discriminating power between different decay modes,
and between signal and backgrounds. This is a promising method to employ with
the additional data that the LHCb experiment has collected in Run 2 and will
collect in the future.

## 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); MinES
and FASO (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).

## Appendix

##  Appendix A Derivation of the $\boldsymbol{{{B}^{-}}}$ meson energy

Consider a known ${B}^{-}$ momentum direction with unknown energy and a kaon
of momentum $p_{K}$ at an angle $\theta$ in the laboratory frame with respect
to it. Taking the ${B}^{-}$ direction as the $z$-axis, the squared mass of the
${{B}^{-}}{{K}^{+}}$ system is

$\displaystyle m_{BK}^{2}$ $\displaystyle=\quantity|\matrixquantity(E_{B}\\\
0\\\ 0\\\
\sqrt{E_{B}^{2}-m_{B}^{2}})+\matrixquantity(\sqrt{p_{K}^{2}+m_{K}^{2}}\\\
p_{K}\sin\theta\\\ 0\\\ p_{K}\cos\theta)|^{2}.$ (8) For a particular $m_{BK}$
hypothesis, Eq. 8 can be written $\displaystyle m_{BK}^{2}$
$\displaystyle=\quantity(E_{B}+\sqrt{p_{K}^{2}+m_{K}^{2}})^{2}-p_{K}^{2}\sin^{2}\theta$
(9)
$\displaystyle\phantom{{}={}}-\quantity(\sqrt{E_{B}^{2}-m_{B}^{2}}+p_{K}\cos\theta)^{2}$
$\displaystyle=E_{B}^{2}+2E_{B}E_{K}+m_{K}^{2}+\quantity(p_{K}^{2}-p_{K}^{2}\sin^{2}\theta)$
(10)
$\displaystyle\phantom{{}={}}-E_{B}^{2}+m_{B}^{2}-2p_{K}\cos\theta\sqrt{E_{B}^{2}-m_{B}^{2}}-p_{K}^{2}\cos^{2}\theta.$
Rearranging terms, squaring to remove the root, and using
$\Delta^{2}=m_{BK}^{2}-m_{B}^{2}-m_{K}^{2}$ gives $\displaystyle 0$
$\displaystyle=E_{B}^{2}\quantity(4\quantity(E_{K}^{2}-p_{K}^{2}\cos^{2}\theta))+E_{B}\quantity(-4E_{K}\Delta^{2})$
(11)
$\displaystyle\phantom{{}={}}+\quantity(4m_{B}^{2}p_{K}^{2}\cos^{2}\theta+\Delta^{4}).$
The solution to the quadratic equation for $E_{B}$ is $\displaystyle E_{B}$
$\displaystyle=\frac{\Delta^{2}}{2E_{K}}\frac{1}{1-\quantity(p_{K}/E_{K})^{2}\cos^{2}\theta}\quantity[1\pm\sqrt{d}],$
(12) where $\displaystyle d$
$\displaystyle=\frac{p_{K}^{2}}{E_{K}^{2}}\cos^{2}\theta-\frac{4m_{B}^{2}p_{K}^{2}\cos^{2}\theta}{\Delta^{4}}\quantity(1-\frac{p_{K}^{2}}{E_{K}^{2}}\cos^{2}\theta).$
(13)

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LHCb collaboration

R. Aaij27, B. Adeva41, M. Adinolfi48, C.A. Aidala73, Z. Ajaltouni5, S. Akar59,
P. Albicocco18, J. Albrecht10, F. Alessio42, M. Alexander53, A. Alfonso
Albero40, S. Ali27, G. Alkhazov33, P. Alvarez Cartelle55, A.A. Alves Jr41, S.
Amato2, S. Amerio23, Y. Amhis7, L. An3, L. Anderlini17, G. Andreassi43, M.
Andreotti16,g, J.E. Andrews60, R.B. Appleby56, F. Archilli27, P. d’Argent12,
J. Arnau Romeu6, A. Artamonov39, M. Artuso61, K. Arzymatov37, E. Aslanides6,
M. Atzeni44, B. Audurier22, S. Bachmann12, J.J. Back50, S. Baker55, V.
Balagura7,b, W. Baldini16, A. Baranov37, R.J. Barlow56, S. Barsuk7, W.
Barter56, F. Baryshnikov70, V. Batozskaya31, B. Batsukh61, V. Battista43, A.
Bay43, J. Beddow53, F. Bedeschi24, I. Bediaga1, A. Beiter61, L.J. Bel27, S.
Belin22, N. Beliy63, V. Bellee43, N. Belloli20,i, K. Belous39, I.
Belyaev34,42, E. Ben-Haim8, G. Bencivenni18, S. Benson27, S. Beranek9, A.
Berezhnoy35, R. Bernet44, D. Berninghoff12, E. Bertholet8, A. Bertolin23, C.
Betancourt44, F. Betti15,42, M.O. Bettler49, M. van Beuzekom27, Ia.
Bezshyiko44, S. Bhasin48, J. Bhom29, S. Bifani47, P. Billoir8, A. Birnkraut10,
A. Bizzeti17,u, M. Bjørn57, M.P. Blago42, T. Blake50, F. Blanc43, S. Blusk61,
D. Bobulska53, V. Bocci26, O. Boente Garcia41, T. Boettcher58, A. Bondar38,w,
N. Bondar33, S. Borghi56,42, M. Borisyak37, M. Borsato41, F. Bossu7, M.
Boubdir9, T.J.V. Bowcock54, C. Bozzi16,42, S. Braun12, M. Brodski42, J.
Brodzicka29, A. Brossa Gonzalo50, D. Brundu22, E. Buchanan48, A. Buonaura44,
C. Burr56, A. Bursche22, J. Buytaert42, W. Byczynski42, S. Cadeddu22, H.
Cai64, R. Calabrese16,g, R. Calladine47, M. Calvi20,i, M. Calvo Gomez40,m, A.
Camboni40,m, P. Campana18, D.H. Campora Perez42, L. Capriotti56, A.
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Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina20, M. Cattaneo42, G.
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Charpentier42, G. Chatzikonstantinidis47, M. Chefdeville4, V. Chekalina37, C.
Chen3, S. Chen22, S.-G. Chitic42, V. Chobanova41, M. Chrzaszcz42, A.
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C.M. Costa Sobral50, B. Couturier42, G.A. Cowan52, D.C. Craik58, A.
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Rodriguez1,z, T. Mombächer10, I.A. Monroy66, S. Monteil5, M. Morandin23, G.
Morello18, M.J. Morello24,t, O. Morgunova69, J. Moron30, A.B. Morris6, R.
Mountain61, F. Muheim52, M. Mulder27, C.H. Murphy57, D. Murray56, A. Mödden
10, D. Müller42, J. Müller10, K. Müller44, V. Müller10, P. Naik48, T.
Nakada43, R. Nandakumar51, A. Nandi57, T. Nanut43, I. Nasteva2, M. Needham52,
N. Neri21, S. Neubert12, N. Neufeld42, M. Neuner12, T.D. Nguyen43, C. Nguyen-
Mau43,n, S. Nieswand9, R. Niet10, N. Nikitin35, A. Nogay69, N.S. Nolte42, D.P.
O’Hanlon15, A. Oblakowska-Mucha30, V. Obraztsov39, S. Ogilvy18, R.
Oldeman22,f, C.J.G. Onderwater68, A. Ossowska29, J.M. Otalora Goicochea2, P.
Owen44, A. Oyanguren72, P.R. Pais43, T. Pajero24,t, A. Palano14, M.
Palutan18,42, G. Panshin71, A. Papanestis51, M. Pappagallo52, L.L.
Pappalardo16,g, W. Parker60, C. Parkes56, G. Passaleva17,42, A. Pastore14, M.
Patel55, C. Patrignani15,e, A. Pearce42, A. Pellegrino27, G. Penso26, M. Pepe
Altarelli42, S. Perazzini42, D. Pereima34, P. Perret5, L. Pescatore43, K.
Petridis48, A. Petrolini19,h, A. Petrov69, S. Petrucci52, M. Petruzzo21,q, B.
Pietrzyk4, G. Pietrzyk43, M. Pikies29, M. Pili57, D. Pinci26, J. Pinzino42, F.
Pisani42, A. Piucci12, V. Placinta32, S. Playfer52, J. Plews47, M. Plo
Casasus41, F. Polci8, M. Poli Lener18, A. Poluektov50, N. Polukhina70,c, I.
Polyakov61, E. Polycarpo2, G.J. Pomery48, S. Ponce42, A. Popov39, D.
Popov47,11, S. Poslavskii39, C. Potterat2, E. Price48, J. Prisciandaro41, C.
Prouve48, V. Pugatch46, A. Puig Navarro44, H. Pullen57, G. Punzi24,p, W.
Qian63, J. Qin63, R. Quagliani8, B. Quintana5, B. Rachwal30, J.H.
Rademacker48, M. Rama24, M. Ramos Pernas41, M.S. Rangel2, F. Ratnikov37,x, G.
Raven28, M. Ravonel Salzgeber42, M. Reboud4, F. Redi43, S. Reichert10, A.C.
dos Reis1, F. Reiss8, C. Remon Alepuz72, Z. Ren3, V. Renaudin7, S.
Ricciardi51, S. Richards48, K. Rinnert54, P. Robbe7, A. Robert8, A.B.
Rodrigues43, E. Rodrigues59, J.A. Rodriguez Lopez66, M. Roehrken42, A.
Rogozhnikov37, S. Roiser42, A. Rollings57, V. Romanovskiy39, A. Romero
Vidal41, M. Rotondo18, M.S. Rudolph61, T. Ruf42, J. Ruiz Vidal72, J.J.
Saborido Silva41, N. Sagidova33, B. Saitta22,f, V. Salustino Guimaraes62, C.
Sanchez Gras27, C. Sanchez Mayordomo72, B. Sanmartin Sedes41, R.
Santacesaria26, C. Santamarina Rios41, M. Santimaria18, E. Santovetti25,j, G.
Sarpis56, A. Sarti18,k, C. Satriano26,s, A. Satta25, M. Saur63, D.
Savrina34,35, S. Schael9, M. Schellenberg10, M. Schiller53, H. Schindler42, M.
Schmelling11, T. Schmelzer10, B. Schmidt42, O. Schneider43, A. Schopper42,
H.F. Schreiner59, M. Schubiger43, M.H. Schune7, R. Schwemmer42, B. Sciascia18,
A. Sciubba26,k, A. Semennikov34, E.S. Sepulveda8, A. Sergi47,42, N. Serra44,
J. Serrano6, L. Sestini23, A. Seuthe10, P. Seyfert42, M. Shapkin39, Y.
Shcheglov33,†, T. Shears54, L. Shekhtman38,w, V. Shevchenko69, E. Shmanin70,
B.G. Siddi16, R. Silva Coutinho44, L. Silva de Oliveira2, G. Simi23,o, S.
Simone14,d, N. Skidmore12, T. Skwarnicki61, J.G. Smeaton49, E. Smith9, I.T.
Smith52, M. Smith55, M. Soares15, l. Soares Lavra1, M.D. Sokoloff59, F.J.P.
Soler53, B. Souza De Paula2, B. Spaan10, P. Spradlin53, F. Stagni42, M.
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Zonneveld52, S. Zucchelli15.

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

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
vMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
xNational Research University Higher School of Economics, Moscow, Russia
ySezione INFN di Trieste, Trieste, Italy
zEscuela Agrícola Panamericana, San Antonio de Oriente, Honduras
aaSchool of Physics and Information Technology, Shaanxi Normal University
(SNNU), Xi’an, China
abPhysics and Micro Electronic College, Hunan University, Changsha City, China
†Deceased