Searches for lepton number violating K+ decays

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Articlehistory: Received21May2019

Receivedinrevisedform1July2019 Accepted18July2019

Availableonline23July2019 Editor: W.-D.Schlatter

TheNA62experimentatCERNreportsasearchfortheleptonnumberviolatingdecaysK+→

π

−e+e+ and K+_→

π

−

μ

+

μ

+usingadata samplecollectedin2017.Nosignalsare observed,andupperlimits onthebranchingfractionsofthesedecaysof2.2×10−10 _and4.2×10−11 _{areobtained,respectively,at}

90%confidencelevel.Theseupper limitsimproveonpreviouslyreportedmeasurementsbyfactorsof3 and2,respectively.

©2019TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

0. Introduction

In the Standard Model (SM), neutrinos are strictly massless duetotheabsenceofright-handedchiralstates.Thediscoveryof neutrinooscillationshasconclusivelydemonstratedthatneutrinos havenon-zero masses. Therefore the observationof lepton num-berviolatingprocessesinvolvingchargedleptonswouldverifythe Majorananatureoftheneutrino.

The decays of the charged kaon K+

→

π

−



+



+ (where



=

e

,

μ

), violating conservationoflepton numberby twounits,may be mediated by a massive Majorana neutrino [1,2]. The current limits at 90% CL on the branching fractions of these decays are

B(

K+

→

π

−e+e+

)

<

6

.

4

×

10−10 _{obtainedby the BNL E865}

ex-periment [3],and

B(

K+

→

π

−

μ

+

μ

+

)

<

8

.

6

×

10−11 _obtainedby

theCERNNA48/2 experiment [4].A searchfortheseprocessesin about30%ofthedatacollected bytheNA62experimentatCERN in2016–18isreportedhere.

1. Beam,detectoranddatasample

The layout of the NA62 beamline and detector [5] is shown schematically in Fig. 1. An unseparated beam of

π

+ (70%), pro-tons(23%)andK+ (6%)iscreatedbydirecting400 GeV/c protons extractedfromthe CERN SPS onto a berylliumtarget inspillsof 3 seffectiveduration.Thenominalcentralmomentumofthis

sec-ondarybeamis75 GeV/c with amomentum spreadof1% (rms).

Beamkaonsare taggedwith70 pstime resolutionbya differen-tialCherenkovcounter(KTAG)usinganitrogenradiatorat1.75 bar pressurecontainedina 5 m longvessel. Beamparticlemomenta aremeasured bya three-stationsiliconpixelspectrometer (GTK); inelasticinteractionsofbeamparticleswiththelaststation(GTK3) are detected by an array of scintillator hodoscopes (CHANTI). A dipolemagnet(TRIM5)providing a90 MeV/c horizontal momen-tumkick is located infront of GTK3.The beam isdelivered into avacuumtankcontaininga75 mlongfiducialdecayvolume(FV)

starting 2.6 m downstreamof GTK3.The beamdivergenceat the FV entrance is 0.11 mrad (rms) in both horizontal and vertical planes.DownstreamoftheFV,undecayedbeamparticlescontinue theirpathinvacuum.

Momenta of charged particles produced in K+ decays in the FVare measuredby a magneticspectrometer(STRAW)located in

the vacuum tank downstream of the FV. The spectrometer

con-sistsoffourtrackingchambersmadeofstrawtubes,andadipole

magnet(MNP33)locatedbetweenthesecondandthirdchambers

providingahorizontalmomentumkickof270 MeV/c inadirection oppositetothatproducedbyTRIM5.Theachievedmomentum res-olution

σ

p

/

p liesintherangeof0.3–0.4%.

A ring-imaging Cherenkov detector (RICH), consisting of a

17.5 m long vessel filled with neon at atmospheric pressure, is usedfortheidentificationandtime measurementofcharged par-ticles. The RICH provides a reference trigger time, typically with 70 ps precision.TheCherenkovthresholdforpionsis12.5 GeV/c. Positively andnegatively charged particles havedifferent angular distributionsdownstreamoftheMNP33magnet;theRICHoptical systemisoptimizedto collectlightemitted bypositively charged particles.TwoscintillatorhodoscopesCHOD, whichincludea ma-trix oftiles, aswell astwo orthogonal planesof slabs, arranged infourquadrants)downstreamoftheRICHprovidetriggersignals andtimemeasurementswith200 psprecision.

A27X0 thick quasi-homogeneousliquidkrypton(LKr)

electro-magneticcalorimeterisusedforparticleidentificationandphoton detection. The calorimeterhas an active volume of7 m3_,is

seg-mented in the transverse directioninto 13248projective cells of approximately 2

×

2 cm2_{, and provides an energy resolution of}

σ

E

/

E

= (

4

.

8

/

√

E

⊕

11

/

E

⊕

0

.

9

)

%, where E is expressed in GeV. To achieve hermetic acceptance for photons emitted in K+ de-cays intheFVatanglesup to50 mradtothebeamaxis,theLKr calorimeterissupplementedbyannularleadglassdetectors(LAV) installed in 12 positions around and downstream ofthe FV, and twolead/scintillatorsamplingcalorimeters(IRC,SAC)locatedclose

https://doi.org/10.1016/j.physletb.2019.07.041

0370-2693/©2019TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Fig. 1. Schematic side view of the NA62 beamline and detector. tothebeamaxis.Aniron/scintillatorsamplinghadronic

calorime-terformedoftwomodules(MUV1,2)andamuondetector(MUV3) consistingof 148 scintillatortiles located behind an 80 cm thick ironwallareusedforparticleidentification.

Thedata sampleused forthisanalysisisobtainedfrom2

.

3

×

105 SPS spills recorded over three months of operation in 2017. The typical beamintensity was 2

.

0

×

1012 _{protons per spill,}

cor-respondingtoa meaninstantaneousbeamparticlerateattheFV

entrance of 450 MHz, and a mean K+ decay rate in the FV of

3.5 MHz. Dedicated multi-track, di-electron and di-muon trigger chainsareused.Thelow-level(L0)multi-tracktriggerisbasedon RICH signal multiplicity and a requirement for a coincidence of signalsintwooppositeCHODquadrants.Thedi-electronL0trigger additionally requiresthat atleast 20GeV of energyis deposited in the LKr calorimeter, while the di-muon L0 trigger requires a coincidenceofsignalsfromtwoMUV3tiles.Thesoftware(L1) trig-gerinvolvesbeamK+identificationbyKTAGandreconstructionof a negativelycharged trackinSTRAW.Forsignal-like samples,the measuredinefficienciesoftheCHOD(STRAW)conditionsareatthe 2% (4%)level,whilethose oftheother triggercomponentsare of theorderof 10−3_{.Themulti-track, di-electronanddi-muon}

trig-gerchains were downscaled typically by factorsof 100, 8 and2, respectively.

2. Eventselection

The processes of interest K+

→

π

−



+



+ (denoted “LNV

de-cays”) and the flavour-changing neutral current decays K+

→

π

+



+



−(denoted“SMdecays”)arecollectedconcurrentlythrough thesame triggerchains. The SM decayswith

O(

10−7

₎

_branching

fractionsknownexperimentally toa fewpercentaccuracy [6] are usedfornormalization.Undertheassumptionofsimilarkinematic distributions,thisapproachleadstofirst-ordercancellationofthe effects of detectorinefficiencies, trigger inefficiencies and pileup. Both theLNVandSM decayswithelectrons (muons) inthe final state are denoted as Kπee (Kπμμ), and collectively as Kπ. The principalselectioncriteriaforKπ decaysarelistedbelow.

•

Thedi-electronandmulti-tracktriggerchainsareusedto col-lectKπee candidates,andthedi-muontriggerchainisusedto collectKπμμ candidates.

•

Three-track vertices are reconstructed by extrapolation of STRAWtracks upstream intothe FV, takinginto account the measuredresidualmagneticfieldinthevacuumtank,and se-lecting tripletsoftracks consistent withoriginatingfromthe same point. The presence of exactly one vertex is required. The vertex should be located within the FV and have a

to-talelectricchargeofq

= +

1.Theextrapolationoftheselected tracksintothetransverseplanesofthedownstreamdetectors should be within the corresponding geometrical acceptance. Each pair of selected tracks should be separated by at least

15 mminthefirstSTRAWchamberplanetosuppressphoton

conversions andfaketracks,andinthe Kπee casebyatleast 200 mmintheLKrfrontplanetoavoidshoweroverlap.

•

Reconstructed track momenta should be 8

(

5

)

GeV

/

c

<

p

<

45 GeV

/

c intheKπee (Kπμμ)case.Thetotalmomentum,pvtx,

ofthethreetracksshouldsatisfythecondition

|

pvtx

−

pbeam

|

<

2

.

5 GeV

/

c,where pbeam isthecentral beammomentum. The

total transverse momentum with respect to the beam axis

should be pT

<

30 MeV

/

c.The quantity pbeam andthebeam

axis direction are measured continuously using fully recon-structed K+

→

π

+

π

+

π

−decays.

•

Track times are defined using CHOD information, as well as RICH information inthe Kπee case. The vertextracks are re-quired to be in time within 15 ns ofeach other.The vertex time isdefinedasaweighted averageofthetracktimes, tak-ingintoaccountCHODandRICHtimeresolution.

•

Pioncandidatesarerequiredtohavetheratioofenergy depo-sition intheLKrcalorimeterto momentummeasured by the spectrometer E

/

p

<

0

.

85

(

0

.

9

)

inthe Kπee (Kπμμ) case,and noassociatedin-timeMUV3signalsintheKπμμ case.Electron (e±) candidates are required to have0

.

9

<

E

/

p

<

1

.

1. Muon candidates are identified by requiring E

/

p

<

0

.

2 and a geo-metrically associated MUV3signal within 5 ns ofthe vertex time.Thevertexshouldincludeapioncandidateandtwo lep-ton candidates of the same flavour. The conditions used for

π

±, e± and

μ

± identification are mutually exclusive within eachselection.

ThefollowingadditionalconditionsareappliedintheKπee case.

•

An identification algorithm basedon the likelihoods of mass hypothesesevaluated usingtheRICHsignal pattern [7] is ap-plied to e+ candidates. The algorithm considers each track independently. The angles between track pairs in the RICH

are required to exceed 4 mrad to reduce overlaps between

Cherenkovlight-cones, decreasingthe acceptanceofboth the SM and LNV selections by 7% in relative terms. A selection withoute+identificationintheRICHandwithouttheangular separationrequirementisusedforbackgroundvalidation;itis referredtoastheauxiliaryselection,asopposedtothestandard selection.

•

To suppress backgrounds from K+

→

π

+

π

0

D and K+

→

π

0

Forthe SM decays,the signal regions are definedin termsof thereconstructed

π



massas470 MeV

/

c2

_<

_mπee

_<

_{505 MeV}

_/

_c2

in the Kπee case (asymmetric with respect to the nominal K+

massmK [6] to accountfortheradiativetail),and484 MeV

/

c2

<

mπμμ

<

504 MeV

/

c2 _{inthe Kπμμ case.ForLNVdecays,themass}

regionsdefinedaboveweremaskedfordataeventsuntilthe com-pletionofthebackgroundevaluation.TheLNVsignalmassregions aredefinedby tighter conditions

|

mπ

−

mK

|

<

3

· δ

mπ,where

δ

mπee

=

1

.

7 MeV

/

c2 and

δ

mπμμ

=

1

.

1 MeV

/

c2 are themass

res-olutionsmeasured fromthe datafor the SM decays. The control regionsmπee

<

470 MeV

/

c2 andmπμμ

<

484 MeV

/

c2 withinboth

theSM andLNVselections were usedforvalidation ofthe back-groundevaluationprocedures.

3. Backgroundevaluation

Acceptancesandbackgroundsareevaluated usingMonteCarlo (MC)simulationbasedontheGeant4toolkit [8] todescribe detec-torgeometryand response.Certain aspectsof thesimulation are tunedusinginputfromthedata,anddata-drivenmethodsare em-ployedtoaddressspecificbackgroundsources.

3.1. Kπeeanalysis

Backgrounds to the Kπee processes arise from misidentifica-tion ofpions aselectrons andvice versa. Background evaluation is based on simulations involving the measured pion (

π

±) and electron(e±) identificationefficiencies

ε

_{π ,}±

ε

e±,aswellaspionto

electron( P±_πe)andelectrontopion( P±_{eπ )}misidentification proba-bilities.Eachquantityismeasuredasafunctionofmomentum us-ingpionandpositronsamplesobtainedfromkinematicselections of K+

→

π

+

π

+

π

− and K+

→

π

0_e+

_ν

_{decays, withthe residual}

K+

→

π

+

π

0 _{background subtracted in the latter case. The}

re-sults of the measurements are summarized in Table 1. The LKr calorimeterresponse is known to be the same forelectrons and positrons [9].Thetypicalinefficiencies1

−

ε

±_π,e and

misidentifica-tionprobabilitiesare

O(

10−2

)

withweakmomentumdependence, exceptfor the

π

+ misidentificationprobability P_πe+ whichhas a minimumof10−5 _{atamomentum of25 GeV/c,andincreasesto}

2

×

10−3 at10 GeV/c andto10−4 at45 GeV/c. The momentum-dependenceofP+_πe isduetotheRICHCherenkovthresholdatlow momentum,andthesimilarityofRICHresponsetoe+ and

π

+ at

highmomentum.

The reconstructed

π

+e+e− mass spectra obtained within the standard andauxiliary SM selections, along with thebackground estimates,areshowninFig.2(left).Theprincipalbackgroundsin

1 _{Itshouldbenotedhoweverthatthe K}+_→π+_e+_e− _{decayisobservedwith} negligiblebackgroundalsointhemassrangemee<100 MeV/c2.

decays inflight

π

±

→

e±

ν

are found to be negligible.The back-ground in the SM control mass region is simulated to 15% (1%) relative precision within the standard (auxiliary) selection. The limited precision in theformer case stems fromthe dependence of the response of the RICH positron identificationalgorithm on theeventtopologyinamulti-trackenvironmentduetothepartial overlapofCherenkovlight-cones,whichisdifficulttoaccount for accurately.

The reconstructed

π

−e+e+ mass spectra obtained within the standard and auxiliary LNV selections are displayed in Fig. 2

(right).DuetothepresenceoftwopositronsintheLNVfinalstate, backgrounds in the control mass region from K+

→

π

+

π

+

π

− and K+

→

π

+

π

−e+

ν

decaysare reduced by positron identifica-tion intheRICH by factorsof5

×

104 _{and200, respectively. Five}

events are observed in the control mass region within the stan-dard selection, inagreement withtheexpected backgroundfrom simulation of5

.

58

±

0

.

06stat. The background inthe LNVcontrol

mass region within the auxiliary selection is described by simu-lationto 4% relative precision.Positronidentification intheRICH suppressestheotherwise dominantbackgroundtotheLNVsignal from K+

→

π

+

π

0

D and K+

→

π

+e+e− decays with

π

+ and e−

misidentification,andreducestheoverallestimatedbackgroundto theLNVsignalbyafactorof 6.ContributionsfromK+

→

π

+

π

0

D D

decaysandmultiplephotonconversionsare concludedtobe neg-ligiblefromastudyofthedatasampleselectedwithvertexcharge requirementq

= +

3.

The remaining backgrounds in the LNV signal region are due to K+

→

π

0

De+

ν

and K+

→

e+

ν

e+e− decays withe−

misidenti-fied as

π

−.The K+

→

e+

ν

e+e− decay issimulatedaccording to Ref. [10]. The contributionsfrom thesetwo decaysare estimated to be 0

.

12

±

0

.

02stat and0

.

04

±

0

.

01stat events, respectively.The

totalexpectedbackgroundintheLNVsignalregionis

NB

=

0

.

16

±

0

.

03

,

wheretheerrorincludes asystematicuncertaintyof15% in rela-tivetermstoaccountfortheprecisionofthebackground descrip-tioninthecontrolmassregions.

3.2. Kπμμ analysis

BackgroundstotheKπμμ processesarisefromthree-trackkaon decays (mainly K+

→

π

+

π

+

π

−) via pion decays in flight and

π



μ

misidentification. Whilethepiondecaysareimplemented accuratelyinthesimulation,misidentificationprocessescannotbe reproducedreliablyandrequirededicatedstudiesbasedoncontrol datasamples.

•

Apioncanbe misidentifiedasamuon duetopunchthrough the iron wall or pileup activityin MUV3. The pileup is sim-ulated using the measured out-of-time signal rates in each

Fig. 2. ReconstructedmassspectrafortheSM(leftcolumn)and LNV(rightcolumn)πee candidatesobtainedwithinthestandard selection(toprow)andtheauxiliary selectionwithoutpositronidentificationintheRICH(bottomrow).Dataareoverlayedwithbackgroundestimatesbasedonsimulations.TheSMsignalregionisindicated witharrows.Theshadedverticalbandsindicatetheregionmaskedduringtheanalysis,includingtheLNVsignalregionboundedbydashedlines.

MUV3tile(themeantotalsignalrateintheMUV3detectoris 16 MHz).Theestimatedpiontomuonmisidentification proba-bility,Pπμ

(

p

)

,variesasafunctionofmomentump from0.9% at5 GeV/c to0.4%at45 GeV/c.Thisdependencearisesmainly becausethegeometricalassociationofMUV3signalstotracks involvesasearchradiuswhosesizevariesinverselywith mo-mentumtoaccountformultiplescattering.Thisoptimizesthe performance,leading to uniformidentificationefficiencyover

momentumandminimalmisidentification.

•

A muon can be misidentified asa pion due to MUV3

ineffi-ciency,whichismeasuredusingdatasamplesofkinematically selectedK+

→

μ

+

ν

decaysandbeamhalomuonstobe0.15%,

withnegligiblegeometricandmomentumdependence.

ThecontributiontotheLNVsamplefrom K+

→

π

+

π

+

π

− de-cays with no pion decays in flight, and both

π

+ misidentified as

μ

+, is estimated using a control data sample collected with the multi-track trigger chain (i.e. without muon identification at thetriggerlevel).ThefullLNVeventselectionisapplied,however

theparticleidentificationcriteriaareinvertedtoselect

π

+

π

+

π

− vertices. Identification of the

μ

+

μ

+ pair is then enforced, and a weight of Pπμ

(

p1

)

·

Pπμ

(

p2

)

·

D1

/

D2 is applied to the event,

where p1,2 are the reconstructed momentaof the twoidentified

π

+ tracks, D1 is the downscaling factor of the multi-track

trig-gerchain,and D2 is thatofthe di-muonchain.The contribution

from K+

→

π

+

π

+

π

− decayswithone

π

+ decayingandanother

π

+ misidentified as

μ

+ isestimated in a similar wayusing the samedatasample,selecting

π

+

π

−

μ

+ vertices,enforcing identifi-cationofthesecond

μ

+andassigningaweightofPπμ

(

p

)

·

D1

/

D2,

where p isthemomentumoftheidentified

π

+track.

The contributionfrom K+

→

π

+

π

+

π

− decaytopologieswith atleasttwo piondecaysinflight,accountingfor70%ofthe back-ground in the control mass region, does not necessarily involve

pion misidentification and cannot be estimated with the above

data-drivenmethod.Itisthereforestudiedwithadedicated simu-lation.ToproducetherequiredMC sampleequivalent to

O(

1011

)

K+

→

π

+

π

+

π

− decays, only the topologies with at least two pion decays in flight (accounting for 4% of all events) are

simu-isreplacedby afastemulation oftheir responses.Pion decaysin flighttypicallyleadtoreconstructed

π μμ

massvalueswellbelow the K+mass.However highmassvalueswithinthesignal region

may be reconstructed due to pion decays in the 7 m long

vol-umebetweentheMNP33 magnetandthethird STRAW chamber

leadingtoabiasedmomentummeasurement.Thesimulationalso includesK+

→

π

+

π

+

π

−decaysupstreamofthevacuumtank,in whichcase trackbending by the TRIM5magnet maylead to re-constructionofthedecayvertexintheFVwithalteredkinematic properties.

Contributionsto the background fromthe rare decays K+

→

π

+

μ

+

μ

−,K+

→

π

+

π

−

μ

+

ν

,K+

→

π

+

π

−e+

ν

, K+

→

μ

+

μ

−

μ

+

ν

areestimatedwithfullsimulations.Thelastprocess,notmeasured yet, is simulated according to Ref. [10]. Contributions from the

K+

→

π

0

D

μ

+

ν

andK+

→

π

+

π

D0 decayswith

O(

10−3

)

branching

fractionsande± particles inthe final state are found tobe neg-ligibleusing a technique similar to that described inSection 3.1. Thecontributionfrommultiplein-timekaondecaysisfoundtobe negligibleusingselectionswithmodifiedtracktimingconsistency requirements,andallowingformultiplevertices.

Thereconstructed

π μμ

massspectraobtainedwithin the SM andtheLNVselectionsareshowninFig.3.Thecontrol-region pop-ulationsobtainedfromdataandsimulationagreetowithin3%for both selections, which validates the background description. The estimatedbackgroundcontributionsintheLNVsignalmassregion fromallidentifiedsourcesarelistedinTable2.Theexpected back-groundis

NB

=

0

.

91

±

0

.

41

,

wheretheuncertaintyisstatisticalduetothesizesofthecontrol andsimulated data samples, while the systematic uncertainty is expectedtobenegligible.

4. Results

Theinformationquantifyingthesensitivitiesofthetwosearches issummarizedinTable3.ItincludesthenumbersofselectedSM

assumptions, aswell as the charge asymmetry of the geometric acceptance induced by the magnetsin the beamline and detec-tor, and also the SM selection condition mee

>

140 MeV/c2 _and

positronidentificationintheRICHinthe Kπee case.Uncertainties on the ratios Aπ

/

ALNV_π are negligible withrespect to statistical uncertaintieson Nπ andexternaluncertainties on

B

π.The ra-tioNπ μμ_K

/

Nπ_Kee

=

3

.

7 isdeterminedbythedownscalingfactorsof thetriggerchainsusedforthetwoanalyses.

AfterunmaskingtheLNVmassregions,noeventsareobserved inthe Kπee signal regionandoneeventisobserved inthe Kπμμ

signal region. An additional cross-check of the background

esti-mate is performed in the LNV masked regions but outside the

signal regions: no events are (one event is) observed for Kπee

(Kπμμ),whichisconsistentwiththeexpectationof0

.

46

±

0

.

04stat

(1

.

05

±

0

.

46stat)backgroundevents.

Upperlimitsonthesignalbranchingfractionsareobtained us-ing the CLs method [13]. In each case, the number of observed

events in the LNV signal region and the single event sensitivity with its uncertainty are takenas inputs, and theexpected back-grounds are treated using Bayesian inference involving posterior PDFsevaluatedassuminguniformpriorprobabilities.Theresulting upperlimitsat90% CLobtainedundertheassumptionofuniform phasespacedensityare

B

(

K+

→

π

−e+e+

) <

2

.

2

×

10−10

,

B

(

K+

→

π

−

μ

+

μ

+

) <

4

.

2

×

10−11

.

Weemphasizethattheseresults,andallother resultsofsearches forLNVdecays,dependonthephasespacedensityassumptions.

5. Summary

Searches for lepton number violating decays K+

→

π

−e+e+

andK+

→

π

−

μ

+

μ

+havebeenperformedusingabout30%ofthe datacollected by the NA62experiment atCERNin 2016–18.The sensitivities arenot limitedby backgrounds,andtheupperlimits obtainedonthedecayratesimproveonpreviously reported mea-surementsbyfactorsof3and2,respectively.

Table 3

Quantitiesinvolvedinthecomputationofthesingleeventsensitivities.ThemostaccurateBπ μμmeasurement [12] is

usedratherthanthelessprecisePDGaverage [6].ThestatisticaluncertaintiesonAπ andALNVπ arenegligibleandthe

systematicuncertainties,whichlargelycancelintheacceptanceratiosbetweenSMandLNVdecays,arenotquoted.

Kπeeanalysis Kπ μμanalysis

SM candidates selected Nπ  2484 8357

Background contamination f negligible 7×10−4

Acceptance Aπ  3.87% 10.93%

Acceptance ALNV

π  4.98% 9.81%

Branching fractionBπ ×107 3.00±0.09 [6] 0.962±0.025 [12]

Number of decays in FV Nπ 

K /1011 2.14±0.04stat±0.06ext 7.94±0.09stat±0.21ext Single event sensitivity Sπ  (0.94±0.03)×10−10

Fig. 3. ReconstructedmassspectraoftheSMπ+μ+μ−(left)andLNVπ−μ+μ+ (right)finalstates:dataareoverlayedwithbackgroundestimatesbasedonsimulations. Backgroundestimatesbasedoncontroldatasamplesarenotshown.TheSMsignalregionisindicatedwitharrows.Theshadedverticalbandindicatestheregionmasked duringtheanalysis,includingtheLNVsignalregionboundedbydashedlines.

Acknowledgements

Itis a pleasureto expressourappreciation tothe staffofthe CERN laboratoryandthe technicalstaffs of theparticipating lab-oratoriesanduniversities fortheir effortsinthe operationofthe experimentanddataprocessing.

Thecostofthe experimentandits auxiliarysystemswas sup-portedbythefundingagenciesoftheCollaborationInstitutes.We are particularly indebted to: F.R.S.-FNRS (Fonds De La Recherche Scientifique- FNRS), Belgium;BMES(MinistryofEducation,Youth and Science), Bulgaria; NSERC (Natural Sciences and Engineer-ing Research Council), Canada; NRC (National Research Council Canada)contributiontoTRIUMF,Canada;MEYS(Ministryof Educa-tion,YouthandSports),CzechRepublic;BMBF(Bundesministerium

für Bildung und Forschung) contracts 05H12UM5, 05H15UMCNA

and 05H18UMCNA, Germany; INFN (Istituto Nazionale di Fisica

Nucleare), Italy; MIUR (Ministero dell’Istruzione, dell’Università e dellaRicerca),Italy; CONACyT(ConsejoNacionaldeCienciay Tec-nología),Mexico;IFA (InstituteofAtomic Physics),Romania; INR-RAS(InstituteforNuclearResearchoftheRussianAcademyof Sci-ences),Moscow,Russia;JINR(JointInstituteforNuclearResearch), Dubna, Russia; NRC (National Research Center) “Kurchatov Insti-tute”andMESRF(MinistryofEducationandScienceoftheRussian Federation), Russia; MESRS (Ministry of Education, Science, Re-searchandSportoftheSlovakRepublic),Slovakia;CERN(European OrganizationforNuclearResearch),Switzerland;STFC(Scienceand TechnologyFacilitiesCouncil),UnitedKingdom;NSF(National

Sci-ence Foundation)Award Number 1506088, U.S.A.;ERC (European

ResearchCouncil)“UniversaLepto”advancedgrant 268062, “Kaon-Lepton”startinggrant336581,Europe.

Individualshavereceived supportfrom:CharlesUniversity Re-search Center (UNCE/SCI/013), Czech Republic; Ministry of Edu-cation, Universities and Research (MIUR “Futuro in ricerca 2012” grant RBFR12JF2Z, Project GAP),Italy; RussianFoundation for Ba-sicResearch(RFBRgrants 18-32-00072,18-32-00245),Russia;the

Royal Society (grants UF100308, UF0758946), United Kingdom;

STFC(RutherfordfellowshipsST/J00412X/1,ST/M005798/1),United Kingdom; ERC(grants268062, 336581 andstarting grant802836 “AxScale”).

References

[1]L.Littenberg,R.Shrock,Phys.Lett.B491(2000)285. [2]A.Atre,etal.,J.HighEnergyPhys.0905(2009)030. [3]R.Appel,etal.,Phys.Rev.Lett.85(2000)2877. [4]J.R.Batley,etal.,Phys.Lett.B769(2017)67. [5]E.CortinaGil,etal.,J.Instrum.12(2017)P05025. [6]M.Tanabashi,etal.,Phys.Rev.D98(2018)030001. [7]U.Müller,etal.,Nucl.Instrum.MethodsA343(1994)279. [8]S.Agostinelli,etal.,Nucl.Instrum.MethodsA506(2003)250. [9]V.Fanti,etal.,Nucl.Instrum.MethodsA574(2007)433. [10]J.Bijnens,G.Ecker,J.Gasser,Nucl.Phys.B396(1993)81. [11]J.R.Batley,etal.,Phys.Lett.B677(2009)246. [12]J.R.Batley,etal.,Phys.Lett.B697(2011)107. [13]A.L.Read,J.Phys.G28(2002)2693.

NA62Collaboration

E. Cortina Gil,

A. Kleimenova,

E. Minucci

1

,

S. Padolski

2

,

P. Petrov,

A. Shaikhiev

3

,

R. Volpe

UniversitéCatholiquedeLouvain,Louvain-La-Neuve,Belgium

T. Numao,

Y. Petrov,

B. Velghe

A. Cotta Ramusino,

A. Gianoli

INFN,SezionediFerrara,Ferrara,Italy

E. Iacopini,

G. Latino,

M. Lenti,

A. Parenti

DipartimentodiFisicaeAstronomiadell’UniversitàeINFN,SezionediFirenze,SestoFiorentino,Italy

A. Bizzeti

8

,

F. Bucci

INFN,SezionediFirenze,SestoFiorentino,Italy

A. Antonelli,

G. Georgiev

9

,

V. Kozhuharov

9

,

G. Lanfranchi,

G. Mannocchi,

S. Martellotti,

M. Moulson,

T. Spadaro

LaboratoriNazionalidiFrascati,Frascati,Italy

F. Ambrosino,

T. Capussela,

M. Corvino,

D. Di Filippo,

P. Massarotti,

M. Mirra,

M. Napolitano,

G. Saracino

DipartimentodiFisica“EttorePancini”eINFN,SezionediNapoli,Napoli,Italy

G. Anzivino,

F. Brizioli,

E. Imbergamo,

R. Lollini,

R. Piandani,

C. Santoni

DipartimentodiFisicaeGeologiadell’UniversitàeINFN,SezionediPerugia,Perugia,Italy

M. Barbanera

10

,

P. Cenci,

B. Checcucci,

P. Lubrano,

M. Lupi

11

,

M. Pepe,

M. Piccini

INFN,SezionediPerugia,Perugia,Italy

F. Costantini,

L. Di Lella,

N. Doble,

M. Giorgi,

S. Giudici,

G. Lamanna,

E. Lari,

E. Pedreschi,

M. Sozzi

DipartimentodiFisicadell’UniversitàeINFN,SezionediPisa,Pisa,Italy

C. Cerri,

R. Fantechi,

L. Pontisso,

F. Spinella

INFN,SezionediPisa,Pisa,Italy

I. Mannelli

ScuolaNormaleSuperioreeINFN,SezionediPisa,Pisa,Italy

G. D’Agostini,

M. Raggi

DipartimentodiFisica,SapienzaUniversitàdiRomaeINFN,SezionediRomaI,Roma,Italy

A. Biagioni,

E. Leonardi,

A. Lonardo,

P. Valente,

P. Vicini

INFN,SezionediRomaI,Roma,Italy

R. Ammendola,

V. Bonaiuto

12

,

A. Fucci,

A. Salamon,

F. Sargeni

13

R. Arcidiacono

14

,

B. Bloch-Devaux,

M. Boretto

15

,

E. Menichetti,

E. Migliore,

D. Soldi

DipartimentodiFisicadell’UniversitàeINFN,SezionediTorino,Torino,Italy

C. Biino,

A. Filippi,

F. Marchetto

INFN,SezionediTorino,Torino,Italy

J. Engelfried,

N. Estrada-Tristan

16

InstitutodeFísica,UniversidadAutónomadeSanLuisPotosí,SanLuisPotosí,Mexico

A.M. Bragadireanu,

S.A. Ghinescu,

O.E. Hutanu

HoriaHulubeinationalInstituteofPhysicsandNuclearEngineering,Bucharest-Magurele,Romania

T. Enik,

V. Falaleev,

V. Kekelidze,

A. Korotkova,

L. Litov

9

,

D. Madigozhin,

M. Misheva

17

,

N. Molokanova,

S. Movchan,

I. Polenkevich,

Yu. Potrebenikov,

S. Shkarovskiy,

A. Zinchenko

†

JointInstituteforNuclearResearch,Dubna,Russia

S. Fedotov,

E. Gushchin,

A. Khotyantsev,

Y. Kudenko

18

,

V. Kurochka,

M. Medvedeva,

A. Mefodev

InstituteforNuclearResearchoftheRussianAcademyofSciences,Moscow,Russia

S. Kholodenko,

V. Kurshetsov,

V. Obraztsov,

A. Ostankov,

V. Semenov

†

,

V. Sugonyaev,

O. Yushchenko

InstituteforHighEnergyPhysics–StateResearchCenterofRussianFederation,Protvino,Russia

L. Bician,

T. Blazek,

V. Cerny,

Z. Kucerova

FacultyofMathematics,PhysicsandInformatics,ComeniusUniversity,Bratislava,Slovakia

J. Bernhard,

A. Ceccucci,

H. Danielsson,

N. De Simone

19

,

F. Duval,

B. Döbrich,

L. Federici,

E. Gamberini,

L. Gatignon,

R. Guida,

F. Hahn

†

,

E.B. Holzer,

B. Jenninger,

M. Koval,

P. Laycock

2

,

G. Lehmann Miotto,

P. Lichard,

A. Mapelli,

R. Marchevski,

K. Massri,

M. Noy,

V. Palladino

20

,

M. Perrin-Terrin

21

,

22

_,

_{J. Pinzino,}

V. Ryjov,

S. Schuchmann,

S. Venditti

CERN,EuropeanOrganizationforNuclearResearch,Geneva,Switzerland

T. Bache,

M.B. Brunetti,

V. Duk,

V. Fascianelli

23

,

J.R. Fry,

F. Gonnella,

E. Goudzovski

∗

,

L. Iacobuzio,

C. Lazzeroni,

N. Lurkin,

F. Newson,

C. Parkinson,

A. Romano,

A. Sergi,

A. Sturgess,

J. Swallow

UniversityofBirmingham,Birmingham,UnitedKingdom

H. Heath,

R. Page,

S. Trilov

UniversityofBristol,Bristol,UnitedKingdom

B. Angelucci,

D. Britton,

C. Graham,

D. Protopopescu

UniversityofGlasgow,Glasgow,UnitedKingdom

J. Carmignani,

J.B. Dainton,

R.W.L. Jones,

G. Ruggiero

UniversityofLancaster,Lancaster,UnitedKingdom

L. Fulton,

D. Hutchcroft,

E. Maurice

24

,

B. Wrona

UniversityofLiverpool,Liverpool,UnitedKingdom

A. Conovaloff,

P. Cooper,

D. Coward

25

,

P. Rubin

GeorgeMasonUniversity,Fairfax,VA,USA

*

Correspondingauthor.

E-mailaddress:Evgueni.Goudzovski@cern.ch(E. Goudzovski). † _Deceased.

Presentaddress:InstituteofNuclearResearchandNuclearEnergyofBulgarianAcademyofScience(INRNE-BAS),BG-1784Sofia,Bulgaria.

18 _{AlsoatNationalResearchNuclearUniversity(MEPhI),115409MoscowandMoscowInstituteofPhysicsandTechnology,141701Moscowregion,Moscow,Russia.} 19 _{Presentaddress:DESY,D-15738Zeuthen,Germany.}

20 _{Presentaddress:PhysicsDepartment,ImperialCollegeLondon,London,SW72BW,UK.}

21 _{Presentaddress:CentredePhysiquedesParticulesdeMarseille,UniversitéAixMarseille,CNRS/IN2P3,F-13288,Marseille,France.} 22 _{AlsoatUniversitéCatholiquedeLouvain,B-1348Louvain-La-Neuve,Belgium.}

23 _{Presentaddress:DipartimentodiPsicologia,UniversitàdiRomaLaSapienza,I-00185Roma,Italy.} 24 _{Presentaddress:LaboratoireLeprinceRinguet,F-91120Palaiseau,France.}