EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2020-008 LHCb-PAPER-2019-030 12 August 2020

Measurement of the branching fraction of the decay
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$

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

A measurement of the branching fraction of the decay
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ is
performed using proton–proton collision data corresponding to an integrated
luminosity of $5\text{\,}\text{\,fb}^{-1}$ collected by the LHCb experiment
between 2011 and 2016. The branching fraction is determined to be

${\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})=[8.3\pm
1.6\,(\text{stat})\pm 0.9\,(\text{syst})\pm 0.8\,(\text{norm})\pm
0.3\,(\nicefrac{{f_{s}}}{{f_{d}}})]\times 10^{-6}\,,$

where the first uncertainty is statistical, the second is systematic, and the
third and fourth are due to uncertainties on the branching fraction of the
normalization mode ${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ and the
ratio of hadronization fractions $\nicefrac{{f_{s}}}{{f_{d}}}$. This is the
most precise measurement of this branching fraction to date. Furthermore, a
measurement of the branching fraction of the decay
${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ is
performed relative to that of the
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
channel, and is found to be

$\frac{{\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})}{{\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})}=[7.5\pm
3.1\,(\text{stat})\pm 0.5\,(\text{syst})\pm
0.3\,(\nicefrac{{f_{s}}}{{f_{d}}})]\times 10^{-2}\,.$

Published in Phys. Rev. D 102 (2020) 012011

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

##  1 Introduction

Flavour-changing neutral current processes, especially neutral $B$ meson
decays to kaons and excited kaons, can be used as probes of the Standard Model
and of the CKM unitarity triangle angle $\beta_{(s)}$. While decays such as
$B^{0}_{(s)}\\!\rightarrow{{K}^{*0}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$,
$B^{0}_{s}\\!\rightarrow{{K}^{*0}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$, and
${{B}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}}$ have already been measured at the
LHC [1, 2, 3, 4], decays of $b$ hadrons to final states containing only long-
lived particles, such as ${K}^{0}_{\mathrm{S}}$ mesons or $\mathchar
28931\relax$ baryons, have never before been reported in a hadronic production
environment. A measurement of the branching fraction of
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$ decays can be used as input to
future SM predictions, and is a first step toward a time-dependent measurement
of $C\\!P$ violation in this channel using future LHC data.

In the Standard Model, the decay amplitude of
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$ is dominated by
${b}\rightarrow{s}{\overline{d}}{d}$ loop transitions with gluon radiation,
while other contributions, including color singlet exchange, are suppressed to
the level of $5\text{\,}\mathrm{\char 37\relax}$ [5] in the decay amplitude.
Predictions of this branching fraction within the SM lie in the range
$(15-25)\times 10^{-6}$ [6, 7, 8, 9], with calculations relying on a variety
of theoretical approaches such as soft collinear effective theory, QCD
factorisation, and perturbative leading-order and next-to-leading-order QCD.
Beyond the Standard Model, possible contributions from new particles or
couplings [10, 11, 5, 12, 13] can be probed by improved experimental precision
on the branching fraction measurement.

The decay ${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$ was first observed by the
Belle collaboration in 2016 [14]. The branching fraction was determined to be
${\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$})=(19.6^{+5.8}_{-5.1}\pm
1.0\pm 2.0)\times 10^{-6}$, where the first uncertainty is statistical, the
second systematic and the third due to the uncertainty of the total number of
produced ${B}^{0}_{s}$–${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ pairs. The related decay
${{B}^{0}}\\!\rightarrow{{K}^{0}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$ has a branching fraction of
$(1.21\pm 0.16)\times 10^{-6}$[15, 16, 17] in the world average.

This paper presents measurements of the branching fraction of
${{B}^{0}_{({s})}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
decays using proton-proton collision data collected by the LHCb experiment at
centre-of-mass energies $\sqrt{s}=7$, $8$, or
$13\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}$. The
${{B}^{0}_{({s})}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
branching fraction is assumed to be half of the
${{B}^{0}_{({s})}}\\!\rightarrow{{K}^{0}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$ branching fraction, as the
${K}^{0}$ ${\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}$ final state
is $C\\!P$ even. These ${B}^{0}_{({s})}$ branching fractions are determined
relative to the ${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ branching
fraction, where the notation $\phi$ is used for the $\phi(1020)$ meson
throughout. This normalization mode has a corresponding branching fraction
equal to half of
${\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}}$})=$(7.3\pm\pm
0.7)\text{\times}{10}^{-6}$$ [18, 19], and is chosen for its similarity to the
signal mode. Despite the smaller branching fraction, the yield of the
normalization mode is much larger than that of the signal mode, because the
near-instantaneous $\phi$ decay can be reconstructed more efficiently than a
long-lived ${K}^{0}_{\mathrm{S}}$, and because for LHCb the production
fraction of ${B}^{0}$ mesons is approximately four times that of ${B}^{0}_{s}$
mesons. [44, 45]. Throughout this paper, the decays
${{B}^{0}_{({s})}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
and ${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ are reconstructed
using the decays ${{K}^{0}_{\mathrm{S}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$
and $\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}$.

The paper is structured as follows. A brief description of the LHCb detector
as well as the simulation and reconstruction software is given in Sec. 2.
Signal selection and strategies to suppress background contributions are
outlined in Sec. 3. The models to describe the invariant-mass components, the
fitting and the normalization procedure are introduced in Sec. 4. Systematic
uncertainties are discussed in Sec. 5. Finally, the results are summarized in
Sec. 6.

##  2 LHCb detector

The LHCb detector [20, 21] 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 (VELO) surrounding the
$pp$ interaction region [22], 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 [23, 24]
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$\text{\,Ge\kern-1.00006ptV\\!/}c$.
The minimum distance of a track to a primary vertex (PV), the impact parameter
(IP), is measured with a resolution of
$(15+29/p_{\mathrm{T}})\,\upmu\text{m}$, where $p_{\mathrm{T}}$ is the
component of the momentum transverse to the beam, in
$\text{\,Ge\kern-1.00006ptV\\!/}c$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
[25]. 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.

The online event selection is performed by a trigger [26], 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 contain a muon with high
$p_{\mathrm{T}}$ or a hadron, photon or electron with high transverse energy
in the calorimeters. In the software trigger, events are selected by a
topological $b$-hadron trigger. At least one charged particle must have a
large transverse momentum and be inconsistent with originating from any PV. A
two- or three-track secondary vertex is constructed, which must have a large
sum of the $p_{\mathrm{T}}$ of the charged particles and a significant
displacement from any PV. A multivariate algorithm [27] is used for the
identification of secondary vertices consistent with the decay of a
$b$-hadron. This is used to collect both
${{B}^{0}_{({s})}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
and ${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ decays. In addition to
this topological trigger and algorithm, some
${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ decays are also collected
using dedicated $\phi$ trigger requirements that exploit the topology of the
$\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}$ decay and apply additional particle
identification requirements to the charged kaons.

Simulation is required to model the effects of the detector acceptance and the
imposed selection requirements. In simulation, $pp$ collisions are generated
using Pythia [28, *Sjostrand:2007gs] with a specific LHCb configuration [30].
Decays of hadronic particles are described by EvtGen [31], in which final-
state radiation is generated using Photos [32]. The interaction of the
generated particles with the detector, and its response, are implemented using
the Geant4 toolkit [33, *Agostinelli:2002hh] as described in Ref. [35].

##  3 Event selection

The decays
${{B}^{0}_{({s})}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
and ${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ are reconstructed
using the decay modes
${{K}^{0}_{\mathrm{S}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ and
$\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}$.111The inclusion of charge-conjugate
processes is implied throughout the paper The long-lived
${K}^{0}_{\mathrm{S}}$ mesons are reconstructed in two different categories,
depending on whether the ${K}^{0}_{\mathrm{S}}$ meson decays early enough that
the pions can be tracked inside the VELO, or whether the
${K}^{0}_{\mathrm{S}}$ meson decays later and its products can only be tracked
downstream. These are referred to as long and downstream track categories, and
are abbreviated as L and D, respectively. The ${K}^{0}_{\mathrm{S}}$ mesons
reconstructed in the long track category have better mass, momentum and vertex
resolution than the downstream track category. However, due to the boost of
the $B$ meson, the lifetime of the ${K}^{0}_{\mathrm{S}}$ meson, and the
geometry of the detector, there are approximately twice as many
${K}^{0}_{\mathrm{S}}$ candidates reconstructed in the downstream category
than in the long category, before any selections are applied.

This analysis is based on ${p}{p}$ collision data collected by the LHCb
experiment. Data collected in 2011 (2012) were recorded at a center-of-mass
energy of $7\text{\,}\text{\,Te\kern-1.00006ptV}$
($8\text{\,}\text{\,Te\kern-1.00006ptV}$), while in 2015 and 2016 the center-
of-mass energy was increased to $13\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}$.
Data recorded at center-of-mass energies of 7 and (Run 1) are combined and
then treated separately from data recorded at
$13\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}$ (Run 2). Due to low trigger
efficiency for ${{B}^{0}_{s}}$ mesons decaying into two downstream
${K}^{0}_{\mathrm{S}}$ mesons, these are discarded from the analysis.
Consequently, there are four data categories that are considered in the
following—Run 1 LL, Run 1 LD, Run 2 LL and Run 2 LD—and measurements are
performed separately in each of these data categories before being combined in
the final fit.

Signal ${B}^{0}_{s}$ or ${B}^{0}$ candidates are built in successive steps,
with individual ${K}^{0}_{\mathrm{S}}$ candidates reconstructed first and then
combined. The ${K}^{0}_{\mathrm{S}}$ candidates are constructed by combining
two oppositely charged pions that meet certain requirements on the minimum
total momentum and transverse momentum; on the minimum $\chi^{2}_{\text{IP}}$
of the ${K}^{0}_{\mathrm{S}}$ candidate with respect to the associated PV
(where $\chi^{2}_{\text{IP}}$ is defined as the difference in the impact
parameter $\chi^{2}$ of a given PV reconstructed with and without the
considered particle); on the maximum distance of closest approach (DOCA)
between the two particles; and on the quality of the vertex fit. An event can
have more than one PV, in which case the associated PV is defined as that with
which the B candidate forms the smallest value of $\chi^{2}_{\text{IP}}$. The
invariant mass of ${K}^{0}_{\mathrm{S}}$ candidates constructed from long
(downstream) tracks must be within 35$\text{\,Me\kern-1.00006ptV\\!/}c^{2}$
(64$\text{\,Me\kern-1.00006ptV\\!/}c^{2}$) of the known ${K}^{0}_{\mathrm{S}}$
mass [15]. The DOCA between the two ${K}^{0}_{\mathrm{S}}$ candidates is
required to be smaller than $1\text{\,}\mathrm{mm}$ for the LL category and
$4\text{\,}\mathrm{mm}$ for the LD category. Signal ${B}^{0}_{s}$ or ${B}^{0}$
candidates are then formed by combining two ${K}^{0}_{\mathrm{S}}$ candidates
that result in an invariant mass close to the known ${B}^{0}_{({s})}$ masses,
discussed further below and in Sec. 4.

The normalization decay ${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ is
constructed in a similar way. The $\phi$ meson is constructed by combining two
oppositely charged kaon candidates that result in an invariant mass within of
the nominal $\phi$ mass, as a first loose selection. Due to the vanishing
lifetime of the $\phi$ meson, the charged kaon candidates are only
reconstructed from long tracks, and thus all $\phi$ are reconstructed in the L
category. The ${K}^{0}_{\mathrm{S}}$ meson of the normalization decay can be
either L or D, so that the ${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$
decay has both LL and LD reconstructions.

The rest of the candidate selection process consists of a preselection
followed by the application of a multivariate classifier, and then some
additional selections are applied to further reduce combinatorial background.
In the preselection, loose selection requirements are applied to remove
specific backgrounds from other $b$-hadron decays and suppress combinatorial
background. These backgrounds for the signal and normalization modes are
discussed further below. Additional suppression of the combinatorial
background is included using a final selection after the multivariate
classifier is applied, where particle identification (PID) requirements are
added such that all final-state particles must be inconsistent with the muon
hypothesis based on the association of hits in the muon stations.

Possible background decays are studied using simulated samples. For the signal
channel, these include:
$B_{(s)}^{0}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$;
$B_{(s)}^{0}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{K}^{-}}$ with
kaon–pion misidentification;
$B_{(s)}^{0}\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{+}}{{K}^{-}}$ with double
kaon–pion misidentification; and ${{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{{K}^{0}_{\mathrm{S}}}{{\pi}^{-}}$ with
proton–pion misidentification. Backgrounds from
${{K}^{0}_{\mathrm{L}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ decays are
negligible. Applying the ${K}^{0}_{\mathrm{S}}$ mass window requirement to the
two-hadron system originating directly from a $b$-hadron decay reduces the
background yields by a factor of $10$ to $100$, depending on the decay
channel. To further suppress the contribution of these modes, a requirement on
the distance along the beam axis direction (the $z$-direction) between the
decay vertices of the ${{K}^{0}_{\mathrm{S}}}$ and ${{B}^{0}_{s}}$ candidates,
$\Delta z>$15\text{\,}\mathrm{mm}$$, is applied to ${{K}^{0}_{\mathrm{S}}}$
candidates reconstructed from long tracks for both decay channels.

An additional background comes from the requirements used to identify
${K}^{0}_{\mathrm{S}}$ candidates, which may also select $\mathchar
28931\relax$ baryons due to their long flight distance. The ${\mathchar
28931\relax}\rightarrow{p}{{\pi}^{-}}$ decays are excluded by changing the
mass hypothesis of one pion candidate to the proton hypothesis, reconstructing
the invariant mass, $m({p} {{\pi}^{-}})$, and tightening the pion PID
requirement in an mass window around the known ${\mathchar 28931\relax}$ mass.
This procedure is carried out for each pion from each ${K}^{0}_{\mathrm{S}}$
candidate, in both the signal and normalization channels.

For the normalization channel
${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$, the decays
$B_{(s)}^{0}\rightarrow{{K}^{0}_{\mathrm{S}}}h^{(^{\prime})+}h^{(^{\prime})-}$
with $h^{(^{\prime})\pm}=\pi^{\pm},{K}^{\pm}$ are suppressed by requiring the
invariant mass of the combination of the two final-state kaons to be close to
the $\phi$ mass. The largest contributions are expected from the decay channel
${{B}^{0}_{s}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{K}^{-}}$ with a
fraction of about $1\text{\,}\mathrm{\char 37\relax}$ compared to
${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ decays. This is reduced to
a negligible level by applying PID requirements to the kaon candidates. The
partially reconstructed decays ${{B}^{0}}\rightarrow\phi{{K}^{*0}}$ and
${{{B}^{+}}}\rightarrow\phi{{K}^{*+}}$, with
${{K}^{*0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{0}}$ and
${{K}^{*+}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$, share the same decay
topology as the normalization channel when omitting the pion that originates
from decay of the $K^{*}$ resonance and have a higher branching fraction than
the normalization decay. Due to the missing particle, the $B$ candidates have
a kinematic upper limit on their masses of about . Therefore, the mass window
to determine the yield of the normalization channel is set to
$$5150\text{\,}\mathrm{<}$~{}m({{K}^{0}_{\mathrm{S}}}{{K}^{+}}{{K}^{-}})<$5600\text{\,}\text{\,Me\kern-1.00006ptV\\!/}\mathrm{c}^{2}$$
to fully exclude these contributions.

Further separation of signal from combinatorial background is achieved using
the XGBoost implementation [36] of the Boosted Decision Tree (BDT) algorithm
[37]. For the training, simulated signal (normalization) decays are used as
signal proxy, while the upper mass sideband
$m({{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}})>$5600\text{\,}\text{\,Me\kern-1.00006ptV\\!/}\mathrm{c}^{2}$$
($m(\phi{{K}^{0}_{\mathrm{S}}})>$5600\text{\,}\text{\,Me\kern-1.00006ptV\\!/}\mathrm{c}^{2}$$)
in data is utilized as background proxy. To account for differences in data
and simulation, the simulated decays are weighted in the $B$ meson production
kinematics and detector occupancy (represented by the number of tracks in the
event) to match data distributions.

The BDT exploits the following observables: the flight distance, IP and
$\chi^{2}_{\text{IP}}$ of the $B$ and ${K}^{0}_{\mathrm{S}}$ candidates with
respect to all primary vertices, as well as the decay time, the momentum,
transverse momentum and pseudorapidity of the $B$ candidate. This set of
quantities is chosen such that they have a high separation power between
signal and background and are not directly correlated to the invariant mass.
The same procedure is applied to the
${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ data samples.

In order to choose the optimal threshold on the BDT response, the figure of
merit $\varepsilon_{\text{sig}}/(3/2+\sqrt{N_{\text{bkg}}})$ [38] is used for
the signal mode, where the value $3/2$ corresponds to a target 3 sigma
significance and $\varepsilon_{\text{sig}}$ is the signal efficiency of the
selection, determined from simulation. The figure of merit
$N_{\text{sig}}/\sqrt{N_{\text{sig}}+N_{\text{bkg}}}$ is used for the
normalization channel to minimize the uncertainty on the yield. So as not to
bias the determination of the signal yield, the candidates in the signal
region were not inspected until the selection was finalized. Consequently, the
expected background yield $N_{\text{bkg}}$ is calculated by interpolating the
result of an exponential fit to data sidebands,
$$5000\text{\,}\mathrm{<}$~{}m({{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}})<$5230\text{\,}\text{\,Me\kern-1.00006ptV\\!/}\mathrm{c}^{2}$$,
and
$$5420\text{\,}\mathrm{<}$~{}m({{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}})<$5600\text{\,}\text{\,Me\kern-1.00006ptV\\!/}\mathrm{c}^{2}$$
into the signal region. For the normalization channel, the variation of the
expected signal yield $N_{\text{sig}}$ as a function of the BDT response
threshold is determined from simulation, while the absolute normalization is
set from a single fit to the data.

The figure of merit optimization is performed simultaneously with respect to
the BDT classifier output and an observable based on PID information for long
track candidates, where the latter observable is corrected using a resampling
from data calibration samples [39] to minimize differences in data and
simulation. As a last selection step, the invariant-mass windows of
$m({{\pi}^{+}}{{\pi}^{-}})$ and $m({{K}^{+}}{{K}^{-}})$ are tightened to
further suppress combinatorial background. Finally, multiple candidates, which
occur in about 1 in 10000 of all events, are removed randomly so that each
event contains only one signal candidate.

##  4 Fit strategy and results

For the normalization channel, the total
${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ yield is obtained from
extended unbinned maximum likelihood fits to the reconstructed $B^{0}$ mass in
the range , separately for each data sample and reconstruction category. The
signal component is modelled by a Hypatia function with power-law tails on
both sides [40], where the tail parameters are fixed to values obtained from
fits to simulated samples. The mean, width and signal yield parameters are
free to vary in the fit. An exponential function with a free slope parameter
models the combinatorial background. To account for non-$\phi$ contributions
to the ${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ yield, a subsequent
fit is performed to the $m({{K}^{+}}{{K}^{-}})$ distribution, which is
background-subtracted using the ${}_{s}\mathcal{P}\text{lot}$ technique [41]
and where the $m({{K}^{+}}{{K}^{-}}{{K}^{0}_{\mathrm{S}}})$ distribution is
used as the discriminating variable. The signal $\phi$ component of the
$m({{K}^{+}}{{K}^{-}})$ fit is modelled by a relativistic Breit–Wigner
function [42] convolved with a Gaussian function to take into account the
resolution of the detector, while the non-$\phi$ contributions are described
by an exponential function. The slope parameter of the latter model is
Gaussian-constrained to the results obtained from fits to the simulation of
$f_{0}(980)\rightarrow{{K}^{+}}{{K}^{-}}$ decays, which is found to better
describe the observed distribution than a phase-space model. The measured
yields for the normalization channel are shown in the last row of Table 1.
Plots of the $m({{K}^{+}}{{K}^{-}}{{K}^{0}_{\mathrm{S}}})$ distributions for
the Run 2 LL and LD samples are shown in Figure 1. The remaining
$m({{K}^{+}}{{K}^{-}}{{K}^{0}_{\mathrm{S}}})$ distributions and the
$m({{K}^{+}}{{K}^{-}})$ distributions are shown in the Appendix.

Figure 1: Fits to the invariant-mass distribution
$m({{K}^{0}_{\mathrm{S}}}{{K}^{+}}{{K}^{-}})$ of the normalization decay
channel. The black curve represents the complete model, the
${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ component is given in
green (dashed), while the background component in shown in red (dotted).

A Hypatia function is used to model the
$m({{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}})$ distribution of signal
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
decays. All shape parameters are fixed to values obtained from fits to
simulated samples. To account for resolution differences between simulation
and data, the width is scaled by a factor—determined from the normalization
channel—which takes values in the range 1.05 to 1.20 depending on the data
sample. To model the
${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ signal
component, the same signal shape is duplicated and shifted by the
${{B}^{0}_{s}}-{{B}^{0}}$ mass difference [43]. The background component is
modelled by an exponential function with a free slope parameter.

In contrast to the normalization channel, where each data category is fitted
individually, a simultaneous fit to the
$m({{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}})$ distribution of the four
data categories (Run 1 LL, Run 1 LD, Run 2 LL, Run 2 LD) is performed in the
range . Two parameters are shared across all categories in the simultaneous
fit, the ratio of the
${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ and
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
yields $f_{{{B}^{0}}/{{B}^{0}_{s}}}$ and the branching fraction
${\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})$,
which is itself related to the signal yield of each data category via the
relation

$\displaystyle{\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})$
$\displaystyle=\frac{\varepsilon_{\phi{{K}^{0}_{\mathrm{S}}},\,i}}{\varepsilon_{{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}},\,i}}\frac{f_{d}}{f_{s}}\frac{{\mathcal{B}}(\mbox{$\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}$})}{{\mathcal{B}}(\mbox{${{K}^{0}_{\mathrm{S}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$})}\frac{{\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$})}{N_{i}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$})}\cdot
N_{i}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})$
(1) $\displaystyle\equiv\alpha_{i}\cdot
N_{i}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})\,,$

where the normalization constant $\alpha_{i}$ is introduced for each data
category sample $i$. While the selection efficiencies $\varepsilon$ and signal
yields $N$ are determined in the present analysis, external sources are used
for the ratio of fragmentation fractions $\nicefrac{{f_{d}}}{{f_{s}}}$ [44,
45], and the branching fractions
${\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$})$,
${\mathcal{B}}(\mbox{${{K}^{0}_{\mathrm{S}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$})$
and ${\mathcal{B}}(\mbox{$\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}$})$ [15]. To
increase the robustness of the fit, the $\alpha_{i}$ constants are Gaussian
constrained within their uncertainties, excluding the uncertainties from the
external constants. These external uncertainties are instead applied directly
to the final branching ratio measurement.

The efficiency ratio,
$\varepsilon_{\phi{{K}^{0}_{\mathrm{S}}}}/\varepsilon_{{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}}$,
is determined from simulation and corrected using data control samples. This
ratio is found to be approximately equal to 30 in all data samples except the
Run 1 LD sample, where it is twice as large due to lower trigger efficiency
for downstream tracks in this sample.

Table 1: Results of the simultaneous fit to the invariant mass of the
${{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ system. The fit results for
$\mathcal{B}$ and $f_{{{B}^{0}}/{{B}^{0}_{s}}}$ are shared among all data
categories. The given uncertainties are statistical only. The normalization
constant $\alpha$ and the corresponding normalization channel yields
$N_{\text{norm}}$ are shown for reference.

| Run 1 LL | Run 1 LD | Run 2 LL | Run 2 LD | Status
---|---|---|---|---|---
Parameter |  |  |  |  |
$\mathcal{B}$ $(\times 10^{-6})$ | 8.3 $\pm$ 1.6 | Free
$f_{{{B}^{0}}/{{B}^{0}_{s}}}$ | 0.30 $\pm$ 0.13 | Free
$N_{{{B}^{0}_{s}}}$ | $4.3\pm\pm 1.0$ | $2.1\pm\pm 0.5$ | $12.8\pm\pm 2.7$ | $12.4\pm\pm 2.7$ | ${\mathcal{B}}/\alpha$
$N_{{{B}^{0}}}$ | $1.3\pm\pm 0.5$ | $0.63\pm\pm 0.26$ | $3.8\pm\pm 1.5$ | $3.7\pm\pm 1.5$ | $f_{{{B}^{0}}/{{B}^{0}_{s}}}\times{\mathcal{B}}/\alpha$
$N_{\text{bkg}}$ | $10.4\pm\pm 3.5$ | $3.5\pm\pm 2.2$ | $7.2\pm\pm 3.0$ | $13\pm\pm 4$ | Free
$\alpha$ $(\times 10^{-6})$ | $1.90\pm\pm 0.21$ | $3.9\pm\pm 0.5$ | $0.65\pm\pm 0.05$ | $0.66\pm\pm 0.05$ | Gaussian constr.
$N_{\text{norm}}$ | $179\pm\pm 18$ | $178\pm\pm 22$ | $316\pm\pm 25$ | $400\pm\pm 31$ | Included in $\alpha$

Figure 2:  Combined invariant-mass distribution
$m({{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}})$ of the signal decay channel.
The black (solid) curve represents the complete model, the ${B}^{0}_{s}$
signal component is given in green (dashed), the smaller ${B}^{0}$ signal is
given in blue (dash-dotted) and the background component in red (dotted).

The fit results are shown in Fig. 2. The results of the simultaneous mass fit
are given in Table 1, yielding a branching fraction of
${\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})=$(8.3\pm\pm
1.6)\text{\times}{10}^{-6}$$, where the uncertainty is statistical only. The
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
yield is around 32. The ratio of the branching fractions of the signal and
normalization modes
${\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})/{\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$})$
can also be calculated by removing the contribution of the world-average value
of ${\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$})$
from the fit result. This yields a combined branching fraction ratio
${\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})/{\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$})=$2.3\pm\pm
0.4$$, where the uncertainty is statistical only.

From the same fit, the relative fraction of
${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ decays,
$f_{{{B}^{0}}/{{B}^{0}_{s}}}=$0.3\pm\pm 0.13$$ is also determined. Given that
the final-state particles and selections applied to the ${K}^{0}_{\mathrm{S}}$
candidates are the same for both modes, the ratio of selection efficiencies is
equal to one, so that $f_{{{B}^{0}}/{{B}^{0}_{s}}}$ can be converted to a
ratio of branching fractions by multiplying by $\nicefrac{{f_{s}}}{{f_{d}}}$.
The calculated value of
${\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})/{\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})$
is $(7.5\pm\pm 3.1)\text{\times}{10}^{-2}$, where the uncertainty is
statistical only.

The significances of the
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ and
${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ signal
yields are estimated relative to a background-only hypothesis using Wilks’
theorem [46]. The observed signal yield of 32
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
decays has a large significance of $8.6\text{\,}\sigma$ ($6.5\text{\,}\sigma$
including the effect of systematic uncertainties), while the smaller
${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ signal
yield has a significance of $3.5\text{\,}\sigma$ including systematic
uncertainties.

##  5 Systematic uncertainties

Each source of systematic uncertainty is evaluated independently and expressed
as a relative uncertainty on the branching fraction of
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
decays. A complete list is given in Table 2. The uncertainties are grouped
into three general categories: fit and weighting uncertainties, PID
uncertainties, and detector and trigger uncertainties.

Table 2:  All systematic uncertainties on the ${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ branching fraction, presented as relative measurements. The last row shows the combined systematic uncertainty for each data sample.  | Run 1, LL | Run 1, LD | Run 2, LL | Run 2, LD
---|---|---|---|---
Systematic uncert. |  |  |  |
Fit bias | 0.059 | 0.059 | 0.059 | 0.059
Fit model choice | 0.022 | 0.033 | 0.015 | 0.013
Fit model parameters | 0.026 | 0.026 | 0.026 | 0.026
BDT | 0.023 | 0.040 | 0.014 | 0.031
PID | 0.007 | 0.008 | 0.026 | 0.026
Hardware trigger | 0.063 | 0.062 | 0.063 | 0.062
Software trigger | 0.065 | 0.106 | 0.008 | 0.026
Trigger misconfig. | — | — | 0.007 | 0.004
${\pi}^{\pm}$/${K}^{\pm}$ hadronic interaction | 0.005 | 0.005 | 0.005 | 0.005
VELO misalignment | 0.008 | 0.008 | 0.008 | 0.008
Total | 0.116 | 0.149 | 0.097 | 0.103

Multiple different fit uncertainties are considered. Uncertainty from possible
bias in the combined fit to all four data samples can be estimated using
pseudoexperiments generated and fitted according to the default fit model. In
each pseudoexperiment, the number of signal candidates is drawn from a Poisson
distribution with a mean determined from the baseline fit result. A relative
average difference between the generated and fitted branching fraction of
$5.9\text{\,}\mathrm{\char 37\relax}$ is determined and conservatively
assigned as a systematic uncertainty. The same procedure is performed for the
${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
component, yielding a possible bias of $1.6\text{\,}\mathrm{\char 37\relax}$.
To ensure a conservative approach, the $5.9\text{\,}\mathrm{\char 37\relax}$
value from
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ is
also applied as the systematic for
${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$.

Another systematic uncertainty in the fitting process arises from the specific
fit model choice, which is quantified by the use of alternative probability
density functions to describe the invariant-mass distributions. The
reconstructed-mass shapes for ${B}^{0}$ and ${B}^{0}_{s}$ mesons are modelled
by the sum of two Crystal Ball functions [47]. For the fit to the
$m({{K}^{+}}{{K}^{-}})$ distribution, the $\phi$ meson is modelled by a non-
relativistic Breit–Wigner function. For the normalization channel, the
relative yield difference when refitting the data is taken as the systematic
uncertainty, while for the
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
decay pseudoexperiments are used to estimate the impact of mismodeling the
shape of the signal component. The systematic uncertainty due to the choice of
fit model is then the sum in quadrature of these variations, yielding values
of $1.3\text{\,}\mathrm{\char 37\relax}$ to $3.3\text{\,}\mathrm{\char
37\relax}$ depending on the data category. Another systematic uncertainty of
$2.6\text{\,}\mathrm{\char 37\relax}$, evaluated with a similar procedure, is
assigned due to fixing certain shape parameters to values obtained in fits to
simulated samples.

Additionally, not all differences between data and simulation can be accounted
for using weights in the BDT training. As a conservative upper limit of this
effect, the signal efficiency is calculated with and without weights, and the
differences between these efficiencies are treated as a systematic
uncertainty. This systematic uncertainty is larger by a factor of about 2 for
data categories containing a downstream ${K}^{0}_{\mathrm{S}}$ candidate than
in those that contain only long ${K}^{0}_{\mathrm{S}}$ candidates, indicating
a stronger dependence of the LD channel efficiencies on the weighting.

Three sources of systematic uncertainties from PID efficiencies are
considered. The effect of the finite size of the signal simulation samples is
evaluated using the bootstrap method [48] for each simulation category and
calculating the variance of the signal efficiency. A second systematic
uncertainty is calculated by varying the model used to resample PID
calibration data, and the relative difference in the signal efficiency is
taken as a systematic uncertainty, though this effect is small compared to the
previous source. Finally, the flight distance of the ${K}^{0}_{\mathrm{S}}$
candidate is not considered in the resampling process, while the PID
efficiency does exhibit some correlation with this variable. A systematic
uncertainty is calculated by reweighting the PID distributions in bins of the
${K}^{0}_{\mathrm{S}}$ flight distance, and calculating the relative signal
efficiency on resampled simulation and resampled and reweighted simulation.
The combined PID systematic uncertainty is given by summing over the three
effects in quadrature, which is below $1\text{\,}\mathrm{\char 37\relax}$ for
the Run 1 samples and below $3\text{\,}\mathrm{\char 37\relax}$ for the Run 2
samples.

Systematic uncertainties in the trigger system are divided into hardware and
software trigger uncertainties. For the hardware trigger stage, the efficiency
taken from simulation is compared with data calibration samples. The
calibration data is used to correct the simulated efficiencies, and the
resulting $6\text{\,}\mathrm{\char 37\relax}$ relative difference in
efficiency between the signal and normalization modes is treated as a
systematic uncertainty. For the inclusive $B$ software trigger, possible
differences in efficiency between the signal and normalization channels are
obtained by reweighting the
${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ simulation to match the
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
simulation and calculating the relative efficiency difference between the raw
and reweighted distributions, yielding a systematic uncertainty of about
$2\text{\,}\mathrm{\char 37\relax}$. An additional, larger systematic
uncertainty is also included to account for the dedicated $\phi$ trigger
requirements, which are only used for the normalization channel. Again,
weighted ${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ data are used to
evaluate a relative efficiency difference between simulation and data,
multiplied by the fraction of events solely triggered by the dedicated $\phi$
trigger requirements. The systematic uncertainty is about
$5\text{\,}\mathrm{\char 37\relax}10\text{\,}\mathrm{\char 37\relax}$ in Run
1, but about 5 times smaller for Run 2. This is because the topological
$b$-hadron trigger is more efficient in Run 2 so that there are far fewer
events triggered only by the dedicated $\phi$ trigger. An additional
systematic uncertainty less than $1\text{\,}\mathrm{\char 37\relax}$ is
assigned to account for a small known misconfiguration of the trigger during
Run 2 data taking.

Two additional detector-related uncertainties are considered. A relative
uncertainty of $0.5\text{\,}\mathrm{\char 37\relax}$ is assigned due to the
different hadronic interaction probabilities between pions and kaons in data
and simulation, and a relative uncertainty of $0.8\text{\,}\mathrm{\char
37\relax}$ is also introduced to account for a possible misalignment in the
downstream positions of the vertex detector.

The combined systematic uncertainty is determined by using a weighted average
of the total systematic uncertainty for each data category, where the
weighting is based on the ${B}^{0}_{s}$ signal yield for each category,
obtained from the nominal combined fit for the branching fraction. This value
is then combined with the systematic uncertainties due to the
$\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}$ and
${{K}^{0}_{\mathrm{S}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ branching
fractions, to produce an overall systematic uncertainty of
$10.7\text{\,}\mathrm{\char 37\relax}$. The systematic uncertainties due to
${\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$})$ or
$\nicefrac{{f_{s}}}{{f_{d}}}$ are provided separately when necessary. The
total systematic uncertainty in the measurement of the ${B}^{0}$ branching
fraction is also $10.7\text{\,}\mathrm{\char 37\relax}$.

These measurements of the branching ratio are calculated using the time-
integrated event yield, without taking into account ${B}^{0}_{s}$–${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ mixing effects. The
conversion into a branching ratio that is independent of ${B}^{0}_{s}$–${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ mixing can be performed
according to the computation given in Ref. [49], where
$\mathcal{A}^{f}_{\Delta\Gamma}$ is calculated from the decay amplitudes of
the $B_{s}^{\text{H}}$ and $B_{s}^{\text{L}}$ states. In this work, the
simulation is generated using the average ${B}^{0}_{s}$ lifetime,
corresponding to the $\mathcal{A}^{f}_{\Delta\Gamma}=0$ scenario. For this
scenario the mixing-corrected SM prediction of the branching ratio is
equivalent to the quoted time-integrated branching ratio within uncertainties,
because the impact of the scaling from $\Delta\Gamma_{s}/\Gamma_{s}=0.135\pm
0.008$ [15] is small.

Considering that the final state of the decay is $C\\!P$-even, the relevant
decay lifetime of the ${B}^{0}_{s}$ is expected to be closer to that of the
$B_{s}^{\text{L}}$ state, corresponding to a SM prediction of
$\mathcal{A}^{f}_{\Delta\Gamma}$ close to $-1$. This change in lifetime
corresponds to a change in the expected efficiency of the
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
reconstruction of approximately $-4.5\text{\,}\mathrm{\char 37\relax}$ for
$\mathcal{A}^{f}_{\Delta\Gamma}=-1$, or $4.5\text{\,}\mathrm{\char 37\relax}$
for the less-likely $\mathcal{A}^{f}_{\Delta\Gamma}=1$. These scaling factors
are not included in the systematic uncertainty for the time-integrated
branching ratios presented below.

##  6 Conclusion

Data collected by the LHCb experiment in 2011–2012 and 2015–2016 was used to
measure the
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
branching fraction. The measured ratio of this branching fraction relative to
that of the normalization channel is

$\displaystyle\frac{{\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})}{{\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$})}=2.3\pm
0.4\,(\text{stat})\pm 0.2\,(\text{syst})\pm
0.1\,(\nicefrac{{f_{s}}}{{f_{d}}}),$

where the first uncertainty is statistical, the second is systematic, and the
third is due to the ratio of hadronization fractions. This is compatible with
the ratio
${\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})/{\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$})=2.7\pm
0.9$ calculated from the current world average values [15].

From this measurement, the
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
branching fraction is determined to be

$\displaystyle{\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})=[8.3\pm
1.6\,(\text{stat})\pm 0.9\,(\text{syst})\pm 0.8\,(\text{norm})\pm
0.3\,(\nicefrac{{f_{s}}}{{f_{d}}})]\times 10^{-6},$

where the first uncertainty is statistical, the second is systematic, and the
third and fourth are due to the normalization channel branching fraction and
the ratio of hadronization fractions $\nicefrac{{f_{s}}}{{f_{d}}}$. This
result is the most precise to date and is compatible with SM predictions [6,
7, 8, 9] and the previous measurement from the Belle collaboration [14].

In the same combined fit used for the
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
measurement, the fraction of
${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ decays
is also determined. Using this measured fraction of yields, the branching
fraction of
${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$ decays
measured relative to
${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
decays is found to be

$\displaystyle\frac{{\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})}{{\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})}=[7.5\pm
3.1\,(\text{stat})\pm 0.5\,(\text{syst})\pm
0.3\,(\nicefrac{{f_{s}}}{{f_{d}}})]\times 10^{-2},$

where the first uncertainty is statistical, the second is systematic, and the
third is due to the ratio of hadronization fractions. For comparison,
calculating
${\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})/{\mathcal{B}}(\mbox{${{B}^{0}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})$
based on world average-values [15] yields $(6.0\pm 2.0)\%$, which is
compatible with the obtained result.

The ${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$
branching fraction relative to the
${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ normalization mode is
determined to be

$\displaystyle\frac{{\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{0}_{\mathrm{S}}}$})}{{\mathcal{B}}(\mbox{${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$})}=0.17\pm
0.08\,(\text{stat})\pm 0.02\,(\text{syst}),$

where the first uncertainty is statistical, and the second is systematic.

## Acknowledgements

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

## Appendix: Normalization channel fits

Figure 3 shows the $m({{K}^{0}_{\mathrm{S}}}{{K}^{+}}{{K}^{-}})$ distributions
for the Run 1 LL and LD categories. The $m({{K}^{+}}{{K}^{-}})$ distributions
for all four data categories are shown in Fig. 4.

Figure 3: Fits to the invariant-mass distribution
$m({{K}^{0}_{\mathrm{S}}}{{K}^{+}}{{K}^{-}})$ of the normalization decay
channel. The black curve represents the complete model, the
${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ component is given in
green (dashed), while the background component in shown in red (dotted).

Figure 4: Fits to the invariant-mass distribution $m({{K}^{+}}{{K}^{-}})$ of
${{B}^{0}}\\!\rightarrow\phi{{K}^{0}_{\mathrm{S}}}$ data weighted using the
${}_{s}\mathcal{P}\text{lot}$ technique. The blue curve represents the
complete model, the signal $\phi$ component is given in green (dashed), and
the background $f_{0}(980)\rightarrow{{K}^{+}}{{K}^{-}}$ model is shown in
black (dotted).

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LHCb collaboration

R. Aaij31, C. Abellán Beteta49, T. Ackernley59, B. Adeva45, M. Adinolfi53, H.
Afsharnia9, C.A. Aidala79, S. Aiola25, Z. Ajaltouni9, S. Akar64, P.
Albicocco22, J. Albrecht14, F. Alessio47, M. Alexander58, A. Alfonso Albero44,
G. Alkhazov37, P. Alvarez Cartelle60, A.A. Alves Jr45, S. Amato2, Y. Amhis11,
L. An21, L. Anderlini21, G. Andreassi48, M. Andreotti20, F. Archilli16, J.
Arnau Romeu10, A. Artamonov43, M. Artuso67, K. Arzymatov41, E. Aslanides10, M.
Atzeni49, B. Audurier26, S. Bachmann16, J.J. Back55, S. Baker60, V.
Balagura11,b, W. Baldini20,47, A. Baranov41, R.J. Barlow61, S. Barsuk11, W.
Barter60, M. Bartolini23,47,h, F. Baryshnikov76, G. Bassi28, V. Batozskaya35,
B. Batsukh67, A. Battig14, V. Battista48, A. Bay48, M. Becker14, F.
Bedeschi28, I. Bediaga1, A. Beiter67, L.J. Bel31, V. Belavin41, S. Belin26, N.
Beliy5, V. Bellee48, K. Belous43, I. Belyaev38, G. Bencivenni22, E. Ben-
Haim12, S. Benson31, S. Beranek13, A. Berezhnoy39, R. Bernet49, D.
Berninghoff16, H.C. Bernstein67, E. Bertholet12, A. Bertolin27, C.
Betancourt49, F. Betti19,e, M.O. Bettler54, Ia. Bezshyiko49, S. Bhasin53, J.
Bhom33, M.S. Bieker14, S. Bifani52, P. Billoir12, A. Bizzeti21,u, M. Bjørn62,
M.P. Blago47, T. Blake55, F. Blanc48, S. Blusk67, D. Bobulska58, V. Bocci30,
O. Boente Garcia45, T. Boettcher63, A. Boldyrev77, A. Bondar42,x, N. Bondar37,
S. Borghi61,47, M. Borisyak41, M. Borsato16, J.T. Borsuk33, T.J.V. Bowcock59,
C. Bozzi20, S. Braun16, A. Brea Rodriguez45, M. Brodski47, J. Brodzicka33, A.
Brossa Gonzalo55, D. Brundu26, E. Buchanan53, A. Büchler-Germann49, A.
Buonaura49, C. Burr47, A. Bursche26, J.S. Butter31, J. Buytaert47, W.
Byczynski47, S. Cadeddu26, H. Cai71, R. Calabrese20,g, S. Cali22, R.
Calladine52, M. Calvi24,i, M. Calvo Gomez44,m, A. Camboni44,m, P. Campana22,
D.H. Campora Perez47, L. Capriotti19,e, A. Carbone19,e, G. Carboni29, R.
Cardinale23,h, A. Cardini26, P. Carniti24,i, K. Carvalho Akiba31, A. Casais
Vidal45, G. Casse59, M. Cattaneo47, G. Cavallero47, R. Cenci28,p, J.
Cerasoli10, M.G. Chapman53, M. Charles12,47, Ph. Charpentier47, G.
Chatzikonstantinidis52, M. Chefdeville8, V. Chekalina41, C. Chen3, S. Chen26,
A. Chernov33, S.-G. Chitic47, V. Chobanova45, M. Chrzaszcz47, A. Chubykin37,
P. Ciambrone22, M.F. Cicala55, X. Cid Vidal45, G. Ciezarek47, F. Cindolo19,
P.E.L. Clarke57, M. Clemencic47, H.V. Cliff54, J. Closier47, J.L.
Cobbledick61, V. Coco47, J.A.B. Coelho11, J. Cogan10, E. Cogneras9, L.
Cojocariu36, P. Collins47, T. Colombo47, A. Comerma-Montells16, A. Contu26, N.
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R. Currie57, C.L. Da Silva66, E. Dall’Occo31, J. Dalseno45,53, C.
D’Ambrosio47, A. Danilina38, P. d’Argent16, A. Davis61, O. De Aguiar
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De Paula2, M. De Serio18,d, P. De Simone22, J.A. de Vries31, C.T. Dean66, W.
Dean79, D. Decamp8, L. Del Buono12, B. Delaney54, H.-P. Dembinski15, M.
Demmer14, A. Dendek34, V. Denysenko49, D. Derkach77, O. Deschamps9, F.
Desse11, F. Dettori26,f, B. Dey7, A. Di Canto47, P. Di Nezza22, S. Didenko76,
H. Dijkstra47, F. Dordei26, M. Dorigo28,y, A.C. dos Reis1, L. Douglas58, A.
Dovbnya50, K. Dreimanis59, M.W. Dudek33, L. Dufour47, G. Dujany12, P.
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Dziurda33, A. Dzyuba37, S. Easo56, U. Egede60, V. Egorychev38, S.
Eidelman42,x, S. Eisenhardt57, R. Ekelhof14, S. Ek-In48, L. Eklund58, S.
Ely67, A. Ene36, S. Escher13, S. Esen31, T. Evans47, A. Falabella19, J. Fan3,
N. Farley52, S. Farry59, D. Fazzini11, M. Féo47, P. Fernandez Declara47, A.
Fernandez Prieto45, F. Ferrari19,e, L. Ferreira Lopes48, F. Ferreira
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C. Frei47, D.A. Friday58, J. Fu25,q, Q. Fuehring14, W. Funk47, E. Gabriel57,
A. Gallas Torreira45, D. Galli19,e, S. Gallorini27, S. Gambetta57, Y. Gan3, M.
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P. Gironella Gironell44, L. Giubega36, C. Giugliano20, K. Gizdov57, V.V.
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C. Haen47, S.C. Haines54, P.M. Hamilton65, Q. Han7, X. Han16, T.H. Hancock62,
S. Hansmann-Menzemer16, N. Harnew62, T. Harrison59, R. Hart31, C. Hasse47, M.
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Hennequin47, K. Hennessy59, L. Henry46, J. Heuel13, A. Hicheur68, R. Hidalgo
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Hu7, W. Huang5, Z.C. Huard64, W. Hulsbergen31, T. Humair60, R.J. Hunter55, M.
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John62, D. Johnson47, C.R. Jones54, B. Jost47, N. Jurik62, S. Kandybei50, M.
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M. Kenzie54, T. Ketel32, B. Khanji47, A. Kharisova78, K.E. Kim67, T. Kirn13,
V.S. Kirsebom48, S. Klaver22, K. Klimaszewski35, S. Koliiev51, A.
Kondybayeva76, A. Konoplyannikov38, P. Kopciewicz34, R. Kopecna16, P.
Koppenburg31, M. Korolev39, I. Kostiuk31,51, O. Kot51, S. Kotriakhova37, L.
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Kudryavtsev42,x, H.S. Kuindersma31, G.J. Kunde66, A.K. Kuonen48, T.
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J.J. Lane61, G. Lanfranchi22, C. Langenbruch13, T. Latham55, F. Lazzari28,v,
C. Lazzeroni52, R. Le Gac10, R. Lefèvre9, A. Leflat39, F. Lemaitre47, O.
Leroy10, T. Lesiak33, B. Leverington16, H. Li70, X. Li66, Y. Li6, Z. Li67, X.
Liang67, R. Lindner47, F. Lionetto49, V. Lisovskyi11, G. Liu70, X. Liu3, D.
Loh55, A. Loi26, J. Lomba Castro45, I. Longstaff58, J.H. Lopes2, G. Loustau49,
G.H. Lovell54, Y. Lu6, D. Lucchesi27,o, M. Lucio Martinez31, Y. Luo3, A.
Lupato27, E. Luppi20,g, O. Lupton55, A. Lusiani28,t, X. Lyu5, S.
Maccolini19,e, F. Machefert11, F. Maciuc36, V. Macko48, P. Mackowiak14, S.
Maddrell-Mander53, L.R. Madhan Mohan53, O. Maev37,47, A. Maevskiy77, K.
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Malinin75, T. Maltsev42,x, H. Malygina16, G. Manca26,f, G. Mancinelli10, R.
Manera Escalero44, D. Manuzzi19,e, D. Marangotto25,q, J. Maratas9,w, J.F.
Marchand8, U. Marconi19, S. Mariani21, C. Marin Benito11, M. Marinangeli48, P.
Marino48, J. Marks16, P.J. Marshall59, G. Martellotti30, L. Martinazzoli47, M.
Martinelli24,i, D. Martinez Santos45, F. Martinez Vidal46, A. Massafferri1, M.
Materok13, R. Matev47, A. Mathad49, Z. Mathe47, V. Matiunin38, C. Matteuzzi24,
K.R. Mattioli79, A. Mauri49, E. Maurice11,b, M. McCann60,47, L. Mcconnell17,
A. McNab61, R. McNulty17, J.V. Mead59, B. Meadows64, C. Meaux10, G. Meier14,
N. Meinert73, D. Melnychuk35, S. Meloni24,i, M. Merk31, A. Merli25, M.
Mikhasenko47, D.A. Milanes72, E. Millard55, M.-N. Minard8, O. Mineev38, L.
Minzoni20,g, S.E. Mitchell57, B. Mitreska61, D.S. Mitzel47, A. Mödden14, A.
Mogini12, R.D. Moise60, T. Mombächer14, I.A. Monroy72, S. Monteil9, M.
Morandin27, G. Morello22, M.J. Morello28,t, J. Moron34, A.B. Morris10, A.G.
Morris55, R. Mountain67, H. Mu3, F. Muheim57, M. Mukherjee7, M. Mulder31, D.
Müller47, K. Müller49, V. Müller14, C.H. Murphy62, D. Murray61, P. Muzzetto26,
P. Naik53, T. Nakada48, R. Nandakumar56, A. Nandi62, T. Nanut48, I. Nasteva2,
M. Needham57, N. Neri25,q, S. Neubert16, N. Neufeld47, R. Newcombe60, T.D.
Nguyen48, C. Nguyen-Mau48,n, E.M. Niel11, S. Nieswand13, N. Nikitin39, N.S.
Nolte47, A. Oblakowska-Mucha34, V. Obraztsov43, S. Ogilvy58, D.P. O’Hanlon19,
R. Oldeman26,f, C.J.G. Onderwater74, J. D. Osborn79, A. Ossowska33, J.M.
Otalora Goicochea2, T. Ovsiannikova38, P. Owen49, A. Oyanguren46, P.R. Pais48,
T. Pajero28,t, A. Palano18, M. Palutan22, G. Panshin78, A. Papanestis56, M.
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J. Plews52, M. Plo Casasus45, F. Polci12, M. Poli Lener22, M. Poliakova67, A.
Poluektov10, N. Polukhina76,c, I. Polyakov67, E. Polycarpo2, G.J. Pomery53, S.
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Punzi28,p, W. Qian5, J. Qin5, R. Quagliani12, B. Quintana9, N.V. Raab17, R.I.
Rabadan Trejo10, B. Rachwal34, J.H. Rademacker53, M. Rama28, M. Ramos
Pernas45, M.S. Rangel2, F. Ratnikov41,77, G. Raven32, M. Ravonel Salzgeber47,
M. Reboud8, F. Redi48, S. Reichert14, F. Reiss12, C. Remon Alepuz46, Z. Ren3,
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Zucchelli19,e.

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

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mDS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Vietnam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vUniversità di Siena, Siena, Italy
wMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
xNovosibirsk State University, Novosibirsk, Russia
yINFN Sezione 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
abUniversidad Nacional Autonoma de Honduras, Tegucigalpa, Honduras
†Deceased