Search for heavy neutral lepton production in K + decays

.

The

NA62

Collaboration

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received4December2017

Receivedinrevisedform10January2018 Accepted12January2018

Availableonline28January2018 Editor: W.-D.Schlatter

AsearchforheavyneutralleptonproductioninK+decaysusingadatasamplecollectedwithaminimum biastriggerbytheNA62experimentatCERNin2015isreported.Upperlimitsatthe10−7_to10−6_level are establishedonthe elements oftheextendedneutrino mixingmatrix|Ue4|2 and |Uμ4|2 forheavy neutralleptonmassintheranges170–448 MeV/c2_{and250–373 MeV/c}2_{,respectively.Thisimproveson} thepreviouslimitsfromHNLproductionsearchesoverthewholemassrangeconsideredfor|Ue4|2,and above300 MeV/c2_for|U

μ4|2.

©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

0. Introduction

Non-zeromassesandmixingoftheStandardModel(SM) neu-trinos are now firmly established. However many SM extensions have been proposed, involving massive “sterile” neutrinos, also calledheavy neutralleptons (HNLs),whichmixwiththeordinary light“active”neutrinos.For example,theNeutrinoMinimal Stan-dardModel(

ν

MSM)postulatesthreeHNLs,explainingdarkmatter andbaryon asymmetry of the universe ina way consistent with the results of neutrino oscillation experiments [1]. One of these HNLs with the expected mass of

O(

10 keV

/

c2

₎

_{is a dark} mat-ter candidate, while the others are expected to have masses of

O(

1 GeV

/

c2

)

.

MixingbetweenHNLs(denotedN below)andactivelight neu-trinos gives rise to HNL production in meson decays, including

K+

→ 

+N (



=

e

,

μ

).The branching fraction ofthe latterdecay isdeterminedbythe HNLmassmN andmixingparameter

|

U4

|

2 asfollows[2,3]:

B

(

K+

→ 

+N

)

=

B

(

K+

→ 

+

ν

)

·

ρ



(

mN

)

· |

U4

|

2

.

(1) Here

B(

K+

→ 

+

ν

)

isthemeasured branchingfractionoftheSM leptonicdecay (includinginner bremsstrahlung),and

ρ



(

mN

)

isa kinematicfactor:

ρ



(

mN

)

=

(

x

+

y

)

− (

x

−

y

)

2 x

(1

−

x

)

2

· λ

1/2

_(1,

_x

_,

_y

_),

withx

= (

m

/

mK

)

2, y

= (

mN

/

mK

)

2 and

λ(

a

,

b

,

c

)

=

a2

+

b2

+

c2

−

2

(

ab

+

bc

+

ac

)

.Bydefinition,

ρ



(

0

)

=

1.Numerically,theproduct

B(

K+

→ 

+

ν

)

·

ρ



(

mN

)

is

O(

1

)

overmostoftheallowedmN range. However it drops to zero at the kinematic limit mN

=

mK

−

m and,in thepositron case,reduces to

B(

K+

→

e+

ν

)

=

1

.

582

(

7

)

×

10−5 [4]formN

→

0 duetohelicitysuppression.

A search for K+

→ 

+N decays in HNL mass range 170–448 MeV/c2usingadatasamplecollectedwithaminimumbiastrigger by the NA62 experiment at CERN during the first physics data-taking in 2015 is reported here. The obtained upper limits on

|

U4

|

2complement,andimproveon,thoseobtainedinearlierHNL productionsearchesinpionandkaondecays[5–9].

1. Beam,detectoranddatasample

The layout of the NA62 beamline anddetector [10] is shown schematically inFig. 1.Asecondary positivehadron beamwitha centralmomentumof75GeV/c and1%momentumspread(rms)is derivedfromprimary 400GeV/c protonsextractedfromtheCERN SPS andinteractingwitha berylliumtarget inspillsof3 s effec-tive duration atnominal intensity of1

.

1

×

1012 protons/s. Beam kaons are tagged witha 70 ps time resolution by a differential Cherenkovcounter(KTAG)withnitrogenradiatorat1.73 bar pres-surecontainedin a5 mlong vessel.Beamparticle momentaare measured by a silicon pixel detector(GTK, under commissioning in 2015 and not used for this analysis). Inelastic interactions of beamparticleswiththelastofthethreeGTKstationsaredetected by an arrayof scintillatorhodoscopes (CHANTI).The beamis de-liveredintoavacuumtank containinga75 m longfiducialdecay volume(FV)starting2.6 mdownstreamofthelastGTKstation.The beamtransversesizeattheFVentranceis53

×

24 mm2,andthe beamdivergence in2015 was 0.22 (0.11) mradinthe horizontal (vertical)plane.ThenominalinstantaneousparticlerateattheFV entranceis750 MHz,mainlydueto

π

+ (70%),protons(23%)and

K+ (6%). The fraction of kaons decaying in the FV is 13%, lead-ing to 6 MHznominal K+ decayrate. The beamis accompanied by aflux ofmuonsproducedby K+ and

π

+ decaysupstream of thevacuumtank(thebeamhalo),with3 MHznominalrateinthe detectoracceptance.Centralholes indetectorsdownstreamofthe FVanda beampipetraversing mostofthesedetectorsallowthe

https://doi.org/10.1016/j.physletb.2018.01.031

0370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Fig. 1. Schematic side view of the NA62 beamline and detector.

undecayed beamparticles to continue their pathin vacuum. The beam intensity during the 2015run was typically

O(

1%

)

of the nominalvalue.

Themomentaofcharged K+ decayproducts are measuredby

a magnetic spectrometer (STRAW) located in the vacuum tank

downstream of the FV. The spectrometer consists of four track-ing chambersmade ofstraw tubes, anda dipole magnetlocated betweenthesecondandthethirdchamberprovidingahorizontal momentum kick of approximately 270 MeV

/

c. The spectrometer momentum resolution is

σ

p

/

p

= (

0

.

30

⊕

0

.

005

·

p

)

%, where the momentum p isexpressedinGeV/c.

A27X0 thickquasi-homogeneous liquidkrypton(LKr) electro-magnetic calorimeter, builtfor the earlier NA48 experiment [11]

andequippedwithanewreadoutsystem, isusedforphoton de-tection. The calorimeter has an active volume of 7 m3, and is segmentedtransversally into 13248projective

∼

2

×

2 cm2 cells. ItsenergyresolutionintheNA62conditionsis

σ

E

/

E

= (

4

.

8

/

√

E

⊕

11

/

E

⊕

0

.

9

)

%, where E is expressed inGeV. To achieve hermetic acceptanceforphotonsemitted in K+ decaysintheFVatangles up to 50 mrad, the LKrcalorimeter is supplemented by annular leadglasslarge-angleveto(LAV)detectorsinstalledin12 positions along and downstream of the FV, and two lead/scintillator sam-pling calorimeters(intermediate-ring calorimeter, IRC,and small-anglecalorimeter,SAC)locatedclosetothebeamaxis.

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

17.5 mlongvesselfilledwithneonatatmosphericpressureisused for identification of charged K+ decay products. Its Cherenkov thresholdformuonsis9.5 GeV/c,anditprovidestiming measure-ment fortracks above threshold tobetter than 100 ps precision. TheLKrcalorimeter,ahadroniciron/scintillatorsampling calorime-terformedof twomodules (MUV1,2) andascintillator-tile muon detector(MUV3)locatedbehind an80cmthickironwallarealso used for particle identification. A plastic scintillator hodoscope (CHOD) built for the NA48 experiment, located in front of the calorimeters,providesafasttriggerwithefficiencyabove99%and track-timingmeasurementto200 psprecision.

Thedata sampleused forthisanalysisisobtainedfrom1

.

2

×

104 _{SPS spills recorded in 5 days of operation in 2015 at beam} intensityvarying from0.4% to 1.3% ofthe nominal value with a minimum-biastriggerscheme.Thelow-levelhardware trigger re-quired a CHOD signal (downscaled typically by a factor of 3) to collect K+ decaystomuons(which accountfor67%ofthe decay rate), and a CHOD signal in anti-coincidence with a MUV3 sig-nal(notdownscaled)tocollectdecayswithnomuonsinthefinal state.Thehigh-levelsoftwaretriggerrequiredakaonsignalinthe KTAGdetectorwithin

±

10 nsofthelow-leveltriggersignal.Loose timingconditionsare usedinthisanalysisbecausetheaccidental ratesaresmall,duetothelowbeamintensity.

2. Eventselection

Assuming

|

U4

|

2

<

10−4 andconsidering HNLdecays intoSM particles[12],thesmallestpossibleaveragedecaylengthofaHNL produced in the K+

→ 

+N decays in NA62 conditions exceeds 10 km. Underthe above assumption,HNL decaysinflight in the 156 m long volume fromthe startof theFV tothe last detector (SAC)canbeneglected,andthe K+

→ 

+N decayischaracterized by a single detected track inthe final state, similarly to the SM

K+

→ 

+

ν

decay.Theprincipalselectioncriteriaarelistedbelow.

•

A single positively charged track reconstructed in the spec-trometerwithmomentumintherange5–70 GeV/c isrequired. AdditionalspectrometertracksandLKrenergydeposition clus-ters not geometrically compatible withthe trackare not

al-lowed within

±

100 ns of the track time measured by the

CHOD.Activityinthelarge-angleandsmall-anglephotonveto detectorsandtheCHANTIdetectorwithin

±

10 nsofthetrack time is not allowed. Track impact points in thestraw cham-bers,LKrcalorimeter,CHODandMUV1–3detectorsshouldbe withintheirfiducialgeometricalacceptances.

•

Thekaondecayvertexisreconstructedasthepointofclosest approach ofthetrackandthe beamaxis(the latteris moni-toredwithfullyreconstructedK+

→

π

+

π

+

π

−decays),taking into account the measured stray magnetic field map in the vacuum tank. The reconstructed closest distanceof approach (CDA) betweenthe track andbeamaxis should be lessthan 25 mm,asdeterminedbythebeamtransversesize.

•

TosuppressbeamhalobackgroundfromK+ decaysupstream oftheKTAGandbeam

π

+decays,thepresenceofakaon sig-nal intheKTAG isrequired within

±

10 ns ofthetracktime

measuredbytheCHOD.

•

Beamhalo backgroundfrom K+

→

μ

+

ν

decaysoverthe ap-proximately 30 mlong path betweenthe KTAG andthe last GTK station(withthemuon deflectedbymagneticfieldsand scatteredinmagnetyokesandcollimatorsbeforereachingthe vacuumtank) issuppressed by geometricalconditions estab-lished bystudiesofupstream K+ decays.Forthe K+

→

e+N

selection, the reconstructed vertexposition is required tobe at least 10 m downstream of the start of the FV. For the

K+

→

μ

+N selection,theminimalrequireddistancebetween thedecayvertexandthestartoftheFVdependsonthemuon emission anglewithrespecttothe beamaxisandlies inthe range10–33 m.

•

Positrons and muons are identified by the ratio of energy

deposit, E, in the LKr calorimeter to momentum, p,

mea-sured by the spectrometer: 0

.

9

<

E

/

p

<

1

.

15 and E

/

p

<

0

.

2, respectively. No signalsin MUV1–3 detectorswithin

±

20 ns of the track time and geometrically consistent with e+

can-Fig. 2. Distributionsofthem2

miss variablefordataandsimulatedeventspassingthe(a)e+and(b)μ+selections.Thebinwidthsare0.004 GeV

2_/c4_{.Pairsofverticallines} ineachplotindicatetheboundariesoftheSMandHNLsignalregions.TheHNLsignalregionsdefinedinSection2correspondapproximatelyto0.03–0.20 GeV2_/c4_and 0.06–0.14 GeV2_/c4_inm2

missvaluesinthee+andμ+case,respectively.

didate tracks (accounting for detector granularity and mul-tiple scattering) are allowed; MUV1–3 signals are required for

μ

+ candidate tracks. Additionally, an identification algo-rithmbasedontheRICHhitpatternisappliedfortrackswith

p

<

40 GeV/c.

Thesquaredmissingmassiscomputedasm_miss2

= (

PK

−

P

)

2, where PK and P are the kaon and lepton 4-momenta, respec-tively.PK isobtainedfromthebeamaverage3-momentum (mon-itoredwith K+

→

π

+

π

+

π

− decays) inthe K+ masshypothesis, while P isevaluated fromthe reconstructedtrack3-momentum inthecorresponding



+masshypothesis.

Simulation of particle interactions with the detector and its

response is performed with a Monte Carlo (MC) simulation

package based on the Geant4 toolkit [13]. The m2

miss spectra of the selected events from both data and simulation are dis-played inFig. 2.Signals fromthe SM leptonic decays K+

→ 

+

ν

are observed as peaks at m2_miss

=

0 with m2_miss resolutions of 4

.

9

(

4

.

7

)

×

10−3 GeV2

/

c4 in the e+ (

μ

+) case. These

reso-lutions are dominated by the momentum spread and

diver-gence of the beam, and are reproduced by MC simulations to

1% relative precision. The SM and HNL signal regions are de-finedinthee+ (

μ

+)caseas

|

m2

miss

| <

0

.

014

(

0

.

020

)

GeV 2

/

c4 _and 170

(

250

) <

mmiss

<

448

(

373

)

MeV/c2, respectively. The search for K+

→ 

+N decaysconsistsofa searchfor peaksabove back-groundintheHNLsignalregions.

3. Measurementprinciple

The K+

→ 

+N decayrates aremeasured withrespect tothe rates of the normalization SM K+

→ 

+

ν

decays with similar topologiesandknown branchingfractions.Theexpectednumbers ofK+

→ 

+N signaleventsN

S arerelatedtotheassumed branch-ingfractions

B(

K+

→ 

+N

)

andacceptances AN_ oftheK+

→ 

+N

selectionsas

N_S

=

N_K

·

B

(

K+

→ 

+N

)

·

AN_

.

(2)

HereN_K arethenumbersofK+decaysintheFV,computedfrom thenumbers Nofselecteddataeventswithm2miss intheSM sig-nalregion:

Ne_K

=

Ne

Aee

·

B

(

K+

→

e+

ν

)

+

Aμe

·

B

(

K+

→

μ

+

ν

)

= (

3.00

±

0.11)

×

108

Table 1

InputstothecomputationofthenumbersN

K ofkaondecaysintheFV:numbers ofselecteddataeventsinthe SMsignalregion,acceptancesevaluatedwithMC simulationsandtheirstatisticalerrors(notationisdefinedinthetext),and K+→

+νbranchingfractions[4].

K+→e+νselection K+→μ+νselection

Number of data events N 1767 2.403×107

Acceptance Aμ (1.30±0.17)×10−6 0.3579±0.0001 Acceptance Ae  0.3197±0.0008 – B(K+→ +ν) (1.582±0.007)×10−5 _{0.6356±0.0011} and Nμ_K

=

Nμ Aμ_μ

·

B

(

K+

→

μ

+

ν

)

= (

1.06

±

0.02)

×

10 8

_,

where A2

1 is the acceptance of the K

+

_{→ }

+

1

ν

selection (with

m2_miss intheSM signalregion)fortheK+

→ 

+₂

ν

decayevaluated withMC simulations,and

B(

K+

→ 

+

ν

)

isthebranchingfraction oftheK+

→ 

+

ν

decay[4].TheinputstothecomputationofN

K are summarizedinTable 1.Thenumberof K+ decays inthe

μ

+ caseis smaller than that inthe e+ casedue to thedownscaling factoroftypically3appliedtothemuontriggerchain.

The above approach relieson first-order cancellationbetween signal,normalizationandbackgroundyieldsoftheeffectsof resid-ualdetectorinefficiencies,triggerefficienciesandrandomvetonot fullyaccountedforbytheMCsimulation.

The background in the K+

→

e+

ν

sample from K+

→

μ

+

ν

decays, due to both

μ

+ mis-identification and decay in flight,

is taken into account in the computation of Ne

K. This back-ground is dominated by

μ

+ mis-identification due to ‘catas-trophic’ bremsstrahlungin the LKrcalorimeterattrackmomenta

p

>

40 GeV

/

c, where identificationrelies on calorimetry only as the RICH doesnot provide usefulinformation. Theprobability of amuon having E

/

p

>

0

.

90 inthe LKrcalorimeterhasbeen mea-sured in a dedicated study to be

P

μe

∼

10−5, and found to be reproducedbysimulationto10%relativeprecision[14].The back-groundinthe K+

→

μ

+

ν

sampleisnegligible.

Thequoted uncertaintyon Ne_K receives contributionsfromthe statistical error(2.4%), precision on the simulation (evaluated by stability checks versus variation of the selection conditions and considering the precision on

P

μe simulation, 2.0%), MC statisti-cal precision on the acceptance for the K+

→

μ

+

ν

background (1.9%)andtheexternalparameter

B(

K+

→

e+

ν

)

(0.4%),combined in quadrature to obtain a total relative errorof 3.7%. The uncer-tainty on Nμ_K receives two contributions of similar size: due to

Fig. 3. (a)Missingmassresolutionσ

mevaluatedfromMCsimulations:valuesobtainedforasetofHNLmasseswiththeirstatisticalerrors,andpolynomialfunctionsusedto definetheHNLselectioncriterion.Thecorrespondingresolutiononthesquaredmissingmassinthesignalregionsisafew10−3_GeV2_/c4_{,andhasaweakmassdependence.} (b)AcceptancesAN

 oftheK+→ +N selectionsobtainedfromMCsimulations;thedashedlinecorrespondstothelooseK+→e+N selectionappliedforHNLmassesof

350 MeV/c2_{andabove.VerticalarrowsindicatetheextentoftheHNLsignalregions.} theprecision ofthe simulation(evaluated byvariation ofthe se-lectionconditions) andduetothe externalinput

B(

K+

→

μ

+

ν

)

, combinedinquadraturetoobtainatotalrelativeerrorof1.9%.

4. BackgroundestimateswithMCsimulations

TheHNLsearchprocedure,presentedinSection5,isbasedon adata-drivenbackgroundestimationmethod,butthisisonlyvalid provided thereare no peakingbackgroundstructures inthe HNL massregion.BackgroundstoHNLproductionhavebeenestimated byMCsimulations(Fig. 2)tounderstandqualitativelytheir contri-butions andto optimizethe eventselection. The resultsof these simulationstudies,reportedbelow,justifytheadoptedprocedure.

4.1. BackgroundstoK+

→

e+N

The principal background to K+

→

e+N decays comes from the K+

→

μ

+

ν

decay followed by muon decay in flight

μ

+

→

e+

ν

ν

¯

. It is characterized by a broader CDA distributionthan the signal, and is suppressed by the CDA and vertex position selec-tion criteria (Section 2). The CDA selection criterion and there-forethebackgroundlevelaredeterminedby thebeamtransverse size.The backgrounddue to K+

→

μ

+

ν

decays withmuon mis-identification(Section3)isconstrainedtolowm2_missvaluesoutside theHNLsignalregion.

Beam pion decays

π

+

→

e+

ν

, as well as

π

+

→

μ

+

ν

fol-lowed by muon decay in flight, contribute to the background

via

π

+ mis-identificationby the KTAG due to accidental coinci-dencewithabeamkaonnotdecayingintheFV.Thecontribution fromdirect

π

+ mis-identificationbythe KTAGis negligible.Pion mis-identificationprobability forthe employed KTAG–CHOD tim-ing condition, averaged over thedata sample, is computedto be

(

0

.

9

±

0

.

1syst

)

% fromthe beam K+ ratemeasured viathe rateof out-of-time K+ signals in the KTAG. This estimate is consistent withthenumberofobserved

π

+

→

e+

ν

decaysinthe

(

Pπ

−

Pe

)

2

spectrum,where Pπ isthebeampion4-momentum.

Backgrounds from all other major K+ decays with branching fractionsabove1%, andall K+ decaystopositronsandbranching fractionsabove 10−5 _{[4]havebeenconsidered. Them}2

miss spectra oftheestimatedbackgroundcomponentsaredisplayed inFig. 2a, showinggoodagreementwiththedataspectrum.

4.2. BackgroundstoK+

→

μ

+N

The largest component ofthe background to K+

→

μ

+N

de-cays comes fromthe K+

→

μ

+

νγ

decay,mainly duetophotons emitted atanglesgreater than50 mradwithrespecttothebeam axisandescapingtheLAV geometricalacceptance.Itissimulated includinginnerbremsstrahlungandstructure-dependentprocesses aswell astheirinterference [15];decays withthe photonenergy inthekaonrestframeEγ belowandabove10 MeVaresimulated separatelytoincreasetheMCstatisticsinthelattercase.

Residual backgrounddueto K+decaysbetweentheKTAGand the last GTK station, whichis suppressed by the cut onthe ver-texlongitudinalposition(Section2),isestimatedfromadedicated simulation.Backgrounds fromall other major K+ decaysare also considered:thelargestofthemisduetothe K+

→

π

+

π

+

π

− de-cay.

Them2

miss spectraoftheestimatedbackgroundcomponentsare displayed in Fig. 2b; current agreement with the data spectrum intheHNLsignalregionismarginal.Observationinthedataofa backgroundcomponent(notreproducedwithMCsimulation)with muons propagating close to the yz plane (which is the bending plane ofthe GTK dipole magnets) suggeststhatthe data/MC dis-agreementintheHNLsignalregionisduetothelimitedprecision on the beamline simulation affecting the estimated background from upstream K+ decays. Onthe other hand,the disagreement atnegativem2_missisduetothelimitedprecisionofthedescription oftheresolution,affectedbythesimulationofthebeam momen-tumspectrumanddivergence.

5. SearchforHNLproduction

Mass scans are performed in the HNL signal regions with a step size of 1 MeV/c2. The event selection employed for each HNLmasshypothesis involvesanadditionalcondition:the recon-structed missing massshould be within

±

1

.

5

σ



m of theassumed

HNL mass, where

σ



m is the mass resolution evaluated withMC simulations (Fig. 3a).Theabovewidthofthesignalmasswindow leads to near-optimalexpectedupper limitson

B(

K+

→ 

+N

)

in theabsenceofsignalsacrossthewholeHNLsignalregions.Aloose selectionwitharelaxedvertexlongitudinalpositionconstraint (re-quiring the vertexto be inthe FV) is applied inthe K+

→

e+N

caseformasshypothesesof350 MeV/c2 andhigher,reflectingthe fact that the beamhalobackgrounddoes notpopulate thismass range. Acceptances, AN

Fig. 4. ForeachNHLmasshypothesis,numbersofexpected(Nexp)andobserved(Nobs)events,togetherwiththeuncertaintyonNexp(δNexp,asshownbytheblueband); expectedandobservedupperlimitsat90%CLonthenumbersofK+→ +N eventsN

Sobtainedfromtheseinputs.(a)K+→e+N analysis;(b):K+→μ+N analysis.For completeness,thesquaredmassscaleisalsoshown.Thelegendshowninfigure(b)referstobothpanels.(Forinterpretationofthereferencestocolourinthisfigurelegend, thereaderisreferredtothewebversionofthisarticle.)

masscut)asfunctionsofHNLmassobtainedwithMCsimulations areshowninFig. 3b.

Tocertify that the missing mass resolution andtherefore the signal acceptance are simulated correctlyoutside the SM K+

→



+

ν

peaks,theresolutionon

m2_3π

= (

PK

−

P3

)

2

− (

P1

+

P2

)

2 in fullyreconstructed K+

→

π

+

π

+

π

− decays,where Pi (i

=

1

,

2

,

3) arethepion4-momentareconstructed fromthespectrometer

in-formation and PK is the kaon 4-momentum defined as for the

m2

miss computation (Section 2),has beenstudied asafunction of

(

P1

+

P2

)

2.Giventhat

m2_3π

=

0 by construction, theresolution on

m2_{3π can}be measured forboth data andMC. Data and MC resolutionshave beenfound toagree within 1%. Fortheadopted

±

1

.

5

σ



m masswindow,1% changeon

σ

m translatesinto0.4% rela-tivechangeonthesignalacceptance.

In each HNL mass hypothesis considered, the background is evaluatedfromsidebandsofthedatammiss distribution.The num-berof expectedbackgroundevents Nexp within the

±

1

.

5

σ

m HNL search window is estimatedfrom a least-squares fit to the data

mmiss spectrum witha binwidth of 5 MeV/c2 using third order polynomialfunctionsinthe100–460 (200–385) MeV/c2 _rangefor thee+ (

μ

+) case. Mass binsoverlapping with the

±

1

.

5

σ



m wide HNLsearchwindowareexcludedfromthefittoavoidbiascaused bypossibleHNLsignals.Statisticaluncertainties

δ

Nexponthe back-groundestimates Nexp are computedby propagationofstatistical errors on the fit function parameters: they are typically about 10%inrelativeterms.SystematicuncertaintiesonNexp duetothe choiceofbackgroundfitfunction,estimatedbyusingfourthorder polynomialsforthefits,arenegligible(typically1%).

In each HNL mass hypothesis, the total number of observed eventsNobs within the

±

1

.

5

σ

m HNLsearch window, thenumber ofexpectedbackgroundeventsNexp anditsuncertainty

δ

Nexp are usedtocomputeconfidenceintervalsforthenumberofobserved

K+

→ 

+N decays N

S. The Rolke–López method [16] assuming Poissonian (Gaussian) distributions for the numbers of observed (expected) events is used. The procedure has been tested and found to be unbiased in the presence of artificially injected sta-tisticallysignificant K+

→ 

+N signals.The valuesofNexp,

δ

Nexp and Nobs in each HNLmass hypothesis considered are shownin

Fig. 4. The maximum value of the local signal significance com-putedas

z

= (

Nobs

−

Nexp

)/



Nobs

+ (δ

Nexp

)

2

is2.2, forthe e+ casewithmN

=

283 MeV

/

c2.Inthe absenceof statisticallysignificantHNLproductionsignals,upperlimitsonN_S

are established; the expected andobserved limits at 90% CL are showninFig. 4.Perfectknowledgeofthebackground(

δ

Nexp

=

0) wouldimprovetheselimitstypicallyby30%.

Singleeventsensitivities(SES)definedasthevaluesof

B(

K+

→



+N

)

andthemixingparameter

|

U4

|

2correspondingtothe obser-vationofonesignalevent,

B

SES

(

K+

→ 

+N

)

=

1 N K

·

AN and

|

U4

|

2SES

=

B

SES

(

K+

→ 

+N

)

B

(

K+

→ 

+

ν

)

·

ρ



(

mN

)

,

are displayed as functions of HNL mass in Fig. 5a. They are

O(

10−8

₎

_{, and those in the positron case are smaller than those} inthemuoncaseduetoNe_K beinglargerthanNμ_K.

Upperlimitson thebranching fraction

B(

K+

→ 

+N

)

ineach

HNL mass hypothesis are computed from those on N

S using

eq. (2); the expected and observed limits at 90% CL are shown in Fig. 5b. Upper limitson the mixing parameter

|

U4

|

2 in each HNLmasshypothesis arecomputedfromthoseon

B(

K+

→ 

+N

)

according to eq. (1). These limitsdepend on the external inputs

B(

K+

→ 

+

ν

)

onlyinthee+caseduetothebackground subtrac-tionintheNe_K computation.Systematicuncertaintiesonthelimits are,inrelativeterms,ofthesamemagnitudeasthoseonN

K (Sec-tion3).

The obtained upper limitson

|

U4

|

2 at 90% CL together with thelimitsfrompreviousHNLproductionsearchesin

π

+[5,6]and

K+[7–9]decaysareshowninFig. 6.Thereportedresultimproves theexistinglimitsonboth

|

Ue4

|

2 (overthewholemassrange con-sidered)and

|

Uμ4

|

2(above300 MeV/c2).

6. Summary

A search for HNL production in K+

→ 

+N decays has been performedwithNA62 datarecordedin2015at

∼

1% ofthe nom-inal beam intensity with a minimum bias trigger. Upper limits on the HNL mixing parameters

|

Ue4

|

2 and

|

Uμ4

|

2 in the ranges 170–448 MeV/c2 and 250–373 MeV/c2, respectively, have been established at the level between 10−7 and 10−6. This improves on the previous limits from HNL production searches over the

Fig. 5. (a)SingleeventsensitivitiesBSES(K+→ +N)(dashedlines)and|U4|2SES(solidlines)definedinthetextasfunctionsoftheassumedHNLmass.(b)Expected(dashed lines)andobserved(solidlines)upperlimitsat90%CLonB(K+→e+N)(toppanel)andB(K+→μ+N)(bottompanel)obtainedforeachHNLmasshypothesis.

Fig. 6. Upperlimitsat 90% CLon |U4|2 obtainedfor each assumedHNLmass comparedtothelimitsestablishedbyearlierHNLproductionsearchesinπ+ de-cays:TRIUMF(1992)[5],PIENU(2017)[6]and K+ decays:KEK(1984)[7],E949 (2015)[8],NA62-2007(2017)[9].

whole mass range considered for

|

Ue4

|

2 (and extends the mass range in which the limits exist), and above mN

=

300 MeV/c2 for

|

Uμ4

|

2.

Acknowledgements

Itis a pleasureto expressourappreciation tothe staffofthe CERNlaboratory andthetechnical staffofthe participating labo-ratories and universities for their efforts in the operation ofthe experimentanddataprocessing.

The cost of the experimentand ofits auxiliary systems were supportedby thefundingagenciesoftheCollaboration Institutes. Weareparticularlyindebtedto:F.R.S.-FNRS(FondsdelaRecherche 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 undForschung) contracts05H12UM5 and

05H15UM-CNA,Germany; INFN (Istituto Nazionale diFisica Nucleare),Italy; MIUR (Ministero dell’Istruzione, dell’Università e della Ricerca), Italy; CONACYT (Consejo Nacional de Cienciay Tecnología), Mex-ico; IFA (Institute of Atomic Physics), 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 and Sportof the Slovak Republic), Slovakia; CERN (European Or-ganization for Nuclear Research), Switzerland; STFC (Scienceand Technology FacilitiesCouncil), UnitedKingdom;NSF(National Sci-ence Foundation)Award Number 1506088, U.S.A.;ERC (European ResearchCouncil)“UniversaLepto”advancedgrant 268062, “Kaon-Lepton”startinggrant336581,Europe.

Individuals have received support from: Charles University (project GAUK number404716),Czech Republic;Ministryof Ed-ucation,Universities andResearch(MIUR “Futuroinricerca2012” grant RBFR12JF2Z, Project GAP), Italy; the Royal Society (grants UF100308,UF0758946),UnitedKingdom;STFC(Rutherford fellow-shipsST/J00412X/1, ST/M005798/1),United Kingdom;ERC (grants 268062,336581).

References

[1]T. Asaka, M. Shaposhnikov, Phys. Lett. B 620 (2005) 17. [2]R. Shrock, Phys. Lett. B 96 (1980) 159.

[3]R. Shrock, Phys. Rev. D 24 (1981) 1232.

[4]C. Patrignani, et al., Particle Data Group, Chin. Phys. C 40 (2016) 100001. [5]D. Britton, et al., Phys. Rev. D 46 (1992) R885.

[6]A. Aguilar-Arevalo, et al., arXiv:1712.03275.

[7]T. Yamazaki, et al., in: Proceedings of Neutrino 1984 Conference, 1984. [8]A. Artamonov, et al., Phys. Rev. D 91 (2015) 052001.

[9]C. Lazzeroni, et al., Phys. Lett. B 772 (2017) 712. [10]E. Cortina Gil, et al., J. Instrum. 12 (2017) P05025. [11]V. Fanti, et al., Nucl. Instrum. Methods A 574 (2007) 433.

[12]D. Gorbunov, M. Shaposhnikov, J. High Energy Phys. 0710 (2007) 015. [13]S. Agostinelli, et al., Nucl. Instrum. Methods A 506 (2003) 250. [14]C. Lazzeroni, et al., Phys. Lett. B 698 (2011) 105.

[15]J. Bijnens, G. Ecker, J. Gasser, Nucl. Phys. B 396 (1993) 81. [16]W.A. Rolke, A.M. López, Nucl. Instrum. Methods A 458 (2001) 745.

NA62Collaboration

E. Cortina Gil,

E. Minucci,

S. Padolski

1

,

P. Petrov,

B. Velghe

2

CharlesUniversity,Prague,CzechRepublic

R. Aliberti,

G. Khoriauli,

J. Kunze,

D. Lomidze

6

,

R. Marchevski,

L. Peruzzo,

M. Vormstein,

R. Wanke

InstitutfürPhysikandPRISMAClusterofexcellence,UniversitätMainz,Mainz,Germany

P. Dalpiaz,

M. Fiorini,

E. Gamberini

7

,

I. Neri,

A. Norton,

F. Petrucci,

H. Wahl

DipartimentodiFisicaeScienzedellaTerradell’UniversitàeINFN,SezionediFerrara,Ferrara,Italy

A. Cotta Ramusino,

A. Gianoli

INFN,SezionediFerrara,Ferrara,Italy

E. Iacopini,

G. Latino,

M. Lenti

DipartimentodiFisicaeAstronomiadell’UniversitàeINFN,SezionediFirenze,SestoFiorentino,Italy

A. Bizzeti

8

,

F. Bucci,

R. Volpe

INFN,SezionediFirenze,SestoFiorentino,Italy

A. Antonelli,

F. Gonnella

9

,

G. Lamanna

10

,

G. Lanfranchi,

G. Mannocchi,

S. Martellotti,

M. Moulson,

M. Raggi

11

,

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,

C. Santoni

DipartimentodiFisicaeGeologiadell’UniversitàeINFN,SezionediPerugia,Perugia,Italy

M. Barbanera

12

,

P. Cenci,

B. Checcucci,

V. Duk

9

,

P. Lubrano,

M. Lupi

7

,

M. Pepe,

M. Piccini

INFN,SezionediPerugia,Perugia,Italy

F. Costantini,

L. Di Lella,

N. Doble,

M. Giorgi,

S. Giudici,

E. Pedreschi,

M. Sozzi

DipartimentodiFisicadell’UniversitàeINFN,SezionediPisa,Pisa,Italy

C. Cerri,

R. Fantechi,

R. Piandani,

J. Pinzino

7

,

L. Pontisso,

F. Spinella

INFN,SezionediPisa,Pisa,Italy

I. Mannelli

ScuolaNormaleSuperioreeINFN,SezionediPisa,Pisa,Italy

G. D’Agostini

J. Engelfried,

N. Estrada-Tristan

InstitutodeFísica,UniversidadAutónomadeSanLuisPotosí,SanLuisPotosí,Mexico

A.M. Bragadireanu,

S.A. Ghinescu,

O.E. Hutanu

HoriaHulubeiNational InstituteofPhysicsandNuclearEngineering,Bucharest-Magurele,Romania

T. Enik,

V. Falaleev,

V. Kekelidze,

A. Korotkova,

D. Madigozhin,

M. Misheva

16

,

N. Molokanova,

S. Movchan,

I. Polenkevich,

Yu. Potrebenikov,

S. Shkarovskiy,

A. Zinchenko

†

JointInstituteforNuclearResearch,Dubna,Russia

S. Fedotov,

E. Gushchin,

A. Khotyantsev,

A. Kleimenova

17

,

Y. Kudenko

18

,

V. Kurochka,

M. Medvedeva,

A. Mefodev,

A. Shaikhiev

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,

M. Koval

7

,

Z. Kucerova

FacultyofMathematics,PhysicsandInformatics,ComeniusUniversity,Bratislava,Slovakia

A. Ceccucci,

H. Danielsson,

F. Duval,

B. Döbrich,

L. Gatignon,

R. Guida,

F. Hahn,

B. Jenninger,

P. Laycock,

G. Lehmann Miotto,

P. Lichard,

A. Mapelli,

M. Noy,

V. Palladino

19

,

M. Perrin-Terrin

17

,

G. Ruggiero

20

,

V. Ryjov,

S. Venditti

CERN,EuropeanOrganizationforNuclearResearch,Geneva,Switzerland

M.B. Brunetti,

V. Fascianelli

21

,

E. Goudzovski

∗

,

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.B. Dainton

20

,

J.R. Fry

9

,

L. Fulton,

D. Hutchcroft,

K. Massri

7

,

E. Maurice

22

,

B. Wrona

UniversityofLiverpool,Liverpool,UnitedKingdom

A. Conovaloff,

P. Cooper,

D. Coward

23

,

P. Rubin

Presentaddress:DipartimentodiFisica,UniversitàdiRomaLaSapienza,I-00185Roma,Italy. 12 _{Presentaddress:INFN,SezionediPisa,I-56100Pisa,Italy.}

13 _{AlsoatDepartmentofIndustrialEngineering,UniversityofRomaTorVergata,I-00173Roma,Italy.} 14 _{AlsoatDepartmentofElectronicEngineering,UniversityofRomaTorVergata,I-00173Roma,Italy.} 15 _{AlsoatUniversitàdegliStudidelPiemonteOrientale,I-13100Vercelli,Italy.}

16 _{Presentaddress:InstituteofNuclearResearchandNuclearEnergyofBulgarianAcademyofScience(INRNE-BAS),BG-1784Sofia,Bulgaria.} 17 _{Presentaddress:UniversitéCatholiquedeLouvain,B-1348Louvain-La-Neuve,Belgium.}

18 _{AlsoatNationalResearchNuclearUniversity(MEPhI),115409MoscowandMoscowInstituteofPhysicsandTechnology,141701Moscowregion,Moscow,Russia.} 19 _{Presentaddress:PhysicsDepartment,ImperialCollegeLondon,London,SW72BW,UK.}

20 _{Presentaddress:PhysicsDepartment,UniversityofLancaster,Lancaster,LA14YW,UK.} 21 _{Presentaddress:DipartimentodiPsicologia,UniversitàdiRomaLaSapienza,I-00185Roma,Italy.} 22 _{Presentaddress:LaboratoireLeprinceRinguet,F-91120Palaiseau,France.}