EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2020-140 LHCb-PAPER-2020-007 October 31, 2020

Searches for 25 rare and forbidden decays of ${D}^{+}$ and ${D}^{+}_{s}$
mesons

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

A search is performed for rare and forbidden charm decays of the form
${{D}^{+}_{(s)}}\\!\rightarrow h^{\pm}\ell^{+}\ell^{(\prime)\mp}$, where
$\smash{{h}^{\pm}}$ is a pion or kaon and $\smash{\ell^{(^{\prime})\pm}}$ is
an electron or muon. The measurements are performed using proton-proton
collision data, corresponding to an integrated luminosity of
$1.6\text{\,}{\mathrm{fb}}^{-1}$, collected by the LHCb experiment in 2016. No
evidence is observed for the 25 decay modes that are investigated and
$90\text{\,}\mathrm{\char 37\relax}$ confidence level limits on the branching
fractions are set between $1.4\times 10^{-8}$ and $6.4\times 10^{-6}$. In most
cases, these results represent an improvement on existing limits by one to two
orders of magnitude.

Submitted to JHEP

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

##  1 Introduction

The search for rare and forbidden decays in flavour physics constitutes an
important test of the Standard Model (SM) and provides a window to new
physics. In the charm sector, decays of the form ${{D}^{+}}\\!\rightarrow
h^{\pm}\ell^{+}\ell^{(\prime)\mp}$ and ${{D}^{+}_{s}}\\!\rightarrow
h^{\pm}\ell^{+}\ell^{(\prime)\mp}$, where $h^{\pm}$ is a charged pion or kaon
and $l^{\left(\prime\right)\pm}$ is an electron or muon, are among such
processes.111Throughout this article the inclusion of charge-conjugate
processes and the use of natural units ($c=\hbar=1$) is implied, unless
otherwise indicated. Searches are reported for 25 decay modes, with common
experimental approaches applied to all channels.

The physics processes of these channels vary. Four of the decay channels
(${{D}^{+}}\\!\rightarrow{{\pi}^{+}}{e^{+}}{e^{-}}$,
${{D}^{+}}\\!\rightarrow{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{e^{+}}{e^{-}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{\mu^{+}}{\mu^{-}}$) involve flavour-
changing neutral current (FCNC) transitions. These processes are rare within
the Standard Model as only weak annihilation processes can occur at tree
level. At the loop level, FCNC transitions are suppressed by the
Glashow–-Iliopoulos-–Maiani (GIM) mechanism [1] but are well established in
both $B$-meson and $K$-meson decays [2]. FCNC $B$-meson decays have received
significant attention in recent years: the process
${{B}^{0}_{s}}\\!\rightarrow{\mu^{+}}{\mu^{-}}$ was observed[3, 4]; and
experimental observations in analyses of
${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$ transitions are in tension with the SM
predictions (see Ref. [5] and references therein). The GIM cancellation in the
$D$-meson system is stronger than in the $B$-meson system, leading to short-
distance SM branching fractions of ${\mathcal{O}}(10^{-12})$ [6]. Significant
long-distance contributions occur from dilepton resonances and these are
expected to dominate the SM contribution across the full dilepton invariant-
mass-squared distribution [6, 7].

The eight decay modes with two oppositely charged leptons of different flavour
(${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{+}}{e^{+}}{\mu^{-}}$,
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{+}}{\mu^{+}}{e^{-}}$,
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{+}}{e^{+}}{\mu^{-}}$,
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{+}}{\mu^{+}}{e^{-}}$) are lepton-flavour
violating (LFV) and lepton-number conserving decays. These decays have only
negligible contributions from neutrino mixing in the SM. The nine decay modes
analysed with same-sign leptons
(${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{-}}{e^{+}}{e^{+}}$,
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{-}}{\mu^{+}}{\mu^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{e^{+}}{e^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{\mu^{+}}{\mu^{+}}$,
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{-}}{\mu^{+}}{e^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{\mu^{+}}{e^{+}}$) are both LFV and
lepton-number violating (LNV) decays, and forbidden in the SM. There are three
further LFV and LNV decays
(${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{e^{+}}{e^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{\mu^{+}}{\mu^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{\mu^{+}}{e^{+}}$) which are analysed
here, their ${D}^{+}$ counterparts are not studied due to the presence of
sizeable background contributions.

The potential of ${c}\\!\rightarrow{u}\ell^{+}\ell^{\prime-}$ processes to
constrain new physics has been discussed in the literature [6, 7, 8, 9].
Model-independent constraints on Wilson coefficients in effective field theory
have been considered, as have specific classes of models. Recently particular
attention has been paid to leptoquark models, due to their potential relevance
to the anomalies on ${b}\\!\rightarrow{s}\ell^{+}\ell^{-}$ processes [10, 11,
12, 13, 14].

The analysis reported here is performed on a data sample corresponding to an
integrated luminosity of 1.6$\text{\,fb}^{-1}$ collected by the LHCb
experiment in 2016. Four resonant decays
(${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$
${\pi}^{+}$,
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{e^{-}}{e^{+}}\right)$
${\pi}^{+}$) are used for calibration and normalisation. Non-resonant decays
with a pion and two same-sign or opposite-sign muons in the final state have
previously been searched for by LHCb with no evidence observed [15]. The best
limits in the other channels are measured by the BaBar collaboration [16],
which has studied all channels, or by the CLEO collaboration, from searches in
decay modes with dielectrons in the final state [17].

##  2 Detector and simulation

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, 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 placed downstream of
the magnet. The tracking system provides a measurement of the momentum, $p$,
of charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200 GeV. The minimum distance of a track to a primary $p$
$p$ collision 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  GeV. Different
types of charged hadrons are distinguished using information from two ring-
imaging Cherenkov detectors. Photons, electrons and hadrons are identified by
a calorimeter system consisting of scintillating-pad and preshower detectors,
an electromagnetic and a hadronic calorimeter. Muons are identified by a
system composed of alternating layers of iron and multiwire proportional
chambers.

Simulation is required to model the effects of the detector acceptance and the
selection requirements. In the simulation, $pp$ collisions are generated using
Pythia [20] with a specific LHCb configuration [22]. Decays of unstable
particles are described by EvtGen [23], in which final-state radiation is
generated using Photos [24]. The interaction of the generated particles with
the detector, and its response, are implemented using the Geant4 toolkit [25]
as described in Ref. [27].

##  3 Triggering, reconstruction and selection

The online event selection is performed by a trigger, which consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a two-level software stage. In between the two software stages, an
alignment and calibration of the detector is performed in near real time and
the results are used in the trigger. The same alignment and calibration
information is propagated to the offline reconstruction, ensuring consistent
and high-quality particle identification (PID) performance between the trigger
and offline software.

A hardware trigger selection is made for all decay channels based on observing
a deposit with high transverse energy in the hadronic calorimeter. Depending
on the leptons in the final state, this is supplemented by a selection of
events with high transverse-energy clusters in the electromagnetic calorimeter
and high transverse-momentum muons. At the first software level, inclusive
multivariate selections are used to select charged tracks which do not
originate from any PV.

The second software level builds ${D}^{+}_{(s)}$ candidates using exclusive
selections for each combination of final-state particles. Only events
containing a single reconstructed PV are used. All three tracks are required
to be incompatible with coming from the PV, and to have been reconstructed
with good fit quality, have a transverse momentum exceeding
$300{\text{\,Me\kern-1.00006ptV}}$ and a momentum exceeding
$2000{\text{\,Me\kern-1.00006ptV}}$. The tracks are required to form a
${D}^{+}_{(s)}$ secondary vertex, with good fit quality and all pairs of
tracks intercepting within $150\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The
angle between the reconstructed ${D}^{+}_{(s)}$ and the vector connecting the
PV to the decay vertex of the ${D}^{+}_{(s)}$ candidate (direction angle) must
be within $14\text{\,}\mathrm{mrad}$. Loose PID requirements are made on all
final-state tracks. Eight of the signal channels in this analysis can proceed
via decays through intermediate resonances ($\eta$, ${\rho}^{0}$, $\omega$ and
$\phi$). These are removed by vetoing the region
$[$525\text{\,}\mathrm{MeV}$,$1250\text{\,}\mathrm{MeV}$]$ in dilepton mass.
The resonant channel
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$
${\pi}^{+}$
(${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{e^{-}}{e^{+}}\right)$
${\pi}^{+}$) is further selected by requiring the invariant mass of the
dilepton pair be within $\pm$20$$ (${}^{+$40$}_{-$100$}$)  MeV of the $\phi$
mass[2]. A bremsstrahlung reconstruction procedure is used to correct the
momentum of electron candidates.

A classifier trained using XGBoost[28], is used to further distinguish between
signal and background originating from random combinations of tracks. A single
classifier is trained for each final state, with signal being represented by
an equally weighted mixture of simulated ${D}^{+}$ and ${D}^{+}_{s}$ events.
This approach is found to give equivalent performance when compared to using a
separate classifier for each signal meson. Background candidates for the
training are provided from a data sample where all three final-state particles
have the same electric charge. The classifier is trained using the fit quality
of the primary and secondary vertex, the ${D}^{+}_{(s)}$ pseudorapidity, the
${D}^{+}_{(s)}$ flight distance, the difference in $\chi^{2}$ of the PV
reconstructed with and without each final-state track, the momentum of each
final-state track, the maximum distance of closest approach between all final-
state tracks, the direction angle and the reconstructed proper lifetime of the
${D}^{+}_{(s)}$. To guarantee that no other tracks can be associated to the
secondary vertex, an isolation variable, $A_{p_{\mathrm{T}}}$, is used that
considers the imbalance of $p_{\mathrm{T}}$ of nearby tracks compared to that
of the ${D}^{+}_{(s)}$ candidate,

$A_{p_{\mathrm{T}}}=\frac{p_{\mathrm{T}}({{D}^{+}_{(s)}})-(\sum\overrightarrow{p})_{\rm
T}}{p_{\mathrm{T}}({{D}^{+}_{(s)}})+(\sum\overrightarrow{p})_{\rm T}},$ (1)

where $p_{\mathrm{T}}({{D}^{+}_{(s)}})$ is the $p_{\mathrm{T}}$ of the
${D}^{+}_{(s)}$ meson and $(\sum\overrightarrow{p})_{\rm T}$ is the transverse
component of the vector sum of all charged particles momenta within a cone
around the candidate, excluding the three signal tracks. The cone is defined
by a circle of radius 2.0 in the plane of pseudorapidity and azimuthal angle,
measured in radians, around the ${D}^{+}_{(s)}$ candidate direction. The
signal ${D}^{+}_{(s)}$ candidates tend to be more isolated than the
combinatorial background and show on average greater values of
$A_{p_{\mathrm{T}}}$. The final selection was optimised using a grid search in
the thresholds applied to the classifier output and the PID variables.

##  4 Invariant-mass distributions

The signal yields are determined using maximum-likelihood fits to the
invariant-mass distributions in each of the ${{D}^{+}_{(s)}}\\!\rightarrow
h^{\pm}\ell^{+}\ell^{(\prime)\mp}$ final states, including the resonant
channels. The fit is performed in the mass range of $1802$ to
$2050\text{\,}\mathrm{MeV}$ for all final states where both the ${D}^{+}$ and
${D}^{+}_{s}$ decay channels are analysed. In the final states where only the
${D}^{+}_{s}$ contribution is analysed, the fit is performed in the range of
$1926$ to $2050\text{\,}\mathrm{MeV}$. The invariant-mass distributions are
shown in Figs. 1-5, with fits indicated. No evidence is observed in any of the
25 signal channels. The yields obtained from the fit to the normalisation
channels can be found in Table 1.

Figure 1: Distributions of the three-body invariant mass for the
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow\ell^{-}\ell^{+}\right)$
${\pi}^{+}$ candidates used for normalisation and calibration. The final
states are specified in the mass label. The ${D}^{+}$ (${D}^{+}_{s}$) signal
component is shown as a dashed orange (green) line, peaking backgrounds are
denoted by the solid (hashed) regions and the non-peaking background is
denoted by the blue dotted line.

The mass distributions for the signal contributions are obtained by modelling
the distributions in simulated events with a kernel density estimation (KDE)
technique [29]. The same technique is applied to the
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{e^{-}}{e^{+}}\right)$
${\pi}^{+}$ channels. In the
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$
${\pi}^{+}$ channels, where a clean separation from background can be made, a
fit with a double Gaussian distribution is performed to the data, with the two
Gaussian distributions sharing a common mean.

In decay channels with electrons, the observed mass distribution is dependent
on the number of reconstructed bremsstrahlung photons. For final states with
one electron, separate shapes are extracted from simulation for candidates
with no bremsstrahlung and where one or more reconstructed photon candidates
are associated with the electron. For final states with two electrons,
separate shapes are used for candidates with no bremsstrahlung, one photon per
${D}^{+}_{(s)}$ candidate, and two or more photons per ${D}^{+}_{(s)}$
candidate.

Background arises from random combinations which vary smoothly across the fit
range, and from misidentified and partially reconstructed backgrounds that may
peak in the fitted mass range. The combinatorial backgrounds are fitted with
an exponential distribution where the analysed signal channel contains
dimuons, while third-order Chebyshev polynomials are used in the cases where
the signal channel contains one or two electrons. The form used for modelling
these combinatorial backgrounds is determined using a data sample where all
three final-state tracks have the same charge.

Background from decays involving leptons and neutrinos are found to be
negligible for this analysis, with only three-body ${D}^{+}$ and ${D}^{+}_{s}$
hadronic decays contributing to the signal samples. The backgrounds that
affect a specific signal channel depend on whether the signal-channel hadron
is a pion or a kaon and whether the leptons are of the same or opposite
charge. Simulation samples, which do not use a description of the interaction
of the particles with the detector material, are generated [30], and are
fitted using the same KDE technique as the signal.

The modelling of the backgrounds is validated using data samples where the
nominal kinematic selection is applied, but with the particle identification
requirements reversed and their values modified from those in the signal
selection to enhance the background. The distributions in these enhanced
background samples are then fitted with the shapes obtained from the KDE fit
to the simplified simulation plus a combinatorial-background description. The
four final states of the form
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{+}}\ell^{+}\ell^{(\prime)-}$ have
significant contributions from
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays, and the
seven final states of the form
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{+}}\ell^{\pm}\ell^{(\prime)\mp}$ have
significant contributions from
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays. In
these cases, the KDE description is smeared by a Gaussian function with mean
and width included as free parameters of the fit. After applying the
additional smearing a good description is obtained in the background-enhanced
samples.

Table 1: Reference branching fractions ($\mathcal{B}$) used for the resonant channels alongside signal yields. Channel |  $\mathcal{B}$ [2] | Fitted yield
---|---|---
${{D}^{+}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$ ${\pi}^{+}$ | $(1.63\pm 0.12)\times 10^{-6}$ | $$18\,100$\pm 340$
${{D}^{+}}\\!\rightarrow\left(\phi\\!\rightarrow{e^{-}}{e^{+}}\right)$ ${\pi}^{+}$ | $(1.67\pm 0.07)\times 10^{-6}$ |  00$$2160$\pm 180$
${{D}^{+}_{s}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$ ${\pi}^{+}$ | $(1.33\pm 0.10)\times 10^{-5}$ | $$42\,000$\pm 400$
${{D}^{+}_{s}}\\!\rightarrow\left(\phi\\!\rightarrow{e^{-}}{e^{+}}\right)$ ${\pi}^{+}$ | $(1.37\pm 0.05)\times 10^{-5}$ |  00$$5320$\pm 180$

Figure 2: Distributions of the three-body invariant mass in the signal regions
for decays with two muons. The final states are specified in the mass label.
The left (right) fit with the signal-plus-background (background-only)
hypothesis is overlaid with the peaking backgrounds denoted by dashed lines
and the non-peaking background is denoted by the blue dotted line.

Figure 3: Distributions of the three-body invariant mass in the signal regions
for decays with two electrons. The final states are specified in the mass
label. The left (right) fit with the signal-plus-background (background-only)
hypothesis is overlaid with the peaking backgrounds denoted by dashed lines
and the non-peaking background is denoted by the blue dotted line.

Figure 4: Distributions of the three-body invariant mass in the signal regions
for decays with an oppositely charged electron and muon. The final states are
specified in the mass label. The left (right) fit with the signal-plus-
background (background-only) hypothesis is overlaid with the peaking
backgrounds denoted by dashed lines and the non-peaking background is denoted
by the blue dotted line.

Figure 5: Distributions of the three-body invariant mass in the signal regions
for decays with an electron and a muon with matching charge. The final states
are specified in the mass label. The left (right) fit with the signal-plus-
background (background-only) hypothesis is overlaid with the peaking
backgrounds denoted by dashed lines and the non-peaking background is denoted
by the blue dotted line.

##  5 Branching fraction determination

The signal branching fractions are obtained from fits to the three-body
invariant-mass distributions, shown in Figs. 2-5. The branching fractions are
defined by

$\mathcal{B}_{D_{\left(s\right)}^{+}\rightarrow
h^{\pm}\ell^{+}\ell^{\left(\prime\right)\mp}}=\frac{N_{D_{\left(s\right)}^{+}\rightarrow
h^{\pm}\ell^{+}\ell^{\left(\prime\right)\mp}}}{N_{D_{\left(s\right)}^{+}\rightarrow\left(\phi\rightarrow\mu^{+}\mu^{-}\right)\pi^{+}}}\cdot\frac{\epsilon_{D_{\left(s\right)}^{+}\rightarrow\left(\phi\rightarrow\mu^{+}\mu^{-}\right)\pi^{+}}}{\epsilon_{D_{\left(s\right)}^{+}\rightarrow
h^{\pm}\ell^{+}\ell^{\left(\prime\right)\mp}}}\cdot\mathcal{B}_{D_{\left(s\right)}^{+}\rightarrow\left(\phi\rightarrow\mu^{+}\mu^{-}\right)\pi^{+}}$
(2)

where $N$ is the fitted yield in the channel indicated, $\mathcal{B}$ is the
branching fraction and $\epsilon$ is the efficiency of the selection criteria.
The branching fraction used for
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow\ell^{-}\ell^{+}\right)$
${\pi}^{+}$ can be found in Table 1 and is obtained by combining the
measurements of
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}\right)$
${\pi}^{+}$, $\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}$ and
$\phi\\!\rightarrow\ell^{+}\ell^{-}$ from Ref. [2]. The systematic
uncertainties are described in Section 6 and taken into account with a log-
normal distribution in the branching fraction fit. The potential overlap
between the ${D}^{+}$ and ${D}^{+}_{s}$ signal peaks in the same final state
is accounted for by floating the yield of the other meson in each fit and
treating this as an additional nuisance parameter when computing the
significance of the signal peak.

The effect of discrepancies between data and simulation are reduced by using a
reweighting technique that utilises a multivariate classifier. This classifier
is used to generate per-event weights using the method outlined in Ref. [31].
The procedure is applied separately for each of the calibration channels and
each classifier is trained to distinguish between real and simulated
calibration-channel events. Background subtraction of the data is applied
using the sPlot technique [32] with a fit to the invariant mass of the
calibration channel. The weights obtained from these classifiers are applied
to the simulation and then used throughout this analysis. Decay channels with
two electrons in the final state use weights from the
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{e^{-}}{e^{+}}\right)$
${\pi}^{+}$ classifiers and all other decays use the
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$
${\pi}^{+}$ classifiers. In all cases the same parent particle
(${D}^{+}_{(s)}$) decay as the signal is used.

Equation (2) includes the ratio of efficiencies between the normalisation
channel and the signal channel so that the effects of several systematic
uncertainties cancel. The reconstruction and selection efficiencies are
obtained from simulation with the aforementioned corrections applied. As the
resonant structure in the signal channels is inherently unknown, the
efficiency of each signal decay is obtained under the assumption that the
decay particles are uniformly distributed across the phase space with the
signal contribution extrapolated into any vetoed kinematic regions.

The efficiency with which events pass the PID requirements is obtained using a
set of calibration channels. The PID response is sampled [33] as a function of
the particle kinematics and event multiplicity in simulation, as described in
Ref. [34]. A small correction is made for differences in the track
reconstruction efficiency between data and simulation [35].

For channels containing electrons, an additional correction is applied to the
ratio of electron to muon reconstruction efficiencies. This is computed under
the assumption that the correction for each electron is independent of the
other, and thus the square root of the efficiency-corrected signal-yield ratio
between the calibration channels
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{e^{-}}{e^{+}}\right)$
${\pi}^{+}$ and
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$
${\pi}^{+}$ in data is taken.

The single event sensitivities, i.e. the branching fractions corresponding to
a single observed signal event, vary from $3\text{\times}{10}^{-10}$ to
$1\text{\times}{10}^{-8}$ depending on the channel. To ensure the efficiencies
are sufficiently well understood, cross-check measurements are made of the
branching fractions of
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$
${\pi}^{+}$ and
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{e^{-}}{e^{+}}\right)$
${\pi}^{+}$ decays. The results obtained before and after applying the offline
selection criteria are compared and found to be in agreement.

##  6 Systematic uncertainties

The efficiency ratio in Eq. 2 is affected by several sources of systematic
uncertainty. The finite size of the simulated signal event samples introduces
a systematic uncertainty on the branching fractions varying from
$1.4\text{\,}\mathrm{\char 37\relax}6.4\text{\,}\mathrm{\char 37\relax}$. A
summary of the systematic uncertainties assigned for each effect is given in
Table 2.

The track-reconstruction efficiency from simulation is corrected using a tag-
and-probe technique in data where ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{\mu^{+}}{\mu^{-}}$ decays are selected by making
requirements on only one muon. This is found to have negligible effect on the
efficiency ratio. A $0.8\text{\,}\mathrm{\char 37\relax}$ systematic
uncertainty is assigned for each particle species in the signal decay that
differs from that of the
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$
${\pi}^{+}$ reference. An additional $1.5\text{\,}\mathrm{\char 37\relax}$
systematic uncertainty is assigned to channels containing a kaon to account
for possible hadronic interaction effects with the detector material [35].
Alternative parametrisations [34] are considered for the sampling of the PID
response, but their associated systematic effects have negligible impact
compared to the statistical uncertainties of the analysis and other sources of
systematic uncertainty. For final states with both a muon and an electron, a
further systematic uncertainty of $7.6\text{\,}\mathrm{\char 37\relax}$ is
assigned for the choice of reweighting classifier. This is obtained from the
RMS of the change in efficiency of all mixed-lepton final states, using the
alternative reweighting classifier.

The systematic uncertainties affecting the signal yield are estimated using an
alternative fit model for the normalisation channels. For signal states with
two muons, a KDE parametrisation obtained from simulation is used as an
alternative for the nominal model describing the
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$
${\pi}^{+}$ signal. In all other cases, the differences are most likely to
arise from the treatment of bremsstrahlung radiation in simulation. Therefore,
an alternative model is generated by fixing the relative yield between the
three bremsstrahlung categories of
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{e^{-}}{e^{+}}\right)$
${\pi}^{+}$ from simulation. The signal yield from the alternative models is
compared with the nominal model and the difference is assigned as a systematic
uncertainty.

The uncertainty on the yield of
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$
${\pi}^{+}$ is dominated by the modelling of the
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ backgrounds
in the lower tails of the larger signal components. To account for this, the
data set is refitted neglecting these background components, and the change in
signal yield is assigned as a systematic uncertainty. The same procedure is
applied for
${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{e^{-}}{e^{+}}\right)$
${\pi}^{+}$ with the change in signal yield used as the uncertainty on the
electron efficiency correction factor.

Table 2: Summary of systematic uncertainties for each signal decay. The “$\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}$ yield” column represents the combination of the statistical uncertainty from the ${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$ ${\pi}^{+}$ dataset with the systematic uncertainty from the modelling of the ${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ backgrounds. A further $7.6\text{\,}\mathrm{\char 37\relax}$ uncertainty from the branching fraction of ${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$ ${\pi}^{+}$ and a $1.0\text{\,}\mathrm{\char 37\relax}$ uncertainty from the finite size of the simulated ${{D}^{+}_{(s)}}\\!\rightarrow\left(\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}\right)$ ${\pi}^{+}$ sample apply to all channels. The electron efficiency correction, described at the end of Section 5, is denoted by $\epsilon_{\text{electron}}$. All values are given in percent as a fractional uncertainty on the signal yield. Channel | Simulated signal | Track-reconstruction | Reweighting $\left[\%\right]$ | Signal $\left[\%\right]$ | $\phi\\!\rightarrow{\mu^{-}}{\mu^{+}}$ yield $\left[\%\right]$ | $\phi\\!\rightarrow{e^{-}}{e^{+}}$ $\epsilon_{\text{electron}}$ $\left[\%\right]$
---|---|---|---|---|---|---
sample $\left[\%\right]$ |  efficiency $\left[\%\right]$
$D^{+}\rightarrow K^{+}e^{+}e^{-}$ | $6.4$ | $3.2$ | – | $7.0$ | $2.0$ | $9.1$
$D^{+}\rightarrow K^{+}e^{+}\mu^{-}$ | $2.1$ | $2.5$ | $7.6$ | $7.0$ | $2.0$ | $4.6$
$D^{+}\rightarrow K^{+}\mu^{+}e^{-}$ | $1.8$ | $2.5$ | $7.6$ | $7.0$ | $2.0$ | $4.6$
$D^{+}\rightarrow K^{+}\mu^{+}\mu^{-}$ | $3.0$ | $2.3$ | – | $0.8$ | $2.0$ | –
$D^{+}\rightarrow\pi^{+}e^{+}e^{-}$ | $3.9$ | $2.3$ | – | $7.0$ | $2.0$ | $9.1$
$D^{+}\rightarrow\pi^{-}e^{+}e^{+}$ | $2.6$ | $2.3$ | – | $7.0$ | $2.0$ | $9.1$
$D^{+}\rightarrow\pi^{+}e^{+}\mu^{-}$ | $1.9$ | $1.1$ | $7.6$ | $7.0$ | $2.0$ | $4.6$
$D^{+}\rightarrow\pi^{+}\mu^{+}e^{-}$ | $1.5$ | $1.1$ | $7.6$ | $7.0$ | $2.0$ | $4.6$
$D^{+}\rightarrow\pi^{-}\mu^{+}e^{+}$ | $1.6$ | $1.1$ | $7.6$ | $7.0$ | $2.0$ | $4.6$
$D^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ | $1.9$ | $0.1$ | – | $0.8$ | $2.0$ | –
$D^{+}\rightarrow\pi^{-}\mu^{+}\mu^{+}$ | $1.5$ | $0.0$ | – | $0.8$ | $2.0$ | –
$D_{s}^{+}\rightarrow K^{+}e^{+}e^{-}$ | $6.0$ | $3.2$ | – | $7.0$ | $3.0$ | $7.5$
$D_{s}^{+}\rightarrow K^{-}e^{+}e^{+}$ | $3.2$ | $3.2$ | – | $7.0$ | $3.0$ | $7.5$
$D_{s}^{+}\rightarrow K^{+}e^{+}\mu^{-}$ | $3.0$ | $2.5$ | $7.6$ | $7.0$ | $3.0$ | $3.8$
$D_{s}^{+}\rightarrow K^{+}\mu^{+}e^{-}$ | $2.5$ | $2.5$ | $7.6$ | $7.0$ | $3.0$ | $3.8$
$D_{s}^{+}\rightarrow K^{-}\mu^{+}e^{+}$ | $2.4$ | $2.5$ | $7.6$ | $7.0$ | $3.0$ | $3.8$
$D_{s}^{+}\rightarrow K^{+}\mu^{+}\mu^{-}$ | $3.3$ | $2.3$ | – | $0.8$ | $3.0$ | –
$D_{s}^{+}\rightarrow K^{-}\mu^{+}\mu^{+}$ | $1.8$ | $2.3$ | – | $0.8$ | $3.0$ | –
$D_{s}^{+}\rightarrow\pi^{+}e^{+}e^{-}$ | $4.3$ | $2.3$ | – | $7.0$ | $3.0$ | $7.5$
$D_{s}^{+}\rightarrow\pi^{-}e^{+}e^{+}$ | $3.1$ | $2.3$ | – | $7.0$ | $3.0$ | $7.5$
$D_{s}^{+}\rightarrow\pi^{+}e^{+}\mu^{-}$ | $2.7$ | $1.2$ | $7.6$ | $7.0$ | $3.0$ | $3.8$
$D_{s}^{+}\rightarrow\pi^{+}\mu^{+}e^{-}$ | $2.3$ | $1.1$ | $7.6$ | $7.0$ | $3.0$ | $3.8$
$D_{s}^{+}\rightarrow\pi^{-}\mu^{+}e^{+}$ | $2.2$ | $1.2$ | $7.6$ | $7.0$ | $3.0$ | $3.8$
$D_{s}^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ | $2.5$ | $0.1$ | – | $0.8$ | $3.0$ | –
$D_{s}^{+}\rightarrow\pi^{-}\mu^{+}\mu^{+}$ | $2.2$ | $0.0$ | – | $0.8$ | $3.0$ | –

##  7 Results and conclusions

No significant deviation from the background only hypothesis is found for any
of the channels and all limits are within $\pm 2\sigma$ of the expected limit.
The compatibility of the observed mass-distributions with a signal-plus-
background or a background-only hypothesis is evaluated using the CLs method
with systematic uncertainties included as described in Ref. [36, 37]. Upper
limits on the branching fractions are determined using the observed
distribution of CLs as a function of the assumed branching fraction. The upper
limits at $90\text{\,}\mathrm{\char 37\relax}$ and $95\text{\,}\mathrm{\char
37\relax}$ confidence level (CL) are given in Table 3 and are shown in Fig. 6.

Figure 6: Upper limits at $90\text{\,}\mathrm{\char 37\relax}$ confidence level on the ${D}^{+}_{(s)}$ signal channels. The median (orange), $\pm 1\sigma$ and $\pm 2\sigma$ expected limits are shown as box plots and the observed limit is given by a black cross. The green line shows the previous world’s best limit for each channel where the solid, dotted and dashed lines correspond to BaBar, CLEO and LHCb [16, 17, 15]. Table 3: The single event sensitivities (SES), and upper limits on the branching fractions obtained using the CLs method, for each signal decay channel. Decay | Branching fraction upper limit [$10^{-9}$] |  |
---|---|---|---
${D}^{+}$ | ${D}^{+}_{s}$
SES |  $90\text{\,}\mathrm{\char 37\relax}$ CL |  $95\text{\,}\mathrm{\char 37\relax}$ CL | SES |  $90\text{\,}\mathrm{\char 37\relax}$ CL |  $95\text{\,}\mathrm{\char 37\relax}$ CL
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ | 0.6 | 67 | 74 | 2.4 | 180 | 210
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{-}}{\mu^{+}}{\mu^{+}}$ | 0.3 | 14 | 16 | 1.8 | 86 | 96
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{+}}{\mu^{+}}{\mu^{-}}$ | 1.2 | 54 | 61 | 3.8 | 140 | 160
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{-}}{\mu^{+}}{\mu^{+}}$ | - | - | - | 1.2 | 26 | 30
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{+}}{e^{+}}{\mu^{-}}$ | 0.6 | 210 | 230 | 3.1 | 1100 | 1200
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{+}}{\mu^{+}}{e^{-}}$ | 0.4 | 220 | 220 | 2.2 | 940 | 1100
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{-}}{\mu^{+}}{e^{+}}$ | 0.4 | 130 | 150 | 2.0 | 630 | 710
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{+}}{e^{+}}{\mu^{-}}$ | 0.7 | 75 | 83 | 3.7 | 790 | 880
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{+}}{\mu^{+}}{e^{-}}$ | 0.5 | 100 | 110 | 2.5 | 560 | 640
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{-}}{\mu^{+}}{e^{+}}$ | - | - | - | 2.4 | 260 | 320
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{+}}{e^{+}}{e^{-}}$ | 1.9 | 1600 | 1800 | 8.1 | 5500 | 6400
${{D}^{+}_{(s)}}\\!\rightarrow{{\pi}^{-}}{e^{+}}{e^{+}}$ | 0.9 | 530 | 600 | 4.1 | 1400 | 1600
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{+}}{e^{+}}{e^{-}}$ | 4.4 | 850 | 1000 | 14.8 | 4900 | 5500
${{D}^{+}_{(s)}}\\!\rightarrow{{K}^{-}}{e^{+}}{e^{+}}$ | - | - | - | 4.1 | 770 | 840

In conclusion, searches have been made for 25 previously unobserved three-body
decays of ${D}^{+}$ and ${D}^{+}_{s}$ mesons using
$1.6\text{\,}{\mathrm{fb}}^{-1}$ of $p$ $p$ collision data collected by the
LHCb experiment during 2016. The decays are of the form
${{D}^{+}_{(s)}}\\!\rightarrow h^{\pm}\ell^{+}\ell^{(\prime)\mp}$ where $h$ is
a kaon or pion and $\ell^{(\prime)}$ is an electron or muon. No significant
deviations from the background-only hypotheses are seen. The
$90\text{\,}\mathrm{\char 37\relax}$ CL limits on the branching fractions vary
from $1.4\text{\times}{10}^{-8}$ to $6.4\text{\times}{10}^{-6}$ and represent
the world’s best limits for 23 of these decays. In the majority of the
channels the improvement on previous limits is more than an order of
magnitude, with the largest improvement being a factor of five hundred in
${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{\mu^{+}}{\mu^{+}}$ decays.

## 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); MICINN (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); A*MIDEX, ANR, Labex P2IO
and OCEVU, and Région Auvergne-Rhône-Alpes (France); Key Research Program of
Frontier Sciences of CAS, CAS PIFI, Thousand Talents Program, and Sci. & Tech.
Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal
and GENCAT (Spain); the Royal Society and the Leverhulme Trust (United
Kingdom).

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LHCb collaboration

R. Aaij31, C. Abellán Beteta49, T. Ackernley59, B. Adeva45, M. Adinolfi53, H.
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Berninghoff16, H.C. Bernstein67, C. Bertella47, E. Bertholet12, A. Bertolin27,
C. Betancourt49, F. Betti19,e, M.O. Bettler54, Ia. Bezshyiko49, S. Bhasin53,
J. Bhom33, L. Bian72, M.S. Bieker14, S. Bifani52, P. Billoir12, M. Birch60,
F.C.R. Bishop54, A. Bizzeti21,u, M. Bjørn62, M.P. Blago47, T. Blake55, F.
Blanc48, S. Blusk67, D. Bobulska58, V. Bocci30, J.A. Boelhauve14, O. Boente
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Kucewicz33,l, M. Kucharczyk33, V. Kudryavtsev42,x, H.S. Kuindersma31, G.J.
Kunde66, T. Kvaratskheliya38, D. Lacarrere47, G. Lafferty61, A. Lai26, A.
Lampis26, D. Lancierini49, J.J. Lane61, R. Lane53, G. Lanfranchi22, C.
Langenbruch13, J. Langer14, O. Lantwin49,80, T. Latham55, F. Lazzari28,v, R.
Le Gac10, S.H. Lee83, R. Lefèvre9, A. Leflat39,47, S. Legotin80, O. Leroy10,
T. Lesiak33, B. Leverington16, H. Li71, L. Li62, P. Li16, X. Li66, Y. Li6, Y.
Li6, Z. Li67, X. Liang67, T. Lin60, R. Lindner47, V. Lisovskyi14, R.
Litvinov26, G. Liu71, H. Liu5, S. Liu6, X. Liu3, A. Loi26, J. Lomba Castro45,
I. Longstaff58, J.H. Lopes2, G. Loustau49, G.H. Lovell54, Y. Lu6, D.
Lucchesi27,o, S. Luchuk40, M. Lucio Martinez31, V. Lukashenko31, Y. Luo3, A.
Lupato61, E. Luppi20,g, O. Lupton55, A. Lusiani28,t, X. Lyu5, L. Ma6, S.
Maccolini19,e, F. Machefert11, F. Maciuc36, V. Macko48, P. Mackowiak14, S.
Maddrell-Mander53, L.R. Madhan Mohan53, O. Maev37, A. Maevskiy81, D.
Maisuzenko37, M.W. Majewski34, S. Malde62, B. Malecki47, A. Malinin79, 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. Mariani21,47,h, C. Marin Benito11, M. Marinangeli48, P.
Marino48, J. Marks16, P.J. Marshall59, G. Martellotti30, L. Martinazzoli47, M.
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Materok13, R. Matev47, A. Mathad49, Z. Mathe47, V. Matiunin38, C. Matteuzzi24,
K.R. Mattioli83, A. Mauri49, E. Maurice11,b, J. Mauricio44, M. Mazurek35, M.
McCann60, L. Mcconnell17, T.H. Mcgrath61, A. McNab61, R. McNulty17, J.V.
Mead59, B. Meadows64, C. Meaux10, G. Meier14, N. Meinert75, D. Melnychuk35, S.
Meloni24,j, M. Merk31, A. Merli25, L. Meyer Garcia2, M. Mikhasenko47, D.A.
Milanes73, E. Millard55, M.-N. Minard8, O. Mineev38, L. Minzoni20,g, S.E.
Mitchell57, B. Mitreska61, D.S. Mitzel47, A. Mödden14, A. Mogini12, R.A.
Mohammed62, R.D. Moise60, T. Mombächer14, I.A. Monroy73, S. Monteil9, M.
Morandin27, G. Morello22, M.J. Morello28,t, J. Moron34, A.B. Morris74, A.G.
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Müller47, K. Müller49, C.H. Murphy62, D. Murray61, P. Muzzetto26, P. Naik53,
T. Nakada48, R. Nandakumar56, T. Nanut48, I. Nasteva2, M. Needham57, I.
Neri20,g, N. Neri25,q, S. Neubert16, N. Neufeld47, R. Newcombe60, T.D.
Nguyen48, C. Nguyen-Mau48,n, E.M. Niel11, S. Nieswand13, N. Nikitin39, N.S.
Nolte47, C. Nunez83, A. Oblakowska-Mucha34, V. Obraztsov43, S. Ogilvy58, D.P.
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Palutan22, Y. Pan61, G. Panshin82, A. Papanestis56, M. Pappagallo57, L.L.
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B. Passalacqua20, G. Passaleva21,47, A. Pastore18, M. Patel60, C.
Patrignani19,e, C.J. Pawley78, A. Pearce47, A. Pellegrino31, M. Pepe
Altarelli47, S. Perazzini19, D. Pereima38, P. Perret9, K. Petridis53, A.
Petrolini23,i, A. Petrov79, S. Petrucci57, M. Petruzzo25,q, A. Philippov41, L.
Pica28, M. Piccini76, B. Pietrzyk8, G. Pietrzyk48, M. Pili62, D. Pinci30, J.
Pinzino47, F. Pisani19, A. Piucci16, Resmi P.K10, V. Placinta36, S. Playfer57,
J. Plews52, M. Plo Casasus45, F. Polci12, M. Poli Lener22, M. Poliakova67, A.
Poluektov10, N. Polukhina80,c, I. Polyakov67, E. Polycarpo2, G.J. Pomery53, S.
Ponce47, A. Popov43, D. Popov52, S. Popov41, S. Poslavskii43, K. Prasanth33,
L. Promberger47, C. Prouve45, V. Pugatch51, A. Puig Navarro49, H. Pullen62, G.
Punzi28,p, W. Qian5, J. Qin5, R. Quagliani12, B. Quintana8, N.V. Raab17, R.I.
Rabadan Trejo10, B. Rachwal34, J.H. Rademacker53, M. Rama28, M. Ramos
Pernas45, M.S. Rangel2, F. Ratnikov41,81, G. Raven32, M. Reboud8, F. Redi48,
F. Reiss12, C. Remon Alepuz46, Z. Ren3, V. Renaudin62, R. Ribatti28, S.
Ricciardi56, D.S. Richards56, S. Richards53, K. Rinnert59, P. Robbe11, A.
Robert12, G. Robertson57, A.B. Rodrigues48, E. Rodrigues59, J.A. Rodriguez
Lopez73, M. Roehrken47, A. Rollings62, P. Roloff47, V. Romanovskiy43, M.
Romero Lamas45, A. Romero Vidal45, J.D. Roth83, M. Rotondo22, M.S. Rudolph67,
T. Ruf47, J. Ruiz Vidal46, A. Ryzhikov81, J. Ryzka34, J.J. Saborido Silva45,
N. Sagidova37, N. Sahoo55, B. Saitta26,f, C. Sanchez Gras31, C. Sanchez
Mayordomo46, R. Santacesaria30, C. Santamarina Rios45, M. Santimaria22, E.
Santovetti29,k, D. Saranin80, G. Sarpis61, M. Sarpis16, A. Sarti30, C.
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Scantlebury Smead62, S. Schael13, M. Schellenberg14, M. Schiller58, H.
Schindler47, M. Schmelling15, T. Schmelzer14, B. Schmidt47, O. Schneider48, A.
Schopper47, H.F. Schreiner64, M. Schubiger31, S. Schulte48, M.H. Schune11, R.
Schwemmer47, B. Sciascia22, A. Sciubba30, S. Sellam68, A. Semennikov38, M.
Senghi Soares32, A. Sergi52,47, N. Serra49, J. Serrano10, L. Sestini27, A.
Seuthe14, P. Seyfert47, D.M. Shangase83, M. Shapkin43, I. Shchemerov80, L.
Shchutska48, T. Shears59, L. Shekhtman42,x, Z. Shen4, V. Shevchenko79, E.B.
Shields24,j, E. Shmanin80, J.D. Shupperd67, B.G. Siddi20, R. Silva Coutinho49,
L. Silva de Oliveira2, G. Simi27,o, S. Simone18,d, I. Skiba20,g, N.
Skidmore16, T. Skwarnicki67, M.W. Slater52, J.C. Smallwood62, J.G. Smeaton54,
A. Smetkina38, E. Smith13, I.T. Smith57, M. Smith60, A. Snoch31, M. Soares19,
L. Soares Lavra9, M.D. Sokoloff64, F.J.P. Soler58, A. Solovev37, I.
Solovyev37, F.L. Souza De Almeida2, B. Souza De Paula2, B. Spaan14, E. Spadaro
Norella25,q, P. Spradlin58, F. Stagni47, M. Stahl64, S. Stahl47, P. Stefko48,
O. Steinkamp49,80, S. Stemmle16, O. Stenyakin43, M. Stepanova37, H. Stevens14,
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Zuliani27, G. Zunica61.

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
27Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
28INFN Sezione di Pisa, Pisa, Italy
29INFN Sezione di Roma Tor Vergata, Roma, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
32Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
33Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35National Center for Nuclear Research (NCBJ), Warsaw, Poland
36Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
37Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
38Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia, Moscow, Russia
39Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
40Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
41Yandex School of Data Analysis, Moscow, Russia
42Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
43Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
44ICCUB, Universitat de Barcelona, Barcelona, Spain
45Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
46Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
47European Organization for Nuclear Research (CERN), Geneva, Switzerland
48Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
49Physik-Institut, Universität Zürich, Zürich, Switzerland
50NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
51Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
52University of Birmingham, Birmingham, United Kingdom
53H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
54Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
55Department of Physics, University of Warwick, Coventry, United Kingdom
56STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
57School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
58School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
59Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
60Imperial College London, London, United Kingdom
61Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
62Department of Physics, University of Oxford, Oxford, United Kingdom
63Massachusetts Institute of Technology, Cambridge, MA, United States
64University of Cincinnati, Cincinnati, OH, United States
65University of Maryland, College Park, MD, United States
66Los Alamos National Laboratory (LANL), Los Alamos, United States
67Syracuse University, Syracuse, NY, United States
68Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria,
associated to 2
69School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 55
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71Guangdong Provencial Key Laboratory of Nuclear Science, Institute of Quantum
Matter, South China Normal University, Guangzhou, China, associated to 3
72School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
73Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 12
74Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn,
Germany, associated to 16
75Institut für Physik, Universität Rostock, Rostock, Germany, associated to 16
76INFN Sezione di Perugia, Perugia, Italy, associated to 20
77Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 31
78Universiteit Maastricht, Maastricht, Netherlands, associated to 31
79National Research Centre Kurchatov Institute, Moscow, Russia, associated to
38
80National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 38
81National Research University Higher School of Economics, Moscow, Russia,
associated to 41
82National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
38
83University 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 Firenze, Firenze, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, 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
zUniversidad Nacional Autonoma de Honduras, Tegucigalpa, Honduras