Measurement of the branching fraction for the decay KS → πμν with the KLOE detector

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

branching

fraction

for

the

decay

K

_S

→

π μν

with

the

KLOE

detector

The

KLOE-2

Collaboration

D. Babusci

d

,

M. Berlowski

v

,

C. Bloise

d

,

F. Bossi

d

,

P. Branchini

s

,

A. Budano

r

,

s

,

B. Cao

u

,

F. Ceradini

r

,

s

,

P. Ciambrone

d

,

F. Curciarello

a

,

d

,

E. Czerwi ´nski

c

,

G. D’Agostini

n

,

o

,

E. Danè

d

,

V. De Leo

n

,

o

,

E. De Lucia

d

,

A. De Santis

d

,

P. De Simone

d

,

A. Di Cicco

r

,

s

,

A. Di Domenico

n

,

o

_,

_{D. Domenici}

d

_,

_{A. D’Uffizi}

d

_,

_{A. Fantini}

p

,

q

_,

_{P. Fermani}

d

_,

_{S. Fiore}

t

,

o

_,

A. Gajos

c

,

P. Gauzzi

n

,

o

,

S. Giovannella

d

,

E. Graziani

s

,

V.L. Ivanov

g

,

h

,

T. Johansson

u

,

X. Kang

d

,

D. Kisielewska-Kami ´nska

c

,

E.A. Kozyrev

g

,

h

,

W. Krzemien

v

,

A. Kupsc

u

,

P.A. Lukin

g

,

h

,

G. Mandaglio

f

,

b

,

M. Martini

d

,

m

,

R. Messi

p

,

q

,

S. Miscetti

d

,

D. Moricciani

d

,

P. Moskal

c

,

S. Parzych

c

,

A. Passeri

s

,

V. Patera

l

,

o

,

E. Perez del Rio

n

,

o

,

P. Santangelo

d

,

M. Schioppa

j

,

k

,

A. Selce

r

,

s

,

∗

,

M. Silarski

c

,

F. Sirghi

d

,

e

,

E.P. Solodov

g

,

h

,

L. Tortora

s

,

G. Venanzoni

i

,

W. Wi´slicki

v

,

M. Wolke

u

a_{DipartimentodiFisicaeAstronomia“EttoreMajorana”,UniversitàdiCatania,Italy} b_{INFNSezionediCatania,Catania,Italy}

c_{InstituteofPhysics,JagiellonianUniversity,Cracow,Poland} d_{LaboratoriNazionalidiFrascatidell’INFN,Frascati,Italy}

e_{HoriaHulubeiNationalInstituteofPhysicsandNuclearEngineering,Mˇagurele,Romania}

f_{DipartimentodiScienzeMatematicheeInformatiche,ScienzeFisicheeScienzedellaTerradell’UniversitàdiMessina,Messina,Italy} g_{BudkerInstituteofNuclearPhysics,Novosibirsk,Russia}

h_{NovosibirskStateUniversity,Novosibirsk,Russia} i_{INFNSezionediPisa,Pisa,Italy}

j_{DipartimentodiFisicadell’UniversitàdellaCalabria,Rende,Italy} k_{INFNGruppocollegatodiCosenza,Rende,Italy}

l_{DipartimentodiScienzediBaseedApplicateperl’Ingegneriadell’Università“Sapienza”,Roma,Italy} m_{DipartimentodiScienzeeTecnologieapplicate,Università“GuglielmoMarconi”,Roma,Italy} n_{DipartimentodiFisicadell’Università“Sapienza”,Roma,Italy}

o_{INFNSezionediRoma,Roma,Italy}

p_{DipartimentodiFisicadell’Università“TorVergata”,Roma,Italy} q_{INFNSezionediRomaTorVergata,Roma,Italy}

r_{DipartimentodiMatematicaeFisicadell’Università“RomaTre”,Roma,Italy} s_{INFNSezionediRomaTre,Roma,Italy}

t_{ENEA,DepartmentofFusionandTechnologyforNuclearSafetyandSecurity,Frascati(RM),Italy} u_{DepartmentofPhysicsandAstronomy,UppsalaUniversity,Uppsala,Sweden}

v_{NationalCentreforNuclearResearch,Warsaw,Poland}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received13December2019

Receivedinrevisedform14February2020 Accepted18March2020

Availableonline20March2020 Editor:L.Rolandi

Keywords: e+e−collisions

Based ona sampleof300 million KS mesonsproduced inφ→KLKS decays recorded by theKLOE experimentattheDANEe+e− colliderwehavemeasuredthebranchingfractionforthedecayKS_→

π μν

.The KS mesonsare identifiedbytheinteraction ofKL mesonsinthedetector. The KS→

π μν

decays are selectedby aboosted decisiontreebuilt with kinematic variablesand by atime-of-flight measurement. Signalefficiencies are evaluated withdata control samples of KL→

π μν

decays.A fit tothereconstructedmuonmassdistributionfinds 7223±180 signalevents.NormalisingtotheKS→

π

+

π

−decayeventstheresultforthebranchingfractionis_B(KS_→

π μν

)= (4.56_±0.11stat±0.17syst)×

*

Correspondingauthorat:DipartimentodiMatematicaeFisicadell’Università“RomaTre”,Roma,Italy. E-mailaddress:[email protected](A. Selce).

https://doi.org/10.1016/j.physletb.2020.135378

K0_meson Semileptonicdecay

10−4_{.Itisthefirstmeasurementofthisdecaymodeandtheresultallowsanindependentdetermination}

of|Vus|andatestofthelepton-flavouruniversality.

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

1. Introduction

Thebranching fractionforsemileptonicdecaysofchargedand neutralkaonstogetherwiththelifetimemeasurementsareusedto determine the

|

Vus

|

element ofthe Cabibbo–Kobayashi–Maskawa quark mixingmatrix.The relationamong thematrixelements of thefirstrow,

|

Vud

|

2

+ |

Vus

|

2

+ |

Vub

|

2

=

1,providesthemost strin-genttestoftheunitarityofthequarkmixingmatrix.Different fac-torscontribute totheuncertaintyindetermining

|

Vus

|

fromkaon decays [1–3] andamongthesixsemileptonicdecaysthe contribu-tionofthelifetimeuncertaintyissmallestfortheKS meson. Nev-ertheless, giventhe lack ofpure high-intensity KS mesonbeams contrarytothecaseofK±and KL mesons,the KS

→

π

e

ν

decay providestheleastprecisedeterminationof

|

Vus

|

,andthe branch-ingfraction

B(

KS

→

π μν

)

hasnot yetbeenmeasured. Measure-ment of this decay mode allows an independent determination of

|

Vus

|

and to extend the test of lepton-flavour universality to

KS semileptonicdecaysbycomparisonwiththeexpectedvalueof

(

4

.

69

±

0

.

06

)

×

10−4 _{[4] derivedfrom}

_B(

_K

S

→

π

e

ν

)

.

Wepresentameasurement ofthe KS

→

π μν

branching frac-tionperformedbythe KLOEexperimentattheDA



NE

φ

–factory of theFrascati National Laboratory based on an integrated lumi-nosityof1.6fb−1.DA



NE [5] isanelectron–positroncollider run-ning at the centre-of-mass energy of 1.02 GeV colliding e+ and

e− beamsatan angleof

π

−

0.025 radandwithabunch-crossing periodof2.71ns.The

φ

mesonsareproducedwithasmall trans-versemomentumof13MeVandKL–KS pairsareproducedalmost back-to-back witha crosssectiontimesthe

φ

→

KLKS branching fractionof about1 μb.The beam energy, theenergy spread,the beamstransverse momentum andthe position ofthe interaction pointaremeasuredusingBhabhascatteringevents [6].

The KS (KL) mesons are identified (tagged) by the observa-tion of a KL (KS) meson in the opposite hemisphere. This tag-ging procedure allows the selection efficiency for KS

→

π μν

to be evaluated with good accuracy using a sample of the abun-dant decay KL

→

π μν

tagged by the detection of KS

→

π

+

π

− decays.The branchingfractionis extractednormalisingthe num-ber of KS

→

π μν

eventsto the numberof KS

→

π

+

π

− events recordedinthesamedataset.

2. TheKLOEdetector

Thedetector1 _{consistsofalarge-volumecylindricaldrift}

cham-ber, surrounded by a lead/scintillating fibres finely-segmented calorimeter. A superconducting coil around the calorimeter pro-vides a 0.52T axial magnetic field. The beampipe at the inter-actionregion issphericalin shapewith10cm radius,madeofa 0.5 mm thick beryllium-aluminumalloy. Final-focus quadrupoles are located at

±

50 cm from the interaction region. Two small lead/scintillating-tile calorimeters [7] are wrapped around the quadrupoles.

The drift chamber [8], 4 m in diameterand 3.3 m long, has 12582driftcells arranged in58concentricringswithalternating stereoanglesandisfilled withalow-densitygas mixtureof90%

1 _{KLOEusesacoordinatesystemwherethez axisisthebisectoroftheelectron} andpositronbeams,x andy axesdefinethetransverseplane,thepolarangleis relativetothez axis.

helium–10%isobutane.Thechambershellismadeofcarbon fibre-epoxy compositewithaninternal wallof1.1mmthicknessat25 cm radius. The spatial resolution is

σ

xy

=

0

.

15 mm and

σ

z

=

2 mm in the transverse and longitudinal projections, respectively. Themomentumresolutionis

σ

pT

/

pT

=

0

.

4%,tracksverticesare re-constructedwithaspatialresolutionofabout3mm.

The calorimeter [9] is divided into a barrel andtwo endcaps andcovers98%ofthesolidangle.Thereadoutgranularityis4

.

4

×

4

.

4 cm2_{,foratotalof2440cellsarrangedinfivelayers.Eachcell} isread outatbothendsbyphotomultipliers.Theenergydeposits areobtainedfromsignalamplitudeswhilethearrivaltimeandthe position along the fibres are obtainedfrom time differences be-tween thetwo signals. Cellscloseintime andspaceare grouped into energy clusters. The cluster energy E is the sumof the cell energies, theclustertime andpositionareenergy-weighted aver-ages.Energyandtimeresolutionsare

σ

E

/

E

=

0

.

057

/



E (GeV) and

σ

t

=

54ps

/



E (GeV)

⊕

100 ps,respectively.Theclusterspatial res-olutionis

σ

_

=

1

.

4cm

/



E (GeV) alongthefibres and

σ

_⊥

=

1

.

3 cm intheorthogonaldirection.

The first-level trigger [10] uses both the calorimeter and the driftchamberinformation;thecalorimetertriggerrequirestwo en-ergydepositswithE

>

50 MeVinthebarrelandE

>

150 MeVin the endcaps; the drift chamber trigger is based on the number andtopology ofhitdrift cells.A second-levelcosmic-ray veto re-jectseventswithatleasttwoenergydepositsabove30MeVinthe outermostcalorimeterlayer.Thetriggertimeisdeterminedbythe firstparticlereachingthecalorimeterandissynchronisedwiththe DA



NEradio frequencysignal. The time interval between bunch crossingsissmallerthan thetimespreadofthe signalsproduced by theparticles, thus the time ofthe bunch crossing originating theevent,T0,isdeterminedaftereventreconstructionandallthe times related to that event are shifted accordingly. Data for re-construction are selected by an on-linefilter [11] toreject beam backgrounds. Thefilteralsorecordstheeventsinto different out-put files for analysis according to their properties and topology (eventclassification),5%oftheeventsarerecordedwithout apply-ingthefiltertocontroltheefficiencyoftheeventclassification. 3. Datasampleandeventpreselection

Processes of interest for the analysis are simulated with the GEANFI Monte Carlo (MC) program [11] for an integrated lumi-nosityequaltothatofthedata.All

φ

decaysaregenerated accord-ing to their branching fractions aswell asother final states pro-duced in e+e− annihilation.The operating conditions ofDA



NE during data takingaswell asmeasurements ofbeamparameters are includedintheMConarun-by-runbasis.Calorimeterenergy deposits and drift chamber hitsfrom beambackground acquired witharandomtriggerareoverlaidontothesimulatedevents.The simulatedeventsareprocessedwiththesamereconstruction algo-rithmsasthedata.

Kaonsfrom

φ

-mesondecaysareemittedintwoopposite hemi-sphereswithmeandecaypath

λ

S

=

5

.

9 mmand

λ

L

=

3

.

4 m,thus about 50% of KL mesons reach the calorimeter before decaying. Thevelocity ofthe KL inthe

φ

referencesystemis

β

∗

=

0

.

22. KS mesons are taggedby KL interactions in the calorimeter, named

KL-crashinthefollowing,withaclearsignatureofalatesignalof about25 nsnot associatedto tracks.The following requirements areappliedtoselectKL-crash:

Table 1

Numberofdataandsimulatedeventsafter pre-selection. Events [103_{] Fraction [%]} Data 301646 MC 312019 KS→π+π− 301976 96.78 φ→K+K− 9566 3.07 KS→πeν 259 0.08 KS→π μν 140 0.04 KS→π0π0 30 0.01 Others 47 0.02

Fig. 1. Distribution ofβ∗after preselection for data and simulated events.

•

aclusterwithenergyEclu

>

100 MeVnotassociatedtotracks (neutralcluster);thecentroidoftheneutralclusterdefinesthe

KL directionwitharesolutionof

∼

1◦;

•

polarangleoftheneutralcluster15◦

< θ

clu

<

165◦tosuppress small-anglebeambackgrounds;

•

0

.

17

< β

∗

<

0

.

28 for the velocity in the

φ

reference system of theparticle originatingthe neutralcluster;

β

∗ is obtained fromthevelocityinthelaboratorysystem,

β

=

rclu

/

ctclu,with

tclubeingtheclustertimeandrcluthedistancefromthe nomi-nalinteractionpoint,the

φ

transversemomentumdetermined run-by-runandtheanglebetweenthe

φ

momentumandthe

KL-crashdirection.

Assumingtheneutralkaonmass,the KS 4-momentumisdefined by the KL-crash directionand the

φ

4-momentum: PKS

=

Pφ

−

PKL.

TheKS

→

π μν

candidatesareselectedrequiringtwotracksof oppositecurvatureformingavertexinsidethecylinderdefinedby

ρ

vtx

=



x2

vtx

+

y2vtx

<

5 cm

|

zvtx

| <

10 cm

.

(1) In casemore than one vertex is found, the closest to the inter-actionregionis chosen.The aboverequirements definethe event preselection.

Afterpreselection, thedatasamplecontains about300million eventsanditscomposition,asevaluatedbysimulation,isshownin Table1.Thelargemajorityofeventsare KS

→

π

+

π

−decays,and thereis alsoa large contributionfrom

φ

→

K+K− eventswhere onekaon oritsdecay productsgeneratea fake KL-crashandthe otherkaondecaysearlyinto

π

±

π

0_.

The distribution of

β

∗ is shown in Fig. 1 fordata and simu-latedevents.Twopeaksarevisible,thefirstisassociatedtoevents triggeredby photonsor electrons,andthe second to events trig-geredbychargedpions.Thetriggerissynchronisedwiththebunch crossing andthe time difference betweena photon (or electron)

andapion(ormuon)arrivingatthecalorimetercorresponds toa timeshiftofaboutonebunch-crossing.

4. Selectionofsignalandnormalisationevents

Theselectionofsignaleventsisperformedintwosteps;firsta selection basedonthe eventkinematics usingonlytracking vari-ables and then a selection based on the time-of-flight measured withthecalorimeter.Thetwogroupsofvariablesareuncorrelated. In order to assign a time to the particles each track is associ-atedto acluster. The track-to-clusterassociation(TCA) isapplied asfollows: foreach track connectedto the vertexa cluster with

Eclu

>

20 MeV and15◦

< θ

clu

<

165◦ isrequired whose centroid iswithin60cmofthetrackextrapolationtothecalorimeterfront surface.TheeventisretainedonlyifTCAissatisfiedbybothtracks. Five variables with good discriminating power against back-groundareusedinamultivariateanalysis.Aboosteddecisiontree (BDT)classifierisbuiltwiththefollowingvariables:

p1

,

p

2: thetracksmomenta;

α

1,2: theangleatthevertexbetweenthetwomomenta inthe

KS referencesystem;

α

S L: theanglebetween

psum

=

p1

+

p2andtheKL-crash direc-tion;



p: thedifferencebetween

|

psum

|

andtheabsolutevalue

|

pKS

|

ofthe KS momentumdeterminedusingthetaggingKL;

mππ : the invariant mass reconstructed from

p1 and

p2, in the hypothesisofcharged-pionmass.

ThedistributionsofthevariablesareshowninFig.2fordataand simulatedevents.

After preselection two cuts are applied to suppress the back-groundinthetailsofthedistributions:

p

<

320 MeV for both tracks and



p

<

190 MeV

.

(2)

Thetraining oftheBDTclassifier isdone onasimulated sam-pleof5,000KS

→

π μν

eventsandasampleof50,000background events;samplesofthesamesizeareusedforthetest.After train-ing and test the classification is run on all events of the MC anddata sample. The distributionof the BDT classifier output is showninFig.3fordataandsimulatedevents.Thedata distribu-tionis well reproducedby simulationinthe regionpopulatedby thesignal. Tosuppressthelarge backgroundof KS

→

π

+

π

− and

φ

→

K+K−events,acutisapplied

B D T

>

0

.

18 (3)

chosen to maximise the ratio S

/

√

S

+

B where S and B are the signalandbackgroundyields.

The selected events contain

π π

, K

π

, e

π

track pairs for the main backgrounds and

μπ

for the signal. A selection based on time-of-flight measurement is performed to identify

μπ

pairs. Foreach trackassociatedtoa cluster, thedifference betweenthe timemeasuredbythecalorimeterandthetime-of-flightmeasured alongtheparticletrajectory

δt

i

=

tclu,i

−

Li

/cβ

i i

=

1

,

2

is computed, wheretclu,i is thetime of the cluster associatedto tracki,Liisthelengthofthetrack,and

β

i

=

pi

/



p2_i

+

m2_i is func-tionofthemasshypothesis fortracki.Toreduce theuncertainty duetotheT0 determination,thedifference

Fig. 2. Distributionsofthevariablesusedinthemultivariateanalysisfordataandsimulatedeventsafterpreselection.Fromtopleft:trackmomenta(p1,p2),anglebetween thetwotracksintheKSreferencesystem(α1,2),anglebetween KL and KSdirections(αS L),two-trackinvariantmassinthehypothesisofchargedpions(mπ π),p= | psum|− | pKS|.

isusedto determinethe massassignmentto thetracks.The

π π

hypothesisistestedfirst,thedistributionof

δ

tππ

= δ

t1,π

− δ

t2,π is

showninFig.4(left).Afairagreementisobserved betweendata andsimulation, the KS

→

π μν

and KS

→

π

e

ν

distributions are wellseparatedandtheK+K−backgroundisisolatedinthetailsof thedistribution,howeverthesignalishiddenunderalarge KS

→

π

+

π

−background.Toreducethebackgroundacutisapplied

1 ns

<

|δ

tπ π

| <

3 ns

.

(4)

The

π μ

hypothesis is testedbyassuming the pionandmuon massforeithertrack

δt

π μ

= δ

t1,π

− δ

t2,μ and

δt

μπ

= δ

t1,μ

− δ

t2,π

.

The two-dimensional

(δ

tπμ

,

δ

tμπ

)

distribution for simulated sig-nal events shows that the correct mass assignment corresponds tothesmallerabsolutevalueofthetwohypotheses.The distribu-tion ofthesigned valueof

δ

tμ

=

min



|δ

tπμ

|, |δ

tμπ

|



isshownin Fig. 4 (right) for data andsimulated events. The distribution for thesignalisnarrowandpeakedatzerowhileitisbroaderforthe backgrounds.Afinalcutisapplied

Fig. 3. Distribution of the BDT classifier output for data and simulated events.

Table 2

Numberofeventsaftertheδtμselectionfor dataandsimulatedevents.

Events Fraction [%] Data 38686 MC 36444 KS→π+π− 25853 70.9 φ→K+K− 475 1.30 KS→πeν 448 1.23 KS→π μν 9424 25.9 Others 244 0.7 Table 3

Resultofthefittothem2

μdistribution. Fraction Events

π μν 0.23 7223±180

π+π− 0.77 23764±270

Total 30987

The number of surviving events in the data sample is 38686 anditscompositionasevaluatedbysimulationislistedinTable2. Afterthemassassignmenttothetwotrackstheinvariantmassof thechargedparticleidentifiedasthemuonisevaluatedas

m2_μ

=



EKS

−

Eπ

−

pmiss



2

−

p2_μ withp2 miss

= (

pKS

−

pπ

−

pμ

)

2_,E

KS and

pKS beingtheenergyand

momentumreconstructed using thetagging KL, and

pπ ,

pμ, the momentaofthecandidatepionandmuontrack.

Thenumberofsignal eventsisextractedwithafit tothem2_μ

distributionwiththeMCshapesofthreecomponents:KS

→

π μν

,

KS

→

π

+

π

− andthesumofallotherbackgrounds.Thefitis per-formedintherange

−

6000

<

m2

μ

<

24000 MeV2 with48degrees

offreedom.The thirdcomponent, which ispeakedaroundm2_e,is constrainedtoa negligiblevalue by the fit.Fig.5 showsthe dis-tributionofm2

μ fordata,simulatedeventsandthefit,andTable3

presentstheresultofthefit.Thenumberofsignaleventsis

N_{π μν}

=

7223

±

180 with

χ

2

/

ndf

=

30

/

48

.

ThenormalisationsampleofKS

→

π

+

π

−eventsisselectedby requiring140

<

p

<

280 MeVforbothtracks(Fig.2).This require-mentselects Nππ

= (

282

.

314

±

0

.

017

)

×

106 _{eventswithapurity} of99.9%asdeterminedbysimulation.

5. Determinationofefficiencies

ThebranchingfractionfortheKS

→

π μν

decayisevaluatedas

B

(K

S

→

π μν

)

=

Nπ μν



π μν

×



π π Nπ π

×

R

×

B

(K

S

→

π

+

π

−

),

(6)

where Nπμν andNππ arethenumbersof KS

→

π μν

andKS

→

π

+

π

− events,



π μν and



π π aretherespectiveselection

efficien-cies,and R istheratiooftheefficiencies forthetrigger,on-line filterandpreselectionforthetwodecays.

The signal selection efficiency is determined with KL

→

π μν

controlsamples(CS)andevaluatedas



π μν

=



CS

×



MC π μν



MC CS

,

(7)

where



CSistheefficiencyofthecontrolsampleand



π μν ,MC



CSMCare theefficienciesobtainedfromsimulationforthesignalandcontrol samples,respectively.

The KL

→

π μν

decay [12,13] iskinematically identicalto the signal,the onlydifferencebeingthemuch longerdecaypath.For thecontrolsample thetaggingisdonewithKS

→

π

+

π

− decays, preselected in the same way as for the signal sample with the additional cut

|

mππ

−

m_K0

|

<

15 MeVtoincrease thepurity.The radialdistanceoftheKL vertexisrequiredtobesmallerthan5 cm to matchthe signal selection,butgreaterthan 1cmto minimise the ambiguityin identifying the KL and KS vertices. Thecontrol sample is composed mainly of KL

→

π

e

ν

, KL

→

π

+

π

−

π

0 and

KL

→

π μν

decays,while most of KL

→

π

0

π

0

π

0 decays are re-jected by the requirement of two tracks. The distribution of the missingmass,m2

miss,ofthetwotracksconnectedtothe KL vertex, assigning the charged-pion mass, shows a narrow isolated peak atthe

π

0 _{mass; a cutm}2

miss

<

15000 MeV

2 _{efficientlyrejects the}

KL

→

π

+

π

−

π

0 decays.Thenumberofeventsinthecontrol sam-pleis911757.

Inordertoevaluatethesignal selectionefficiency,twocontrol samplesare used, oneselected basedon kinematicvariables and theotherbasedontime-of-flight(TOF),thetwogroupsofvariables beinglargelyuncorrelated.

Thecontrol sample forevaluating theefficienciesofthe selec-tionwithkinematicvariablesandBDTclassifierisselected apply-ing a cut on the two-dimensional

(δ

tπμ

,

δ

tμπ

)

distribution that removesmostofthe KL

→

π

e

ν

events.The purityofthesample asdeterminedwithsimulationis86%.Theresolutionsinthe mea-surementofthetaggingKS (controlsample)aresimilartothoseof thetagging KL (signalsample)andthesameBDTclassifierisused forbothsamples.TheBDTMCdistributionsforthesignaland con-trolsample are comparedin Fig.6 (left).Applying to thecontrol samplethesameselectionsasforthesignal,theefficiencies eval-uatedwithEq. (7) are



(

kinem. sel.

)

=

0

.

982

±

0

.

004stat and



(

BDT

)

=

0

.

417

±

0

.

003stat

.

ToevaluateTCAandTOFefficienciesforthesignal,the T0 de-termination using the earlier among the two clusters associated withthe KS decayhas to be considered. The control sample se-lectionthereforerequirestheearliestclustertobeassociatedwith oneofchargedsecondaryparticlesfromKL decayandacutonthe

(

mππ

,

m2

miss

)

distributiontorejectKL

→

π

e

ν

events.Thepurityof thesample asdetermined withsimulationis87%. TheMC distri-butions of

δ

tμ forthesignalandcontrolsample arecompared in Fig. 6(right). Applying to thecontrol sample theanalysis proce-dureasforthesignaltheefficienciesevaluatedwithEq. (7) are

Fig. 4. Distributions ofδtπ π(left) andδtμ(right) for data and simulated events.

Fig. 5. The m2

μdistribution for data, MC signal and background (left); comparison of data with the fit (right).

Fig. 6. Normalised Monte Carlo distributions of the BDT classifier output (left) andδtμ(right) for KL→π μνand KS→π μνevents.



(

TCA

)

=

0

.

347

±

0

.

002stat and



(

TOF

)

=

0

.

392

±

0

.

003stat

.

Thecorrection factorsinEq. (7) differ fromoneby lessthan10% butfor



(TOF)whereitdiffersby20%.

Thetailsofthem2_{μ distribution}inFig.5(left)arenotincluded inthefittoimproveitsstability,therelativeefficiencyis0

.

991

±

0

.

001.

The signal selection efficiencies are summarised in Table 4

whereonlythestatisticalerrorsareshown. Combiningthevalues accounting for the correlation of the control samples we obtain



π μν

=

0

.

0552

±

0

.

0005.

Table 4

Efficiencies forthe signalselections.Theerrors arestatistical,theerrorofthetotalefficiency ac-countsforthecorrelationofthecontrolsamples.

Selection Efficiency Kinematic selection 0.982±0.004 BDT selection 0.417±0.003 TCA selection 0.347±0.002 TOF selection 0.392±0.003 FIT range 0.991±0.001 Total 0.0552±0.0005

Table 5

Contributions tothe ratioofefficienciesR in Eq. (6). The error on R is calculatedas the quadraticsumoftheerrorsofthesingleratios.

Selection R Trigger 1.0649±0.0005 On-line filter 1.0113±0.0002 Event classification 1.1406±0.0007 T0determination 1.0135±0.0002 KL-crash andβ∗ 1.1283±0.0022 KSidentification 1.0481±0.0012 R 1.472±0.004

Theratio R inEq. (6) accountsforseveraleffects all depend-ing on the global properties of the event: trigger, on-line filter, eventclassification,T0 determination, KL-crashand KS identifica-tion.ThevariouscontributionstoR evaluatedwithsimulationare listedinTable5whereonlythestatisticalerrorsareshown.

The efficiency of the KS

→

π

+

π

− normalisation sample is measuredusingthepreselecteddatabyvaryingthecutonthe ver-textransverseposition,asinEq. (1),in1cmstepsfrom

ρ

max

vtx

=

1 cmto

ρ

max

vtx

=

4 cm,based on the observationthat

ρ

vtx andthe tracks momenta are very loosely correlated. Using Eq. (7) and extrapolating to

ρ

max

vtx

=

5 cm the efficiency is



π π

= (

96

.

569

±

0

.

004

)

%.Alternatively, theefficiencyisevaluated usingthe KS

→

π

+

π

−datasample(with

ρ

max

vtx

=

5 cm):



π π

= (

96

.

657

±

0

.

002

)

%.

The latter value is used asthe efficiencyand the difference be-tweenthetwovaluesistakenassystematicuncertainty.The num-berofKS

→

π

+

π

−eventscorrectedfortheefficiencyis

Nπ π

/



π π

= (

292

.

08

±

0

.

27

)

×

106

.

6. Systematicuncertainties

Three main systematic uncertainties affect the signal count: BDTandtime-of-flightselection,andthem2

μ fit.

Thedistributions oftheBDT classifieroutput forthedataand simulatedsignalandcontrolsampleeventsareingoodagreement as shown in Figs. 3 and 6. The resolution of the BDT variable predictedby simulationcomparing thereconstructedevents with thoseatgenerationlevelis

σ

BDT

=

0

.

005.Theanalysisisrepeated varyingtheBDTcutofEq. (3),thenumberofsignaleventsisfound tobestableandthermsvalueofthedifferencescorrespondstoa relativeuncertaintyof0.3%.

ThemainsourceofuncertaintyintheTOFselection isthecut on

δ

tππ inEq. (4) becausethesignalandbackgrounddistributions inFig.4(left)aresteepandwithoppositeslopes;thesubsequent selection on

δ

tμ in Eq. (5) has a minor effect.The resolution of the

δ

tππ variableevaluatedwithsimulationandKS

→

π

+

π

−data control samples is 0.27 ns. The analysis is repeated varying the

δ

tππ lowercutintherange0.5–1.25ns,thermsvalueofthe dif-ferencescorresponds toa relativeuncertaintyof3.0%. Thisisthe mainsystematicuncertaintyaffectingthemeasurement.

The fittothe_mμ2 distributioninFig.5isrepeatedvaryingthe rangeandthebinsize.The relativesystematicuncertaintyonthe numberofeventsis0.3%obtainedshiftingtherangeby fivebins oneithersideandincreasingthebinsizebyafactoroftwo.

Thestatisticaluncertaintiesofthesimulationsignalandcontrol samples,andofthedatacontrolsample contributewitharelative uncertaintyof0.8%(Table4).

The dependence of R on systematic effects has been stud-ied in previous analyses for different KS decays selected with the KL-crash method: KS

→

π

+

π

− and KS

→

π

0

π

0 [14], and

KS

→

π

e

ν

[15]. The systematicuncertainties are evaluated by a comparisonofdatawithsimulation,asdescribedinthefollowing.

Table 6

Summaryofsystematicuncertaintiesofπ π,π μν andR. Source π π[%] π μν [%] R[%] KS→π+π−selection 0.1 BDT selection 0.3 TOF selection 3.0 Fit m2 μdistribution 0.3

MC and data CS statistics 0.8

Trigger 0.1

T0determination <0.1

KL-crash andβ∗ 0.1

KSidentification 1.7

Total 0.1 3.1 1.7

Trigger– Two triggers are used forrecording the events, the calorimetertriggerandthedriftchambertrigger.Thevalidationof the MC relative efficiency isderived fromthe comparisonof the single-trigger andcoincidence rates withthe data.The dataover MCratiois0.999withnegligibleerror.

On-linefilter and eventclassification– Theeventclassification produces differentstreams fortheanalyses.The KLKS stream se-lectseventsbasedonthepropertiesofKS andKL decays.Inmore than99%ofthecasestheeventsareselectedbasedonthe KS de-cay topologyandthe KL-crash signatureanddifferencesbetween MCanddataareaccountedforinthesystematicuncertainties de-rivedbelowfortheKS identificationandKL-crash.

T0– Thesystematicuncertaintyisevaluatedanalysing thedata and MC T0 distributions for the decays with the most different timing properties: KS

→

π

+

π

− and KS

→

π

0

π

0 [14]. The data overMCratiosisonewithanuncertaintyoflessthan0.1%.

KL-crash and

β

∗ selection – The systematic uncertainty is evaluated comparing dataandsimulated eventstagged by KS

→

π

+

π

− and KS

→

π

0

π

0 decays which havedifferent timing and topologycharacteristics.ThedataoverMCratiois1.001with neg-ligibleerror.

KS identification– Thesystematic uncertaintydue to the re-quirementoftwo tracksforming avertexinthe cylinderdefined by Eq. (1) is evaluated separately for signal and normalisation samples. The first is evaluated with KL

→

π μν

events selected withthesamevertexrequirementsasforthesignalbuttaggedby

KS

→

π

0

π

0 decays.Forthe KS

→

π

+

π

− sampletheefficiencyis evaluatedbytaggingwithKL-crashandremovingtherequirement ofthevertex.Combiningthetwo valuesgivesadataoverMC ra-tio of1.002

±

0.017 where theerror isdueto the purityof the samples.

The R total systematicuncertaintyisestimatedby combining thedataoverMCratiosandamountsto1.7%.

IncludingthesystematicuncertaintiesthefactorsinEq. (6) are:



π μν

=

0

.

0552

±

0

.

0017 and R

=

1

.

472

±

0

.

025

.

AllsystematicuncertaintiesaresummarisedinTable6. 7. Result

From Eq. (6) with Nπμν

=

7223

±

180, Nππ

/



π π

= (

292

.

08

±

0

.

27

)

×

106,thevaluesoftheefficiencies



π μν

=

0

.

0552

±

0

.

0017, R

=

1

.

472

±

0

.

025, andthe value

B(

KS

→

π

+

π

−

)

=

0

.

69196

±

0

.

00051 measuredbyKLOE [15],wederivethebranchingfraction

B

(K

S

→

π μν

)

= (

4

.

56

±

0

.

11stat

±

0

.

17syst

)

×

10−4

= (

4

.

56

±

0

.

20

)

×

10−4

.

This isthe first measurement ofthis decaymode andcompletes the set of kaon semileptonic decays. The branching fraction for

Vusthroughtherelation

B

(K

S

→

π



ν

)

=

G2

_|

_f +

(

0

)V

us

|

2 192

π

3

τ

sm 5 KIKSEW

(

1

+ δ

EMK

)

2 (8) where f₊

(

0

)

isthehadronicformfactoratzeromomentum trans-fer,mK and

τ

S aretheKS massandlifetime,IK isthephasespace integral, SEW is the short-distance electroweak correction [17] and

δ

_EMK is the long-distance electromagnetic correction [18,19]. Assuming universality of the kaon–lepton coupling the expected value [4] is

B

(K

S

→

π μν

)

PDG

=

B

(K

S

→

π

e

ν

)

×

R(IK

)

×

(

1

+ δ

_EMKμ

)

2

(

1

+ δ

_EMK e

)

2

= (

4

.

69

±

0

.

06

)

×

10−4

asderivedfromthevalueofthebranchingfraction

B(

KS

→

π

e

ν

)

measured by KLOE [15] and the ratio R

(

I

K

)

of the phase space integralsfor the semileptonic decays KL

→

π μν

and KL

→

π

e

ν

measuredbyKTeV [16].

InvertingEq. (8) andusingIμ_K

=

0

.

10262

±

47 [3] wederive

|

f₊

(

0

)V

us

|

KS→π μν

=

0

.

2126

±

0

.

0046

.

The ratioto thevalue for KS

→

π

e

ν

decay,

|

f+

(

0

)

Vus

|

KS→πeν

=

0

.

2153

±

14 [3],allowstoconfirmtheassumptionofkaon–lepton couplinguniversality

rμe

=

|

f₊

(

0

)V

us

|

2KS→π μν

|

f₊

(

0

)V

us

|

2KS→πeν

=

0

.

975

±

0

.

044

.

Theseresults are consistent withthose determined forthe other kaonsemileptonicdecays[1,3] though lessprecisemainlydueto theintrinsiclimitationsrelatedto

μ

–

π

discriminationinthe

mo-mentumrange100–250MeV.

8. Conclusion

Ameasurement ofthebranching fractionforthedecay KS

→

π μν

is presented based on data collected with the KLOE

ex-periment atthe DA



NEe+e− collidercorresponding to an inte-gratedluminosityof1.6fb−1.The

φ

→

KLKS decaysareexploited to select samples of pure and quasi-monochromatic KS mesons anddata control samples of KL

→

π μν

decays. The KS

→

π μν

decays are selected by a boosted decision tree built with kine-matic variables and by a measurement of time-of-flight. The ef-ficiencies for detecting the KS

→

π μν

decays are derived from

KL

→

π μν

data control samples. A fit to the m2μ distribution

finds7223

±

180 signalevents.NormalisingtoKS

→

π

+

π

−decay events, the resultfor the branching fractionis

B(

KS

→

π μν

)

=

(

4

.

56

±

0

.

11stat

±

0

.

17syst

)

×

10−4 to be compared with the ex-pectedvalueof

(

4

.

69

±

0

.

06

)

×

10−4assuminglepton-flavour uni-versality.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

We warmly thank our former KLOE colleagues for the

ac-cess to the data collected during the KLOE data taking

cam-paign. We thank the DA



NE team for their efforts in

main-taining low background running conditions and their collabora-tion during all data taking. We thank our technical staff: G.F. Fortugno and F. Sborzacchi for their dedication in ensuring ef-ficient operation of the KLOE computing facilities; M. Anelli for his continuous attention to the gas system and detector safety; A. Balla, M. Gatta, G. Corradi and G. Papalino for electronics maintenance; C. Piscitelli for his help during major maintenance

periods. This work was supported in part by the Polish

Na-tionalScienceCentrethroughtheGrantsNo.2013/11/B/ST2/04245, 2014/14/E/ST2/00262,2014/12/S/ST2/00459,2016/21/N/ST2/01727, 2016/23/N/ST2/01293,2017/26/M/ST2/00697.

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