EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2020-194 LHCb-PAPER-2020-022 November 10, 2020

Search for heavy neutral leptons

in $W^{+}\rightarrow\mu^{+}\mu^{\pm}\text{\,jet}$ decays

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

A search is performed for heavy neutrinos in the decay of a $W$ boson into two
muons and a jet. The data set corresponds to an integrated luminosity of
approximately $3.0\text{\,fb}^{-1}$ of proton-proton collision data at centre-
of-mass energies of 7 and $8\text{\,Te\kern-1.00006ptV}$ collected with the
LHCb experiment. Both same-sign and opposite-sign muons in the final state are
considered. Data are found to be consistent with the expected background.
Upper limits on the coupling of a heavy neutrino with the Standard Model
neutrino are set at $95\%$ confidence level in the heavy-neutrino mass range
from 5 to $50\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. These are of the order of
$10^{-3}$ for lepton-number-conserving decays and of the order of $10^{-4}$
for lepton-number-violating heavy-neutrino decays.

Submitted to Eur. Phys. J. C

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

##  1 Introduction

Many theories beyond the Standard Model (SM) predict the existence of heavy
neutral leptons (HNLs) to explain the smallness of neutrino masses[1, 2, 3].
These leptons, $N$, could be observed at collider experiments if their masses
are at the electroweak scale. The HNLs may mix with the light SM neutrinos
$\nu_{\ell}$, with a strength governed by the coupling $V_{N\ell}$. The mixing
matrix is not expected to be flavour diagonal, which leads to signatures with
transitions between different lepton flavours. Experimentally, direct searches
for a generic heavy neutrino are performed through their mixing with each
flavour of SM neutrino. The HNL is expected to be long-lived if the coupling
is small enough. This analysis searches for the mixing of a heavy neutrino
with a muon neutrino, taking advantage of the high reconstruction efficiency
for muons at LHCb. The HNL mass range covered is between
$550\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$. The dominant HNL
production mechanism in this mass range is via the decay of gauge bosons,
${W}^{\pm}\rightarrow{\ell}^{\pm}N$ and ${Z}\rightarrow{\nu}N$. Both lepton-
number-violating and lepton-number-conserving decays of a heavy neutrino are
considered. The heavy neutrino is assumed to have negligibly small lifetime.

The DELPHI collaboration was first to set a limit on these types of decays
considering ${Z}\rightarrow\nu N$ decays in $e^{+}e^{-}$ collisions at the $Z$
resonance, where both long- and short-lived signatures were analysed [4]. The
upper limit on the ${Z}\rightarrow\nu N$ branching fraction of
$1.3\text{\times}{10}^{-6}$ at 95% confidence level (CL) for $N$ masses
between $3.550\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ leads to
one of the most stringent constraints on the coupling in this mass range. At
the LHC, a more promising detection approach for $N$ with mass below the weak
scale are leptonic decays of $W$ bosons, ${W}^{\pm}\rightarrow{\ell}^{\pm}N$.
Searches by the ATLAS [5, 6, 7, 8, 9] and CMS [10, 11, 12, 13, 14, 15, 16]
collaborations at centre-of-mass energies of 7, 8 and
$13\text{\,Te\kern-1.00006ptV}$ typically probed larger neutrino masses, from
$40\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ up to
$2700\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, employing a signature of two same-
sign leptons and two jets. A recent search performed by the CMS collaboration
also included final states with at least one jet, extending the probed heavy-
neutrino mass range down to $20\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ [17]. In
the mass range studied in this analysis, searches of promptly decaying heavy
neutrinos in leptonic final states of the $W$ boson at centre-of-mass energy
of $13\text{\,Te\kern-1.00006ptV}$ by the ATLAS [18] and CMS [19]
collaborations set constraints comparable to that of the DELPHI collaboration.
A long-lived signature has also been explored by the ATLAS collaboration,
excluding coupling strengths down to about $10^{-6}$ between 4.5 and
$10\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, and hence representing the most
stringent limit to date in this mass range [18].

The branching fraction ($\mathcal{B}$) for the decay of a $W$ boson into a
muon and a heavy neutrino is suppressed with respect to the SM decay
${W}^{+}\rightarrow{\mu}^{+}{\nu}$ by the mixing of the active neutrino with
the heavy neutrino and a phase-space factor according to Ref. [20]

${\mathcal{B}}({W}\rightarrow{\mu}N)={\mathcal{B}}({W}\rightarrow{\mu}{\nu})\left|V_{{\mu}N}\right|^{2}\left(1-\frac{m_{N}^{2}}{m_{W}^{2}}\right)^{2}\left(1+\frac{m_{N}^{2}}{2m_{W}^{2}}\right).$
(1)

The heavy neutrino decays via neutral or charged current interactions
$N\rightarrow\nu Z^{(*)}$ or $N\rightarrow{\mu}^{\pm}{W}^{\mp(*)}$, where the
$Z$ and $W$ bosons can be on- or off-shell. The corresponding branching
fractions are computed based on Refs. [21, 22]. The total width is given by
the sum of the partial decay widths of charged and neutral current
interactions. If the neutrino is a Majorana particle, an additional lepton-
number-violating decay contributes to the same final state, with the same
partial decay width as the lepton-number-conserving decay. The branching
fraction to any non-charge-specific final state is unaffected, but the
lifetime is a factor of two smaller than if the neutrino were a Dirac
particle.

The left plot of Fig. 1 shows the branching fraction for HNL decay modes with
a muon in the final state as a function of the heavy-neutrino mass. The
difference between the HNL decay modes to quarks is mainly due to CKM matrix
elements [23, 24], with the quark masses only playing a minor role at low
heavy-neutrino masses. The branching fraction of the decay
$N\rightarrow{\mu}{\mu}{\nu}$ is about one order of magnitude smaller than
that of the $N\rightarrow{\mu}{{q}{\overline{q}}}^{\prime}$ mode, due to
negative interference between charged and neutral current interactions. In the
right plot of Fig. 1 the lifetime is shown as a function of the heavy-neutrino
mass assuming a coupling of $10^{-5}$, which is the current bound in the mass
range of interest. In the low-mass regime, the lifetime is of the order of
$10\text{\,ps}$, while at higher masses the lifetime is so small that the
decay can be considered prompt.

Figure 1: Properties of a heavy neutrino as a function of its mass [21, 22]:
(left) the branching fractions to final states with a muon and (right) the
lifetime, assuming a coupling of $10^{-5}$ (current limit).

In this paper, a search is presented for a prompt HNL in the decay111Charge-
conjugate processes are implied throughout the paper.
${W^{+}}\rightarrow{\mu^{+}}N$ with
$N\rightarrow\mu^{\pm}{q}{\overline{q}}^{\prime}$, as depicted in Fig. 2. Data
collected by the LHCb experiment in proton-proton collisions at centre-of-mass
energies of $7\text{\,}\mathrm{TeV}\text{/}$ in 2011 and
$8\text{\,}\mathrm{TeV}\text{/}$ in 2012 are used, corresponding to integrated
luminosities of $1.01.9\text{\,}{\mathrm{fb}}^{-1}$ [25], respectively.

The experimental signature consists of two muons and one or two jets depending
on the HNL mass. The muon from $W$ decay, denoted as $\mu_{{W}}$, carries
significant transverse momentum, while the muon from $N$ decay, denoted as
$\mu_{N}$, has lower momentum. Both same-sign and opposite-sign muons are
considered, allowing for the possibility that the HNL has a Majorana nature.
The signal yields for both categories and several mass hypotheses in the range
$5-50\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ are extracted from the data and
normalized with respect to the ${W^{+}}\rightarrow{\mu^{+}}{\nu}$ decay.
Corresponding upper limits are then set on the product of coupling and
branching ratio.

The paper is organised as follows. In Section 2 the detector, data and
simulation samples are described, and in Section 3 the selection of signal and
normalisation candidates is discussed. Section 4 contains the results and
conclusions are drawn in Section 5.

Figure 2: Feynman diagram for the production of a heavy neutrino via mixing
with a neutrino from the decay of a $W$ boson and semileptonic decay of the
heavy neutrino into a lepton and two quarks. The subscripts $\alpha$ and
$\beta$ indicate the lepton flavour.

##  2 Detector and simulation

The LHCb detector [26, 27] 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 [28], 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 [29] 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$\text{\,Ge\kern-1.00006ptV\\!/}c$.
The minimum distance of a track to a primary proton-proton 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
$\text{\,Ge\kern-1.00006ptV\\!/}c$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
[30]. Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad (SPD) 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
[31]. The online event selection is performed by a trigger [32], 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. For the events selected for this analysis, the trigger
requires at least a single muon with
$p_{\mathrm{T}}{}>1.48\,(1.76)\text{\,Ge\kern-1.00006ptV\\!/}c$ at the
hardware stage in 2011 (2012), and includes an upper threshold of 600 hits in
the SPD to prevent high-particle multiplicity events from dominating the
processing time. A muon with
$p_{\mathrm{T}}{}>10\text{\,Ge\kern-1.00006ptV\\!/}c$ is required at the
software stage.

Simulated samples were generated for the signal decay with both opposite- and
same-sign muons in the final state, in equal amount. Samples were generated
for HNL masses of 5, 10, 15, 20, 30, and
$50\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, using the minimal mixing scenario
model [33]. The parton level process is generated with MadGraph 5 [34, 35],
while Pythia 8 [36], with a specific LHCb configuration [37], is used for the
generation of the underlying event, fragmentation and hadronisation. Decays of
hadronic particles are described by EvtGen [38], in which final-state
radiation is generated using Photos [39]. The interaction of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [40, *Agostinelli:2002hh] as described in Ref. [42]. Simulated
background samples are generated using Pythia 8\. The DYTurbo [43] program is
used to correct the kinematic distributions of the simulated
${W^{+}}\rightarrow{\mu^{+}}{\nu}$ background.

##  3 Event selection

Signal candidates are reconstructed from a pair of charged tracks identified
as muons and a single jet. First, the high-momentum muon, $\mu_{{W}}$, is
selected. Both the hardware and software trigger decisions are required to be
associated to the high-momentum muon candidate. The track is required to have
transverse momentum larger than $20\text{\,Ge\kern-1.00006ptV\\!/}c$, to be of
good quality and to have a high significance of the track curvature to remove
high transverse momentum tracks with poorly determined charge. The high-
momentum muon candidate is also required to have small relative energy
deposition in the calorimeters to reject pions and kaons misidentified as
muons. The muon selection criteria for the normalisation channel
${W^{+}}\rightarrow{\mu^{+}}{\nu}$ are the same as for the high-momentum muon
of the signal.

The lower-momentum muon candidate, $\mu_{N}$, is required to have transverse
momentum higher than $3\text{\,Ge\kern-1.00006ptV\\!/}c$. The combined
invariant mass of the $\mu_{N}$ and $\mu_{{W}}$ candidates must be in the
range $20$ to $70\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ to
suppress the background from ${Z}\rightarrow\mu\mu$ decays. Depending on the
relative charge of the two muons the candidates are classified as same-sign
(SS) or opposite-sign (OS).

Jets are reconstructed following a particle flow approach [44], using tracks
of charged particles and calorimeter energy deposits as inputs. To prevent
overlap between jets and signal muons, tracks identified as muons with a
transverse momentum greater than $2\text{\,Ge\kern-1.00006ptV\\!/}c$ are
excluded from the jet reconstruction. The anti-$k_{T}$ jet clustering
algorithm is used [45], with a distance parameter
$R=\sqrt{(\Delta\phi)^{2}+(\Delta\eta)^{2}}=0.5$, where $\phi$ is the
azimuthal angle and $\theta$ the pseudorapidity. The jet four-momentum is
calculated from the four-vectors of its constituents, and corrected for
pollution from pile-up and the underlying event using the per-event particle
multiplicity [44]. To enhance the jet purity the fraction of the jet energy
carried by charged particles should be at least 0.1, the jet must have
$p_{\mathrm{T}}>10\text{\,Ge\kern-1.00006ptV\\!/}c$ and contain at least one
track with $p_{\mathrm{T}}>1.2\text{\,Ge\kern-1.00006ptV\\!/}c$. Only
candidates with at least one jet passing these criteria are retained. Jets are
combined with lower-momentum muon candidates to form
$N\rightarrow{\mu_{N}}{\text{\,jet}}$ candidates, which are required to have
invariant mass smaller than
$80\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ and a transverse
momentum greater than $10\text{\,Ge\kern-1.00006ptV\\!/}c$. The selected
heavy-neutrino candidates are then combined with a high-momentum muon
candidate to form $W$ candidates. Since the assignment of the two muons is
ambiguous if they both satisfy the high-momentum muon selection, the mass,
$m({\mu_{N}}{\text{\,jet}})$, of the ${\mu_{N}}{\text{\,jet}}$ combination is
required to be smaller than that of the ${\mu_{{W}}}{\text{\,jet}}$
combination. Only the candidates within
$20\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$ of the known $W$
mass [46] are retained.

A scale factor is applied to the jet four-momentum, constraining the invariant
mass of the ${\mu_{{W}}}{\mu_{N}}{\text{\,jet}}$ system to the known mass of
the $W$ boson. This leads to a significant improvement in the resolution of
$m({\mu_{N}}{\text{\,jet}})$ and diminishes the sensitivity of the heavy-
neutrino mass distribution to the jet energy scale.

Dominant background sources are charged weak currents, in particular
$pp\rightarrow W+X$ with ${W}\rightarrow\mu\nu$ or ${W}\rightarrow\tau\nu$,
neutral electroweak Drell-Yan processes $pp\rightarrow\gamma/Z^{(*)}+X$ with
$\gamma/{Z}^{(*)}\rightarrow\mu\mu,\tau\tau$, heavy flavour
${b}{\overline{b}}\rightarrow X\mu$ and ${c}{\overline{c}}\rightarrow X\mu$,
and $X{\mu}$ production from light QCD $({u},{d},{s})$. In the same-sign muon
channel the Drell-Yan type background contributions are highly suppressed,
while in the opposite-sign muon channel the contribution from low-mass Drell-
Yan processes remains a prominent irreducible background.

The background is suppressed by placing requirements on the IP of both muons
and by using three different multivariate classifiers based on a Boosted
Decision Tree (BDT) algorithm [47, 48, 49]. The three classifiers are referred
to as the $\mu_{{W}}$ uBDT, the $\mu_{N}$ uBDT and the kinematics uBDT: the
first two classifiers are dedicated to the identification of the respective
muons, while the latter exploits the event kinematics to distinguish the
signal from the remaining background. All three are trained minimising the
dependence of the signal efficiency on the true neutrino mass using the uBoost
method [50]. The training of all classifiers uses a cross-validation technique
[51]. The classifiers are trained using simulated decays of the heavy neutrino
with same-sign muons in the final state as a proxy for signal. Both charged
and neutral weak background contributions have a muon in the final state with
similar kinematics to the signal high-momentum muon. The $\mu_{{W}}$
classifier discriminates between the signal and heavy flavour background. It
is trained using data candidates where both muons have large impact parameters
($\text{IP}({\mu_{{W}}})>\text{$40\text{\,}\mathrm{\SIUnitSymbolMicro
m}\text{/}$}$,
$\text{IP}({\mu_{N}})>\text{$100\text{\,}\mathrm{\SIUnitSymbolMicro
m}\text{/}$}$) as a proxy for background. For both the $\mu_{N}$ uBDT and the
kinematics uBDT, a combination of the dominant background sources from
simulation is used. The input variables used for each of the muon
identification classifiers are the combined particle identification
information from the RICH, calorimeter and muon systems, the ratio of the
energy deposited in both calorimeters to the measured track momentum, and
observables describing the isolation of the tracks. Additional isolation
variables of different cone sizes are included among the inputs for the
$\mu_{N}$ uBDT classifier. The input variables of the kinematics classifier
comprise the angular distance $R$ between the $\mu_{N}$ and the jet, the angle
between the two muons in the rest frame of the heavy neutrino, the transverse
component of the sum of the four-momentum of all particles used as particle
flow input, the dimuon mass, the combined invariant mass of the dimuon and the
jet, and the jet transverse momentum. The optimal requirement on the output of
each BDT classifier is selected by maximising the Punzi figure-of-merit [52]
for three units of significance. This is first evaluated for the $\mu_{{W}}$
uBDT, followed by the simultaneous optimisation of the $\mu_{N}$ and
kinematics uBDTs. The optimal requirements are found to be the same for all
the simulated signal samples. The selection is optimised for the same-sign
muon signal, but it is verified to be optimal for the opposite-sign category
as well.

The background sources are studied and evaluated in three control regions: one
enhanced in electroweak $W$ background components, one in heavy flavour
background components and one in light QCD background components, indicated as
$W$, $b$ $\overline{b}$ and QCD regions, respectively. The requirements
defining the control regions with respect to the signal region are reported in
Table 1. An additional region, denoted as the ${Z}\rightarrow{\mu}{\mu}$
region, is defined by the following criteria: both muons are required to have
transverse momentum greater than $20\text{\,Ge\kern-1.00006ptV\\!/}c$ and IP
smaller than $40\text{\,}\mathrm{\SIUnitSymbolMicro m}\text{/}$ and the
invariant mass of the muon pair must be between
$60120\text{\,}\mathrm{GeV}\text{/}{\mathrm{\text{$c$}}}^{2}$. In each control
region the predicted background composition and yield are compared to the data
to confirm that no other contribution has been neglected.

Table 1: Requirements on IP and BDT classifiers defining the signal and
control regions.

$\text{IP}({\mu_{{W}}})$ [mm] $\mu_{{W}}$ uBDT $\mu_{N}$ uBDT Kinematic uBDT
$\text{IP}({\mu}_{N})$ [mm] Signal $<0.04$ $>0.55$ $>0.60$ $>0.62$ $<0.1$
${W}$ region $<0.04$ $>0.55$ $<0.60$ $<0.62$ $<0.1$ ${b}{\overline{b}}$ region
$>0.04$ $<0.55$ $<0.60$ $<0.62$ $>0.1$ QCD region $<0.04$ $<0.55$ $>0.60$
$>0.62$ $<0.1$

##  4 Fit strategy and results

The product of the branching fraction
${\mathcal{B}}(N\rightarrow{\mu}{\text{\,jet}})$ and the squared coupling
$\left|V_{{\mu}N}\right|^{2}$ is proportional to the number of signal
candidates, $N_{\text{sig}}$, and can be written with respect to the number of
${W}\rightarrow{\mu}{\nu}$ candidates as

${\mathcal{B}}(N\rightarrow{\mu}{\text{\,jet}})\left|V_{{\mu}N}\right|^{2}=\frac{N_{\text{sig}}}{N_{\text{norm}}}\frac{{\varepsilon}_{\text{norm}}}{{\varepsilon}_{\text{sig}}}\left(1-\frac{m_{N}^{2}}{m_{W}^{2}}\right)^{-2}\left(1+\frac{m_{N}^{2}}{2m_{W}^{2}}\right)^{-1},$
(2)

where $N_{\text{sig}}$ and $N_{\text{norm}}$ denote the yields of the signal
and normalisation channels and ${\varepsilon}_{\text{sig}}$ and
${\varepsilon}_{\text{norm}}$ their efficiencies. The phase-space suppression
factor and the coupling term arise from the heavy-neutrino production process
described by Eq. 1. The ${W^{+}}\rightarrow{\mu^{+}}{\nu}$ branching fraction
in Eq. 1 cancels with the normalisation channel.

###  4.1 Normalisation channel

The yield of the normalisation channel is determined using a binned maximum-
likelihood fit to the muon transverse momentum distribution separately for
each year of data taking and in eight bins of muon pseudorapidity. The fit is
performed separately for positively and negatively charged muons to account
for the difference in production rate at LHCb. The main background
contributions are $\gamma/{Z}^{(*)}\rightarrow\mu\mu$ decays and hadron
misidentification (denoted as QCD). Minor contamination from
${Z}\rightarrow\tau\tau$, ${W}\rightarrow\tau\nu$ and ${{b}{\overline{b}}}$
processes is also present. The templates are obtained in bins of
pseudorapidity from simulation for each component, with the exception of the
QCD background templates that are determined from a control sample
characterised by large energy deposits in the calorimeters. The yields for the
minor background contributions are fixed to their expected values from
simulation. The yield for the ${Z}\rightarrow{\mu}{\mu}$ component is
constrained to the value obtained from the corresponding control region
extrapolated according to simulation. The distribution of the muon transverse
momentum for 2012 data integrated over pseudorapidity is shown in Fig. 3 with
the fit result superimposed.

Figure 3: The (left) positive and (right) negative muon transverse momentum
spectra for the 2012 data set integrated over pseudorapidity for the
normalisation channel. The fit is overlaid.

Systematic uncertainties on the normalisation yield are estimated separately
for the 2011 and 2012 data sets by varying the shape and normalisation of the
templates. Replacing the QCD template with an exponential distribution and
varying the ${W}\rightarrow{\mu}{\nu}$ templates each yield a difference with
respect to the default fit of about 1%, which is assigned as a systematic
uncertainty. The ratio of measured QCD yields per pseudorapidity bin between
positively and negatively charged muons deviates from unity. A systematic
uncertainty of 0.7% is assigned to account for the difference with respect to
the default fit when the normalisation of the QCD component is fixed bin by
bin to the average of the yields. Systematic uncertainties of less than 0.1%
are assigned for each of the components whose yield is fixed in the fit to
account for the largest variation observed with respect to the default fit
when each yield is changed by one standard deviation. For the 2011 data set an
additional source of uncertainty is considered to account for the difference
in templates between 2011 and 2012 simulation, resulting in 0.7% assigned
systematic uncertainty. The total systematic uncertainty on the normalisation
yield is 1.8% and 1.6% for the 2011 and 2012 data sets, respectively.

The total yield for the normalisation channel ${W}\rightarrow{\mu}{\nu}$ is
$(795\pm 1\pm 15)\times 10^{3}$ for 2011 data and $(1719\pm 2\pm 27)\times
10^{3}$ for 2012 data, where the first uncertainty is statistical and the
second systematic. The total yield comprises 57% $W^{+}$ decays and 43%
$W^{-}$ decays. The ratio of the measured yields for positively and negatively
charged muons as a function of pseudorapidity is in good agreement with the
simulation and the measurement of Ref. [53].

###  4.2 Efficiency ratio

The efficiency and corresponding uncertainties of the selection requirements
for both the normalisation and signal samples are determined separately for
each year of data taking using simulation. Corrections to account for
mismodelling in simulation are derived from control samples, such as
${Z}\rightarrow{\mu^{+}\mu^{-}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\rightarrow{\mu^{+}\mu^{-}}$, and are
applied to the efficiencies related to the reconstruction of the two muons,
the required number of hits in the SPD and the $\mu_{{W}}$ uBDT and $\mu_{N}$
uBDT criteria. When sufficient data is available, the corrections are
evaluated in bins of pseudorapidity and momentum or transverse momentum of the
muon. The dominant source of systematic uncertainties arises from the
different detector response to jets between simulation and data. The energy
scale is modelled to an accuracy of about 5%, driven mainly by the response to
neutral particles, while the jet energy resolution is modelled in simulation
to an accuracy of about 10% [44, 54, 55]. The corresponding systematic
uncertainties on the efficiency ratio are evaluated in simulation by varying
the jet energy by 5% for the former and by smearing the jet transverse
momentum by 10% for the latter. Both resulting uncertainties vary between 5%
and 11% depending on the heavy-neutrino mass, where the fluctuation is due to
the limited size of the simulated samples. The overall uncertainty due to jet
identification requirements, which amounts to 1.7%, is taken from Ref. [56]. A
systematic uncertainty to account for the mismatch between simulation and data
of the missing transverse momentum in the event varies between 1% and 2.5%
depending on the heavy-neutrino mass. The uncertainties related to the
efficiency of the $\mu_{{W}}$ selection largely cancel for the signal and
normalisation modes, since their selections are identical. The relative
uncertainty on the correction factors is of the order of 2%. The ratios of
efficiencies between the normalisation and signal channel, for different heavy
neutrino masses, are reported in Table 2.

Table 2: Efficiency ratios, for different heavy-neutrino masses, between
normalisation and signal channels. The first uncertainty is statistical, the
second is systematic.

$N$ mass Same sign Opposite sign $[\text{\,Ge\kern-1.00006ptV\\!/}c^{2}]$ 2011
2012 2011 2012 05 $2$4${}\pm{}$ $1$ ${}\pm{}$ $2$ $2$5${}\pm{}$ $1$ ${}\pm{}$
$3$ $2$2${}\pm{}$ $1$ ${}\pm{}$ $2$ $2$1${}\pm{}$ $1$ ${}\pm{}$ $1$ 10
$2$4${}\pm{}$ $1$ ${}\pm{}$ $2$ $2$4${}\pm{}$ $1$ ${}\pm{}$ $2$ $2$1${}\pm{}$
$1$ ${}\pm{}$ $2$ $1$9${}\pm{}$ $1$ ${}\pm{}$ $2$ 15 $2$5${}\pm{}$ $1$
${}\pm{}$ $3$ $2$6${}\pm{}$ $1$ ${}\pm{}$ $3$ $2$4${}\pm{}$ $1$ ${}\pm{}$ $2$
$2$3${}\pm{}$ $1$ ${}\pm{}$ $2$ 20 $2$9${}\pm{}$ $1$ ${}\pm{}$ $4$
$2$8${}\pm{}$ $1$ ${}\pm{}$ $3$ $2$6${}\pm{}$ $1$ ${}\pm{}$ $4$ $2$5${}\pm{}$
$1$ ${}\pm{}$ $3$ 30 $3$2${}\pm{}$ $1$ ${}\pm{}$ $3$ $3$2${}\pm{}$ $1$
${}\pm{}$ $4$ $2$9${}\pm{}$ $1$ ${}\pm{}$ $4$ $3$0${}\pm{}$ $1$ ${}\pm{}$ $3$
50 $6$1${}\pm{}$ $3$ ${}\pm{}$ $3$ $5$5${}\pm{}$ $2$ ${}\pm{}$ $4$
$4$3${}\pm{}$ $2$ ${}\pm{}$ $4$ $4$3${}\pm{}$ $2$ ${}\pm{}$ $5$

###  4.3 Neutrino mass model

The signal yield for each heavy-neutrino mass hypothesis is determined from a
binned maximum-likelihood fit to the invariant mass
$m({\mu_{N}}{\text{\,jet}})$. In the fits, the normalisation channel yield,
the efficiency ratio, and background yields are Gaussian-constrained to their
expected values within uncertainties.

The yields for the main background components are determined in the respective
control regions. The yields for ${W}\rightarrow\mu{\nu}$ and
${Z}\rightarrow{\mu}{\mu}$ background contributions are obtained from a binned
maximum-likelihood fit of the invariant mass $m({\mu_{N}}{\text{\,jet}})$ in
the $W$ region, and for the ${{b}{\overline{b}}}$ background in the
${{b}{\overline{b}}}$ region. The fits in the control regions are performed
separately for positively and negatively charged $\mu_{{W}}$ and per year of
data taking with templates obtained from simulation. The expected background
yields in the signal region are determined by scaling the fitted yields
according to simulation. The light QCD contribution in the signal region is
estimated with a different method. The efficiency of the $\mu_{{W}}$ uBDT
requirement $\varepsilon_{\text{QCD}}$ is evaluated using the normalisation
channel, assuming that it factorises from the other selection criteria that
suppress the QCD background. The number of light QCD events in the QCD region
is obtained by subtracting from the total number of events the expected yields
for the $W$, $Z$ and heavy flavour background components. The result is scaled
by the ratio $\varepsilon_{\text{QCD}}/(1-\varepsilon_{\text{QCD}})$ to
determine the number of light QCD events in the signal region. The estimated
background yields in the signal region are collected in Table 3 for same-sign
and opposite-sign muons in Run 1 (2011 and 2012 combined) data. The
uncertainty is dominated by the limited size of the simulated samples. The
background predictions are tested in validation regions. These are defined by
inverting one by one the requirements of Table 1 defining the signal region.
The results are found to be in good agreement with the data.

Table 3: Extrapolated background yields in the signal region for same-sign and
opposite-sign muon channels. The uncertainty is statistical.

Background Same sign Opposite sign $W$ $\rightarrow$ $\mu$ $\nu$
$1$.3${}\pm{}$ $1$.3 $3$.8${}\pm{}$ $2$.3 ${b}{\overline{b}}$ $2$.4${}\pm{}$
$2$.4 $2$.4${}\pm{}$ $2$.4 $Z$ $\rightarrow$ $\mu$ $\mu$ $0$.7${}\pm{}$ $0$.5
$1$670${}\pm{}$ $1$50 light QCD $0$.3${}\pm{}$ $1$.4 $3$.1${}\pm{}$ $5$.4

The templates for both signal and background contributions are determined from
simulation. The light QCD background is assumed to have the same shape as the
${{b}{\overline{b}}}$ background and therefore a single component is included
in the fit for both.

###  4.4 Results

The number of events observed in data in the signal region amounts to 8 and
2147 for same-sign and opposite-sign muons, respectively. A single fit to the
Run 1 data is performed since the 2011 and 2012 templates are found to be
compatible. The distributions of the invariant mass
$m({\mu}_{N}{\text{\,jet}})$ for same-sign and opposite-sign muon data are
shown in Fig. 4 with the fits for the $15\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$
neutrino mass hypothesis superimposed. No significant excess of signal is
observed in the data for this or any other mass hypothesis. Upper limits at
95% confidence level on
${\mathcal{B}}(N\rightarrow{\mu}{\text{\,jet}})\left|V_{{\mu}N}\right|^{2}$
are set for each heavy-neutrino mass hypothesis using the CLs method [57] with
a one-sided profile likelihood ratio [58] as test statistic. The upper limits
as a function of heavy-neutrino mass are shown in Fig. 5. For the same-sign
muons sample and neutrino mass in excess of
$20\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, the measured limit is between 2 and
3.8 standard deviations above the expected limit. The worse limit obtained
with respect to the expectation can be attributed to the four data candidates
with $m({\mu}{\text{\,jet}})$ between $20$ and
$40\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. The value of the muon identification
BDTs for three of the candidates are very close to the requirements, defined a
priori with a blinded procedure, indicating that they are background-like and
probably a QCD fluctuation. Each candidate has also a relatively large value
for the missing transverse momentum in the event, which is not characteristic
for the signal. Consequently, the excess at high mass is likely the result of
an imperfectly modelled component of the background. For the opposite-sign
muons samples, the expected limit is a factor 5 to 10 worse due to the
irreducible background from Drell-Yan processes, in agreement with
expectations.

To set upper limits on the coupling, the results of Fig. 5 are scaled by
${\mathcal{B}}(N\rightarrow{\mu}{\text{\,jet}})=0.51$, computed as described
in Section 1 assuming
$\left|V_{{e}N}\right|^{2}=\left|V_{{\tau}N}\right|^{2}=0$. For the
$5\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ heavy-neutrino mass hypothesis, at the
limit set, the heavy neutrino is expected to be long-lived with a lifetime of
$3.8\text{\,ps}$ and $1.1\text{\,ps}$ for same- and opposite-sign muons in the
final states, respectively. Since this search targets prompt heavy neutrinos,
the acceptance is corrected accordingly. The constraints on the coupling as a
function of mass for the opposite- and same-sign muons final state, with and
without the acceptance correction factor applied, are illustrated in Fig. 6.

Figure 4: Distributions of the invariant mass $m({\mu}_{N}{\text{\,jet}})$ for
(left) same-sign and (right) opposite-sign muons. The signal component
corresponds to a $15\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ neutrino.

Figure 5: Expected (dashed line) and observed (solid line) upper limit on
${\mathcal{B}}(N\rightarrow{\mu}{\text{\,jet}})\left|V_{{\mu}N}\right|^{2}$ at
95% C.L. for (left) the same-sign muons sample and (right) the opposite-sign
muons sample. The light and dark green bands show the $1\sigma$ and $2\sigma$
uncertainties, respectively, on the expected upper limits.

Figure 6: Observed upper limit on the mixing parameter
$\left|V_{{\mu}N}\right|^{2}$ between a heavy neutrino and a muon neutrino in
the mass range $5-50\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ for same-sign and
opposite-sign muons in the final states with and without lifetime correction.

##  5 Conclusion

A search for a prompt heavy neutrino in the decay
$N\rightarrow\mu{\text{\,jet}}$ is performed using data from proton-proton
collisions recorded by the LHCb experiment, corresponding to a total
integrated luminosity of $3\text{\,fb}^{-1}$. No evidence for heavy neutrinos
is observed and limits of the order of $10^{-4}$ and $10^{-3}$ are set as a
function of heavy-neutrino mass for lepton-number-conserving and lepton-
number-violating decays, respectively. These represent the first limits on the
coupling to a heavy neutrino in the mass range
5-$50\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ at LHCb. For the first time the
signature of two muons and a low mass jet has been probed for heavy neutrinos
with mass lower than $20\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. Furthermore,
this is the first limit on lepton-number-conserving decays of a prompt heavy
neutrino in the mass range of interest. The observed limits on lepton-number-
violating decays are not yet competitive with the existing limits [4, 19, 18].
With an integrated luminosity of $50\text{\,fb}^{-1}$, a better sensitivity
than the current most stringent limit could be reached for the same-sign muons
channel. While this analysis targets prompt heavy-neutrino decays, better
sensitivity for low heavy-neutrino masses can be achieved by including long-
lived signatures.

## Acknowledgements

We would like to thank Dr. Brian Shuve of the Harvey Mudd College for the help
with the event generation model and for cross-checking the calculations shown
in Fig. 1. 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.
Afsharnia9, C.A. Aidala84, S. Aiola25, Z. Ajaltouni9, S. Akar64, J.
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G. Alkhazov37, P. Alvarez Cartelle47, S. Amato2, Y. Amhis11, L. An21, L.
Anderlini21, A. Andreianov37, M. Andreotti20, F. Archilli16, A. Artamonov43,
M. Artuso67, K. Arzymatov41, E. Aslanides10, M. Atzeni49, B. Audurier11, S.
Bachmann16, M. Bachmayer48, J.J. Back55, S. Baker60, P. Baladron Rodriguez45,
V. Balagura11, W. Baldini20, J. Baptista Leite1, R.J. Barlow61, S. Barsuk11,
W. Barter60, M. Bartolini23,i, F. Baryshnikov80, J.M. Basels13, G. Bassi28, B.
Batsukh67, A. Battig14, A. Bay48, M. Becker14, F. Bedeschi28, I. Bediaga1, A.
Beiter67, V. Belavin41, S. Belin26, V. Bellee48, K. Belous43, I. Belov39, I.
Belyaev38, G. Bencivenni22, E. Ben-Haim12, A. Berezhnoy39, R. Bernet49, D.
Berninghoff16, H.C. Bernstein67, C. Bertella47, E. Bertholet12, A. Bertolin27,
C. Betancourt49, F. Betti19,e, M.O. Bettler54, Ia. Bezshyiko49, S. Bhasin53,
J. Bhom33, L. Bian72, M.S. Bieker14, S. Bifani52, P. Billoir12, M. Birch60,
F.C.R. Bishop54, A. Bizzeti21,s, M. Bjørn62, M.P. Blago47, T. Blake55, F.
Blanc48, S. Blusk67, D. Bobulska58, V. Bocci30, J.A. Boelhauve14, O. Boente
Garcia45, T. Boettcher63, A. Boldyrev81, A. Bondar42,v, N. Bondar37, S.
Borghi61, M. Borisyak41, M. Borsato16, J.T. Borsuk33, S.A. Bouchiba48, T.J.V.
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A. Buonaura49, C. Burr47, A. Bursche26, A. Butkevich40, J.S. Butter31, J.
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Calefice14, L. Calero Diaz22, S. Cali22, R. Calladine52, M. Calvi24,j, M.
Calvo Gomez83, P. Camargo Magalhaes53, A. Camboni44, P. Campana22, D.H.
Campora Perez47, A.F. Campoverde Quezada5, S. Capelli24,j, L. Capriotti19,e,
A. Carbone19,e, G. Carboni29, R. Cardinale23,i, A. Cardini26, I. Carli6, P.
Carniti24,j, L. Carus13, K. Carvalho Akiba31, A. Casais Vidal45, G. Casse59,
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M.G. Chapman53, M. Charles12, Ph. Charpentier47, G. Chatzikonstantinidis52,
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R.E. Geertsema31, D. Gerick16, L.L. Gerken14, E. Gersabeck61, M. Gersabeck61,
T. Gershon55, D. Gerstel10, Ph. Ghez8, V. Gibson54, M. Giovannetti22,k, A.
Gioventù45, P. Gironella Gironell44, L. Giubega36, C. Giugliano20,g, K.
Gizdov57, E.L. Gkougkousis47, V.V. Gligorov12, C. Göbel69, E. Golobardes83, D.
Golubkov38, A. Golutvin60,80, A. Gomes1,a, S. Gomez Fernandez44, F. Goncalves
Abrantes69, M. Goncerz33, G. Gong3, P. Gorbounov38, I.V. Gorelov39, C.
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Günther16, E. Gushchin40, A. Guth13, Y. Guz43,47, T. Gys47, T. Hadavizadeh68,
G. Haefeli48, C. Haen47, J. Haimberger47, S.C. Haines54, T. Halewood-leagas59,
P.M. Hamilton65, Q. Han7, X. Han16, T.H. Hancock62, S. Hansmann-Menzemer16, N.
Harnew62, T. Harrison59, C. Hasse47, M. Hatch47, J. He5, M. Hecker60, K.
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Heuel13, A. Hicheur2, D. Hill62, M. Hilton61, S.E. Hollitt14, P.H. Hopchev48,
J. Hu16, J. Hu71, W. Hu7, W. Huang5, X. Huang72, W. Hulsbergen31, R.J.
Hunter55, M. Hushchyn81, D. Hutchcroft59, D. Hynds31, P. Ibis14, M. Idzik34,
D. Ilin37, P. Ilten52, A. Inglessi37, A. Ishteev80, K. Ivshin37, R.
Jacobsson47, S. Jakobsen47, E. Jans31, B.K. Jashal46, A. Jawahery65, V.
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Jones55, B. Jost47, N. Jurik47, S. Kandybei50, Y. Kang3, M. Karacson47, J.M.
Kariuki53, N. Kazeev81, M. Kecke16, F. Keizer54,47, M. Kenzie55, T. Ketel32,
B. Khanji47, A. Kharisova82, S. Kholodenko43, K.E. Kim67, T. Kirn13, V.S.
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Lucio Martinez31, V. Lukashenko31, Y. Luo3, A. Lupato61, E. Luppi20,g, O.
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Mitchell57, B. Mitreska61, D.S. Mitzel47, A. Mödden14, R.A. Mohammed62, R.D.
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R. Nandakumar56, T. Nanut48, I. Nasteva2, M. Needham57, I. Neri20,g, N.
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Mau48, E.M. Niel11, S. Nieswand13, N. Nikitin39, N.S. Nolte47, C. Nunez84, A.
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Resmi P.K10, V. Placinta36, S. Playfer57, J. Plews52, M. Plo Casasus45, F.
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M. Rotondo22, M.S. Rudolph67, T. Ruf47, J. Ruiz Vidal46, A. Ryzhikov81, J.
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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
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
68School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 55
69Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
70Physics and Micro Electronic College, Hunan University, Changsha City,
China, associated to 7
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
83DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 44
84University 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
mUniversità di Padova, Padova, Italy
nUniversità di Pisa, Pisa, Italy
oUniversità degli Studi di Milano, Milano, Italy
pUniversità di Urbino, Urbino, Italy
qUniversità della Basilicata, Potenza, Italy
rScuola Normale Superiore, Pisa, Italy
sUniversità di Modena e Reggio Emilia, Modena, Italy
tUniversità di Siena, Siena, Italy
uMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
vNovosibirsk State University, Novosibirsk, Russia
wINFN Sezione di Trieste, Trieste, Italy