Search for heavy neutral lepton production in K+ decays to positrons

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Articlehistory:

Received20May2020

Receivedinrevisedform19June2020 Accepted28June2020

Availableonline2July2020 Editor:L.Rolandi

Asearchforheavyneutrallepton(N)productioninK+→e+N decaysusingthedatasamplecollectedby theNA62experimentatCERNin2017–2018isreported.Upperlimitsoftheextendedneutrinomixing matrix element|Ue4|2 are establishedatthe level of10−9 overmost oftheaccessibleheavy neutral

leptonmassrange144–462 MeV/c2_{,withtheassumptionthatthelifetimeexceeds50 ns.Theselimits} improvesignificantlyuponthoseofpreviousproductionanddecaysearches.The_|Ue4|2rangefavoured

byBigBangNucleosynthesisisexcludeduptoamassofabout340 MeV/c2_.

©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

0. Introduction

AllStandardModel(SM)fermionsexceptneutrinosareknown to exhibit right-handed chirality. The existence of right-handed neutrinos, or heavy neutral leptons (HNLs), is hypothesised in manySM extensionsinordertogeneratenon-zero massesofthe SMneutrinosviatheseesawmechanism [1].Forexample,the Neu-trinoMinimalStandardModel [2] simultaneouslyaccountsfordark matter,baryogenesis,andneutrinomassesandoscillationsby pos-tulatingtwoHNLsintheMeV–GeVmassrangeandathirdHNL,a darkmattercandidate,atthekeVmassscale.

MixingbetweenHNLs(alsodenoted N below)andactive neu-trinosgivesriseto HNLproductionindecaysofSMparticles and decaysofHNLsintoSM particles.Bothclassesofprocessescanin principlebedetectedexperimentally.Theexpectedbranching frac-tionofthe K+

→ 

+N decay(



=

e,

μ

)is [3]

B

(

K+

→ 

+N

)

=

B

(

K+

→ 

+

ν

)

·

ρ



(

mN

)

· |

U4

|

2

,

(1) where

B(

K+

→ 

+

ν

)

is the measured branching fraction of the SMleptonicdecay,

|

U4

|

2 isthemixingparameter,mN istheHNL

mass,and

ρ



(m

N

)

isakinematicfactor:

ρ



(

mN

)

=

(

x

+

y

)

− (

x

−

y

)

2

x

(

1

−

x

)

2

· λ

1/2

₍

₁

_,

_x

_,

_y

_),

₍₂₎

withx

= (

m

/m

K

)

2, y

= (

mN

/m

K

)

2 and

λ(a,

b,c)

=

a2

+

b2

+

c2

−

2

(ab

+

bc

+

ac). By definition,

ρ



(

0

)

=

1. Numerically, the prod-uct

B(

K+

→ 

+

ν

)

·

ρ



(m

N

)

is

O(

1

)

overmostoftheallowedmN

range;itdropstozeroatthekinematiclimitmN

=

mK

−

mand,in thepositroncase,reducesto

B(

K+

→

e+

ν

)

=

1

.

582

(

7

)

×

10−5 _[4] formN

→

0 duetohelicitysuppression.

ThelifetimeofanHNLwithmassmN

<

mKanddecaying

exclu-sivelyintoSM particleswillexceed10−4

/

|

U4

|

2 μs,where

|

U4

|

2 is thelargestofthethreecouplingparameters U2

4 (



=

e,

μ

,

τ

) [5].

Assuming conservatively that

|

U4

|

2

<

10−4, the lifetimeexceeds 1 μs andHNLscanbe consideredstableinproduction-search ex-periments.

A search for K+

→

e+N decays in the HNL mass range 144–462 MeV/c2_{usingthedatacollectedbytheNA62experiment} atCERNin2017–2018isreported.The results,whichassume the HNLlifetimeexceeds50 ns,arepresentedasupperlimitsof

|

Ue4

|

2

at90%CLforanumberofmasshypotheses.

1. Beam,detectoranddatasample

The layout of the NA62 beamline and detector [6] is shown schematically in Fig. 1. An unseparated secondary beam of

π

+

(70%),protons(23%)andK+(6%)iscreatedbydirecting400 GeV/c protons extracted from the CERN SPS onto a berylliumtarget in spills of 3 s effective duration. The central beam momentum is 75 GeV/c,withamomentumspreadof1%(rms).

Beam kaons are tagged with 70 ps time resolution by a dif-ferentialCherenkovcounter(KTAG)usingnitrogengasat1.75 bar pressurecontainedina5 mlongvesselasradiator.Beamparticle positions, momenta andtimes(to better than100 ps resolution) are measured by a silicon pixel spectrometer consisting of three stations(GTK1,2,3)andfourdipolemagnets.Amuonscraper(SCR) is installed between GTK1 and GTK2. A 1.2 m thick steel colli-mator (COL) with a central aperture of 76

×

40 mm2 andouter dimensionsof1

.

7

×

1

.

8 m2 _{isplacedupstreamofGTK3 toabsorb} hadronsfromupstream K+ decays(avariableaperturecollimator of0

.

15

×

0

.

15 m2 _{outer dimensionswas used up toearly 2018).} InelasticinteractionsofbeamparticlesinGTK3aredetectedbyan array ofscintillator hodoscopes(CHANTI) locatedjust afterGTK3. Thebeamisdeliveredintoavacuumtankevacuatedtoapressure of10−6 mbar, whichcontainsa 75 mlongfiducialdecayvolume (FV)starting2.6 mdownstreamofGTK3.The beamdivergenceat theFVentranceis0.11 mrad(rms)inbothhorizontalandvertical https://doi.org/10.1016/j.physletb.2020.135599

0370-2693/©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

2 The NA62 Collaboration / Physics Letters B 807 (2020) 135599

Fig. 1. Schematic side view of the NA62 beamline and detector. planes.DownstreamoftheFV,undecayedbeamparticlescontinue

theirpathinvacuum.

MomentaofchargedparticlesproducedbyK+decaysintheFV aremeasuredbyamagneticspectrometer(STRAW)locatedinthe vacuumtank downstreamoftheFV.Thespectrometer consistsof fourtrackingchambersmadeofstrawtubes,andadipolemagnet (M)located betweenthe second andthirdchambers and provid-ing a horizontal momentum kick of 270 MeV/c. The momentum resolutionachievedis

σ

p

/p

= (

0

.

30

⊕

0

.

005

·

p)%,wherethe

mo-mentum p isexpressedinGeV/c.

A ring-imaging Cherenkov detector (RICH), consisting of a 17.5 mlongvesselfilledwithneonatatmosphericpressure(with a Cherenkov threshold for muons of 9.5 GeV/c), is used for the identification of charged particles and time measurements with 70 psprecision(forpositrons).Twoscintillatorhodoscopes(CHOD, whichincludeamatrixoftilesandtwoorthogonalplanesofslabs, arrangedinfourquadrants)downstreamoftheRICHprovide trig-gersignalsandtimemeasurementswith200 psprecision.

A27X0 thickquasi-homogeneous liquidkrypton(LKr) electro-magnetic calorimeter is used for particle identificationand pho-ton detection. The calorimeter has an active volume of 7 m3_{, is} segmentedinthe transverse directioninto13248projective cells of approximately 2

×

2 cm2, and provides an energy resolution

σ

E

/E

= (

4

.

8

/

√

E

⊕

11

/E

⊕

0

.

9

)

%, whereE isexpressedinGeV.To achievehermetic acceptanceforphotonsemittedin K+ decaysin theFVatanglesupto50 mradtothebeamaxis,theLKr calorime-terissupplementedbyannularleadglassdetectors(LAV)installed in12 positions inanddownstream ofthevacuumtank, andtwo lead/scintillatorsampling calorimeters(IRC, SAC) located closeto the beamaxis.An iron/scintillatorsampling hadroniccalorimeter formed of two modules (MUV1,2) and a muon detector (MUV3) consistingof 148 scintillatortiles located behind an 80 cm thick ironwallareusedforparticleidentification.

Thedatasampleusedfortheanalysisisobtainedfrom0

.

79

×

106_{SPSspillsrecordedduring360daysofoperationin2017–2018,} at a typical beam intensity of 2

.

2

×

1012 _{protons per spill} cor-responding to a mean beam particle rate at the FV entrance of 500 MHz, anda mean K+ decayrate inthe FVof 3.7 MHz.The trigger used for the K+

→

π ν

ν

¯

measurement [7], consisting of bothhardware(L0)andsoftware(L1)stages,isusedforthe anal-ysis. Overall trigger efficiencyfor single positrons withmomenta below30 GeV/c ismeasuredtobe

(

90

±

4

)

% usingdatasamples.

2. Eventselection

Assuming an HNL lifetime exceeding 50 ns, and considering that the HNLproduced in K+

→

e+N decayswould be boosted by aLorentz factorof

O(

100

)

,HNLdecaysinflight intoSM

par-ticlesin the156 mlongvolume betweenthe startoftheFVand thelastdetector(SAC)canbeneglected (Section5).Thereforethe K+

→

e+N decayischaracterizedbyasinglepositroninthefinal state,similarlytotheSM K+

→

e+

ν

decay.Theprincipalselection criteriafollow.

•

A positron track reconstructed in the STRAW spectrometer with momentum in the range 5–30 GeV/c is required. The momentum isrestrictedto thisrange,becausethe L0trigger requiredthatthetotalenergydepositedintheLKrnotexceed 30 GeV. The track’s trajectory through the STRAW chambers anditsextrapolationtotheLKrcalorimeter,CHODandMUV3 should bewithinthefiducialgeometricalacceptanceofthese detectors.Thepositrontimeisevaluatedasthemeantimeof theRICHsignalsspatiallyassociatedwiththetrack.

•

Backgrounds dueto particle misidentification are suppressed toa negligiblelevelbyapplyingthefollowingparticle identi-fication criteriatothesingletrack:theratioofenergy, E, de-positedintheLKrcalorimetertomomentum, p,measuredby theSTRAWspectrometerisrequiredtobe 0

.

92

<

E/p

<

1

.

08; a particle identification algorithm based on the RICH signal patternwithin 3 ns ofthepositron RICH time isapplied; no signalintheMUV3detectorspatiallyconsistentwiththe pro-jectedtrackimpactpointandwithin4 nsofthepositrontime isallowed.

•

Backgrounds frombeampiondecays(mainly

π

+

→

e+

ν

,and toalesserextent

π

+

→

μ

+

ν

followedbymuondecay

μ

+

→

e+

ν

ν

¯

)aresuppressedby requiringa kaonsignal intheKTAG detectorwithin1 nsofthepositrontime.

•

Identification of the K+ track in theGTK relies on the time difference,

t

GK, between a GTK trackand the KTAG signal, andspatialcompatibilityoftheGTKandSTRAWtracks quan-tified by the distance,d, of closest approach. A discriminant

D( t

GK

,

d)isdefinedusingthe

t

GKandd distributions mea-sured with K+

→

π

+

π

+

π

− decays.Among GTK trackswith

|

tGK

|

<

0

.

5 ns,thetrackoftheparentkaonisassumedtobe theone givingthe

D

valuemostconsistentwitha K+

→

e+ decay. Itis alsorequired thatd

<

4 mm toreduce the back-groundfrom K+

→

μ

+

ν

decaysinthe FVfollowedbymuon decay

μ

+

→

e+

ν

ν

¯

. The decayvertex isdefined asthe point ofclosestapproachoftheGTKandSTRAWtracks,takinginto accountthestraymagneticfieldinthevacuumtank.

•

Background from K+

→

μ

+

ν

decays upstream of GTK3 fol-lowedby

μ

+ decaysintheFVarisesfrompileupintheGTK, andis suppressedby geometricalconditions. Namely,the re-constructed K+ decayvertexisrequiredto belocated inthe FV at a minimumdistance fromthe start of the FV,varying from2 m to12 m depending onthe anglebetween the K+

Fig. 2. Left:reconstructedsquaredmissingmass(m2

miss)distributionsfordataandsimulatedeventsaftertheselectiondescribedinSection2.Decaystomuonscontribute viamuondecaysinflight.TheboundariesoftheSMsignalregion(upperarrows)andtheHNLsearchregion(lowerarrows)aredefinedinSections2and5.Right:theratio ofdataandsimulatedm2

missspectra.Thestatisticaluncertaintiesshownaredominatedbythoseofthesimulatedspectra.

momentuminthelaboratoryframeandthepositron momen-tumintheK+ restframe.

•

Backgrounds from multi-body K+ decays are suppressed by veto conditions. The positron track must not form vertices with any other STRAW track. LKr energy deposition clusters notspatiallycompatiblewiththepositrontrackwithin8 nsof the positrontime are notallowed. Activity inthelarge-angle (LAV)andsmall-angle(SAC,IRC)photonvetodetectorswithin 3 ns ofthepositrontimeisforbidden.ActivityintheCHANTI detectorwithin4 nsofthepositrontimeisnotallowed;more thantwosignalsintheCHODtileswithin6 nsofthepositron timeandnotspatiallyassociatedwiththepositronarealsonot allowed. Datalossduetothe vetoconditionsfromaccidental activity(“randomveto”)averagedoverthesampleismeasured tobeabout30%.

Thesquaredmissingmassiscomputedasm2

miss

= (

PK

−

Pe

)

2, wherePK andPe arethekaonandpositron4-momenta,obtained

fromthe 3-momentameasuredby theGTK andSTRAWdetectors andusingtheK+ ande+masshypotheses.

Simulationofparticleinteractionswiththedetectorandits re-sponseisperformedwithaMonte-Carlosimulationpackagebased on the Geant4 _{toolkit [8]. The m}2

miss spectra of the events se-lected fromdataandsimulated samples,andtheir ratio,are dis-playedinFig.2.ThesignalfromtheSMleptonicdecayK+

→

e+

ν

is observed as a peak at m2_miss

=

0 with a resolution of 1

.

7

×

10−3 GeV2

/c

4. The simulationis tuned to reproduce this resolu-tion to a 1% relative precision. The SM signal region is defined interms ofthe reconstructed squaredmissingmass as

|

m2

miss

|

<

0

.

01 GeV2

_/c

4_.

3. Measurementprinciple

Apeak-searchprocedure measures the K+

→

e+N decay rate withrespecttothe K+

→

e+

ν

rateforanassumedHNLmassmN.

Thisapproachbenefitsfromfirst-ordercancellationsofresidual de-tectorinefficienciesnotfullyaccountedforinsimulations,aswell astrigger inefficiencies andrandom veto losses, common to sig-nalandnormalizationmodes.TheexpectednumberofK+

→

e+N signaleventsNS canbewrittenas

NS

=

B

(

K+

→

e+N

)/

B

SES

(

K+

→

e+N

)

= |

Ue4

|

2

/

|

Ue4

|

2SES

,

(3)

wherethebranchingfraction

B

SES

(K

+

→

e+N)andthemixing pa-rameter

|

Ue4

|

2_SES corresponding to the observation of one signal

event,thesingleeventsensitivity(SES),aredefinedas

B

SES

(

K+

→

e+N

)

=

1 NK

·

AN and

|

Ue4

|

2SES

=

B

SES

(

K+

→

e+N

)

B

(

K+

→

e+

ν

)

·

ρ

e

(

mN

)

,

(4)

whereNK isthenumberof K+decaysintheFV, AN isthesignal

selection acceptance,and thekinematic factor

ρ

e

(m

N

)

is defined

inEq. (2).

The number of K+ decays in the FV is evaluated using the numberof K+

→

e+

ν

candidatesreconstructed inthe data sam-ple.Data lossesduetotriggerefficiencies andrandomvetoesare includedinthe NK definition,whichmakesthevalue ofNK

spe-cifictothisanalysis.ThedominantbackgroundduetoK+

→

μ

+

ν

decayfollowed by

μ

+

→

e+

ν

ν

¯

decay(0.08% inrelative terms) is takenintoaccount.Otherbackgrounds,includingthecontribution fromK+

→

μ

+

ν

decaywithamisidentifiedmuon,arenegligible.

ThenumberofK+decaysiscomputedas

NK

=

NSM

Ae

·

B

(

K+

→

e+

ν

)

+

Aμ

·

B

(

K+

→

μ

+

ν

)

= (

3

.

52

±

0

.

02

)

×

1012

,

where NSM

=

3

.

495

×

106 isthe number ofselected data events inthe SM signal region; Ae

= (

6

.

27

±

0

.

02stat

)

×

10−2 and Aμ

=

(

1

.

24

±

0

.

19stat

)

×

10−9 are the acceptances of the selection for the K+

→

e+

ν

decay and the K+

→

μ

+

ν

decay (followed by muon decay) evaluated with simulations; and

B(K

+

→

e+

ν

)

=

(

1

.

582

±

0

.

007

)

×

10−5 _and

_B(

_K+

_→

_μ

+

_ν

₎

₌

₀

_.

₆₃₅₆

_±

₀

_.

_{0011 are} thebranchingfractionsofthesedecays [4].Theuncertaintyquoted in NK isduetotheprecision oftheexternalinput

B(

K+

→

e+

ν

)

andthestatisticalandsystematicaccuracyofthesimulation.The systematicuncertaintyisevaluated byvarying theselection crite-ria.

4. Backgroundevaluationwithsimulations

The search procedure is based ona data-driven estimation of the background to K+

→

e+N decays, which is validin the ab-sence of peaking signal-like background structures in the recon-structed mass spectrum. Simulations are usedto understandthe

4 The NA62 Collaboration / Physics Letters B 807 (2020) 135599

Fig. 3. Missingmassresolutionσm (left)andacceptances AN ofthestandardandauxiliaryselections(right)evaluatedfromsimulationsasfunctionsoftheHNLmass,

obtainedbypolynomialfitstomeasurementsbasedon80simulatedsignalsampleswithdifferentHNLmasses.Abovethemassof420 MeV/c2_{,thetwoselectionshave} equalacceptanceasthemomentumofthepositronproducedintheK+→e+N decayisalwaysbelow20 GeV/c.TheboundariesoftheHNLsearchregionareindicatedby verticalarrows.

background qualitatively, to optimizethe eventselection, and to justifythesearchprocedure.

The main background to K+

→

e+N and K+

→

e+

ν

decays comes from K+

→

μ

+

ν

decay followed by muon decay

μ

+

→

e+

ν

ν

¯

. This background is reduced by the requirement of spatial compatibility between the positron and kaon tracks, and its ul-timate level is limited by the resolution on the track directions provided by the STRAW andGTK spectrometers. The background fromK+

→

μ

+

ν

decaysupstreamofthevacuumtankis60 times smallerthanthatfromdecaysinthevacuumtank.

Backgrounds from beam pion decays

π

+

→

e+

ν

and

π

+

→

μ

+

ν

decays, followed by muon decay, arise from

π

+ misidenti-ficationintheKTAGduetothepresenceofanin-timebeamkaon notdecayingintheFV.Consideringthebeamrate,thekaon frac-tioninthebeam,andtheKTAG–RICHtimingconditionsused,the beampionmisidentificationprobabilityduetopileupisabout6%. TheprobabilityofbeampionidentificationasakaonintheKTAG intheabsenceofpileupisnegligible.Thebeampiondecay back-groundpopulatesthe missingmassregionm_miss2

>

0

.

13 GeV2

/c

4_, becauseofthe30 GeV/c upperlimitimposed onthee+ momen-tum.

The reconstructed m2

miss spectrum of dataevents is described bysimulationstoafewpercentrelativeprecision(Fig. 2). The ac-curacyofthesimulationislimitedbysystematiceffects,suchasin themodellingoftheLAV detectorresponse tosoftradiative pho-tons.

5. Searchprocedure

TheK+

→

e+N processisinvestigatedin264masshypotheses, mN,within theHNLsearch regionbetween144and462MeV/c2.

Thedistancesbetweenadjacentmasshypothesesareequaltothe massresolution

σ

m showninFig.3(left),roundedto0.1 MeV/c2.

Thismass resolution is three timesbetter than that of the 2015 data sample collected without the GTK spectrometer [9]. Event selectionrequiresthat

|

mmiss

−

mN

|

<

1

.

5

σ

mforeachmass

hypoth-esis,wheremmiss isthereconstructedmissingmass.

IneachHNLmasshypothesis,sidebandsaredefinedinthe re-constructed missing mass spectrum as 1

.

5

σ

m

<

|

mmiss

−

mN

|

<

11

.

25

σ

m, additionally requiring the missing mass to be within

the range122–465 MeV/c2_{.The number ofexpected background} events,Nexp,withinthe

±

1

.

5

σ

m signalwindowisevaluated with

a second-order polynomial fit to the sidebanddata of the mmiss spectrum, where the bin size is 0

.

75

σ

m. The uncertainty,

δN

exp,

in thenumberof expectedbackgroundevents includesstatistical and systematiccomponents. The formercomes fromthe statisti-cal errorsinthefitparameters, andthe latterisevaluatedasthe differencebetweenNexpobtainedfromfitsusingsecondandthird order polynomials. The dominantcontribution to

δN

exp is statis-tical, exceptneartheboundariesoftheHNLsearch regionwhere the systematic uncertainty is comparable. Further systematic er-rorsduetopossibleHNLsignalsinthesidebandsarefoundtobe negligible; thischeck ismadeassuming

|

Ue4

|

2 tobe equaltothe

expected sensitivityofthe analysis. Theratio

δN

exp

/N

exp is typi-cally0.2–0.3%,butreachesafewpercentclosetothelimitsofthe searchregion.

An auxiliary selection with a tighter maximum positron mo-mentum requirement of 20 GeV/c is used to achieve a locally smoothmmiss spectrumofbackgroundeventsinthesidebandsfor mass hypotheses in the range 356–382 MeV/c2_{. The beam pion} decaybackgroundthresholdinthem2_miss spectrumisshiftedfrom 0

.

14 GeV2

/c

4 _{(Fig. 2) to 0}

_.

_{165 GeV}2

_/c

4 _{within the auxiliary} se-lection because the e+ momentum and the m2_miss reconstructed for the

π

+

→

e+

ν

decay in the K+ mass hypothesis are anti-correlated.

The signalselection acceptances, AN,forthe standardandthe

auxiliary selectionsasfunctionsofmN obtainedwithsimulations

assuming infiniteHNLlifetimeare displayedin Fig.3(right). The acceptanceforameanlifetimeof50 ns(consideringdecaysto de-tectableparticles)islowerthanshownby

O(

1%

)

inrelativeterms, making the results of the search valid for lifetimes in excess of 50 ns.Forsmallerlifetimes,theHNLmeandecaylengthinthe lab-oratoryframebecomescomparabletoorsmallerthanthelengthof the apparatus.Consequently, acceptancesforlifetimes of5 (1) ns decreaseduetothevetoconditionsbyfactorsofupto2 (10), de-pendingontheHNLmass.

The simulation of the missing mass resolution outside the K+

→

e+

ν

peak isvalidatedwithasample offullyreconstructed K+

→

π

+

π

+

π

− decays by studying the resolution of

m

3π

=



(P

K

−

P3

)

2

−



(P

1

+

P2

)

2,where Pi(i

=

1

,

2

,

3)andPK arethe

reconstructedpionandkaon4-momenta.Theresolutionon

m

3π canbemeasuredforbothdataandsimulatedsamplesbecausethe truevalueofthisquantityisalwayszero.Theresolutionvariesin therange0.8–1.3 MeV/c2 _dependingon

_(P

simu-Fig. 4. Left:thevaluesofNobs,theobtainedupperlimitsat90%CLofthenumbersofK+→e+N events,andtheexpected±1σand±2σ bandsinthebackground-only hypothesisforeachHNLmassvalueconsidered.Right:singleeventsensitivitiesBSES(K+→e+N)(dashedline)and|Ue4|SES2 (solidline)asfunctionsoftheHNLmass.Note thereducedsensitivityintheregionof356–382 MeV/c2_{inwhichtheauxiliaryselectionisused.TheboundariesoftheHNLsearchregionareindicatedbyverticalarrows.} lationagreeswiththedatatobetterthan5%,validatingthesignal

acceptanceestimatesto2%relativeprecision.

6. Results

The number ofobserved events, Nobs, within the signal win-dow, the number of expected background events, Nexp, and its uncertainty,

δN

exp, are used to compute the local signal signifi-canceforeachmasshypothesis

z

= (

Nobs

−

Nexp

)/



(δ

Nobs

)

2

+ (δ

Nexp

)

2

,

with

δN

obs

=

√

Nobs.Amaximumlocalsignificanceof3.6isfound for mN

=

346

.

1 MeV

/c

2, based on Nobs

=

236745 and Nexp

=

234678

±

314.Accountingforthelook-elsewhereeffect,theglobal significancebecomes2.2.

Thequantities Nobs, Nexp, and

δN

exp are used toevaluate the upperlimitat90%CLofthenumberof K+

→

e+N decays,NS,in

eachHNLmasshypothesisusingtheCLS method [10].Thevalues of Nobs,the obtainedupper limitsof NS,andthe expected

±

1

σ

and

±

2

σ

bandsofvariationofNS inthebackground-only

hypoth-esisareshowninFig.4(left).

Upperlimitsat90%CLofthebranchingfraction

B(K

+

→

e+N) andthemixingparameter

|

Ue4

|

2areobtainedfromthoseofNS

ac-cordingto Eq. (3),usingthesingle eventsensitivities

B

SES

(K

+

→

e+N) and

|

Ue4

|

2SES shownasfunctionsofthe HNLmassin Fig.4 (right). The obtained limits of

B(

K+

→

e+N

)

are displayed in Fig.5.Theobtainedlimitsof

|

Ue4

|

2,togetherwiththelimitsfrom

previous HNL production searches in K+ [9,11] and

π

+ [12,13] decaysinthe30–470 MeV/c2 _{massrange,andtheBigBang} Nucle-osynthesis(BBN)constraint [14],areshowninFig.6.Thereported resultimprovestheexistinglimitsof

|

Ue4

|

2obtainedinproduction

searchesoverthewholemassrangeconsidered.Comparisonwith HNLdecaysearchesisavailable inRefs. [1,15].The obtained lim-itsof

|

Ue4

|

2 improveoverthedecaysearches [16,17] inthemass

regionbelow400 MeV/c2.

7.Summaryandoutlook

A search for HNL production in K+

→

e+N decays has been performed with the data set collected by the NA62 experiment

Fig. 5. Theobtainedupperlimitsat90%CLofB(K+→e+N)and theexpected

±1σ and±2σ bandsinthebackground-onlyhypothesisforeachHNLmassvalue considered.

atCERN in2017–2018.Upperlimitsofthedecay branching frac-tionandthemixingparameter

|

Ue4

|

2havebeenestablishedatthe

10−9levelovermostoftheHNLmassrange144–462 MeV/c2with theassumptionofmeanlifetimeexceeding50 ns.Theselimits be-come weakerby factors ofup to 2 (10)for lifetimesof5 (1) ns. The

|

Ue4

|

2 resultsaresignificantly betterthanpreviouslimits

ob-tained from HNL production and decay searches [1], and other experimentalconstraints [15,18].Thevaluesof

|

Ue4

|

2 favouredby

theBBNconstraint [14] areexcludedforHNLmassesuptoabout 340 MeV/c2_.

Animprovementinsensitivityofthisanalysisintermsof

|

Ue4

|

2

can only be expected with future NA62 data. Considering the backgroundconditions,thesensitivityto

|

Ue4

|

2 isproportional to

δN

exp

/N

exp,andimprovesastherelativestatisticaluncertaintyin Nexpdecreaseswithsamplesizeas1

/

√

NK.

HNLmassesbelow144 MeV/c2,notaccessible tothisanalysis duetotheshapeofthebackgroundmassspectrum,canbeprobed via the K+

→

π

0_e+_{N decay. The dataset currently available for}

6 The NA62 Collaboration / Physics Letters B 807 (2020) 135599

Fig. 6. Upperlimitsat90%CLof|Ue4|2obtainedforeachassumedHNLmass

com-paredtothelimitsestablishedbyearlierHNLproductionsearchesinK+→e+N

decays:KEK [11],NA62 (2015data) [9];and π+→e+N decays:TRIUMF [12], PIENU [13].Thelowerboundaryon|Ue4|2 imposedbytheBBNconstraint [14] is

shownbyadashedline.

this search, collected with a pre-scaled trigger, corresponds to NK

≈

3

×

1010.Thesingleeventsensitivityinthemassrangeof

in-terestestimatedusingtheformalismofRef. [5] is

|

Ue4

|

2SES

≈

10−8; thesearchis expectedto belimitedbythe K+

→

π

0_e+

_νγ

back-ground.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

Itis a pleasureto expressourappreciation tothe staffofthe CERNlaboratoryandthetechnicalstaffoftheparticipating labora-toriesanduniversitiesfortheireffortsintheoperationofthe ex-perimentanddataprocessing.WearegratefultoMatheusHostert, SilviaPascoli,OlegRuchayskiy,RobertShrock,Jean-LoupTastetand InarTimiryasovfortheinputsprovided ontheHNL phenomenol-ogy.

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 Engineering

Research Council), funding SAPPJ-2018-0017 Canada; NRC (Na-tional ResearchCouncil Canada)contributionto TRIUMF, Canada; MEYS (The Ministry of Education, Youth and Sports), Czech Re-public;BMBF(BundesministeriumfürBildungundForschung) con-tracts 05H12UM5, 05H15UMCNA and 05H18UMCNA, Germany; INFN (Istituto Nazionale di Fisica Nucleare), Italy; MIUR (Minis-terodell’Istruzione, dell’UniversitàedellaRicerca),Italy;CONACyT (Consejo Nacional de Ciencia y Tecnología), Mexico; IFA (Insti-tute of Atomic Physics) Romanian CERN-RO No.1/16.03.2016 and Nucleus Programme PN 19 06 01 04, Romania; INR-RAS (Insti-tute for Nuclear Research of the Russian Academy of Sciences), Moscow,Russia;JINR(JointInstituteforNuclearResearch),Dubna, Russia; NRC (National Research Center)“Kurchatov Institute”and MESRF (Ministry of Education and Science of the Russian Fed-eration), Russia;MESRS (Ministry of Education,Science, Research andSport),Slovakia;CERN(EuropeanOrganizationforNuclear Re-search),Switzerland;STFC(ScienceandTechnologyFacilities Coun-cil), United Kingdom; NSF (National Science Foundation) Award Numbers 1506088 and 1806430, U.S.A.; ERC (European Research Council) “UniversaLepto” advanced grant 268062, “KaonLepton” 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” grantRBFR12JF2Z,ProjectGAP),Italy;RussianFoundationforBasic Research(RFBRgrants18-32-00072,18-32-00245),Russia;Russian Science Foundation (RSF 19-72-10096), Russia; the Royal Society (grants UF100308, UF0758946), United Kingdom; STFC (Ruther-ford fellowships ST/J00412X/1, ST/M005798/1), United Kingdom; ERC(grants268062,336581andstartinggrant802836“AxScale”); EUHorizon2020(MarieSkłodowska-Curiegrants701386,842407, 893101).

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NA62Collaboration

E. Cortina Gil,

A. Kleimenova,

E. Minucci

1

,

2

,

S. Padolski

3

,

P. Petrov,

A. Shaikhiev

4

,

R. Volpe

5

UniversitéCatholiquedeLouvain,Louvain-La-Neuve,Belgium

T. Numao,

Y. Petrov,

B. Velghe

TRIUMF,Vancouver,BritishColumbia,Canada

D. Bryman

6

,

J. Fu

7

E. Iacopini,

G. Latino,

M. Lenti,

A. Parenti

DipartimentodiFisicaeAstronomiadell’UniversitàeINFN,SezionediFirenze,SestoFiorentino,Italy

A. Bizzeti

13

,

F. Bucci

INFN,SezionediFirenze,SestoFiorentino,Italy

A. Antonelli,

G. Georgiev

14

,

V. Kozhuharov

14

,

G. Lanfranchi,

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

15

,

P. Cenci,

B. Checcucci,

P. Lubrano,

M. Lupi

16

,

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

17

,

A. Fucci,

A. Salamon,

F. Sargeni

18

INFN,SezionediRomaTorVergata,Roma,Italy

R. Arcidiacono

19

,

B. Bloch-Devaux,

M. Boretto

20

,

E. Menichetti,

E. Migliore,

D. Soldi

DipartimentodiFisicadell’UniversitàeINFN,SezionediTorino,Torino,Italy

C. Biino,

A. Filippi,

F. Marchetto

8 The NA62 Collaboration / Physics Letters B 807 (2020) 135599

J. Engelfried,

N. Estrada-Tristan

21

InstitutodeFísica,UniversidadAutónomadeSanLuisPotosí,SanLuisPotosí,Mexico

A.M. Bragadireanu,

S.A. Ghinescu,

O.E. Hutanu

HoriaHulubeiNationalInstituteofPhysicsforR&DinPhysicsandNuclearEngineering,Bucharest-Magurele,Romania

A. Baeva,

D. Baigarashev,

D. Emelyanov,

T. Enik,

V. Falaleev,

V. Kekelidze,

A. Korotkova,

L. Litov

14

,

D. Madigozhin,

M. Misheva

22

,

N. Molokanova,

S. Movchan,

I. Polenkevich,

Yu. Potrebenikov,

S. Shkarovskiy,

A. Zinchenko

†

JointInstituteforNuclearResearch,Dubna,Russia

S. Fedotov,

E. Gushchin,

A. Khotyantsev,

Y. Kudenko

23

,

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

20

,

T. Blazek,

V. Cerny,

Z. Kucerova

FacultyofMathematics,PhysicsandInformatics,ComeniusUniversity,Bratislava,Slovakia

J. Bernhard,

A. Ceccucci,

H. Danielsson,

N. De Simone

24

,

F. Duval,

B. Döbrich,

L. Federici,

E. Gamberini,

L. Gatignon,

R. Guida,

F. Hahn

†

,

E.B. Holzer,

B. Jenninger,

M. Koval

25

,

P. Laycock

3

,

G. Lehmann Miotto,

P. Lichard,

A. Mapelli,

R. Marchevski,

K. Massri,

M. Noy,

V. Palladino

26

,

M. Perrin-Terrin

27

,

28

,

J. Pinzino

29

,

30

,

V. Ryjov,

S. Schuchmann

31

,

S. Venditti

CERN,EuropeanOrganizationforNuclearResearch,Geneva,Switzerland

T. Bache,

M.B. Brunetti

32

,

V. Duk

33

,

V. Fascianelli

34

,

J.R. Fry,

F. Gonnella,

E. Goudzovski

∗

,

J. Henshaw,

L. Iacobuzio,

C. Lazzeroni,

N. Lurkin

28

,

F. Newson,

C. Parkinson

9

,

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

35

,

B. Wrona

UniversityofLiverpool,Liverpool,UnitedKingdom

A. Conovaloff,

P. Cooper,

D. Coward

36

,

P. Rubin

GeorgeMasonUniversity,Fairfax,VA,USA

*

Correspondingauthor.

E-mailaddress:[email protected](E. Goudzovski). † _Deceased.

1 _{Presentaddress:LaboratoriNazionalidiFrascati,I-00044Frascati,Italy.}

2 _{AlsoatCERN,EuropeanOrganizationforNuclearResearch,CH-1211Geneva23,Switzerland.} 3 _{Presentaddress:BrookhavenNationalLaboratory,Upton,NY11973,USA.}

4 _{AlsoatInstituteforNuclearResearchoftheRussianAcademyofSciences,117312Moscow,Russia.}

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

23 _{AlsoatNationalResearchNuclearUniversity(MEPhI),115409MoscowandMoscowInstituteofPhysicsandTechnology,141701Moscowregion,Moscow,Russia.} 24 _{Presentaddress:DESY,D-15738Zeuthen,Germany.}

25 _{Presentaddress:CharlesUniversity,11636Prague1,CzechRepublic.} 26

Presentaddress:PhysicsDepartment,ImperialCollegeLondon,London,SW72BW,UK.

27 _{Presentaddress:CentredePhysiquedesParticulesdeMarseille,UniversitéAixMarseille,CNRS/IN2P3,F-13288,Marseille,France.} 28 _{AlsoatUniversitéCatholiquedeLouvain,B-1348Louvain-La-Neuve,Belgium.}

29 _{Presentaddress:DepartmentofPhysics,UniversityofToronto,Toronto,Ontario,M5S1A7,Canada.} 30 _{AlsoatINFN,SezionediPisa,I-56100Pisa,Italy.}

31 _{Presentaddress:InstitutfürPhysikandPRISMAClusterofexcellence,UniversitätMainz,D-55099Mainz,Germany.} 32 _{Presentaddress:DepartmentofPhysics,UniversityofWarwick,Coventry,CV47AL,UK.}

33 _{Presentaddress:INFN,SezionediPerugia,I-06100Perugia,Italy.}

34 _{Presentaddress:DipartimentodiPsicologia,UniversitàdiRomaLaSapienza,I-00185Roma,Italy.} 35 _{Presentaddress:LaboratoireLeprinceRinguet,F-91120Palaiseau,France.}