Search for dark Higgsstrahlung in e(+0)e(-) -> mu(+)mu(-) and missing energy events with the KLOE experiment

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Search

for

dark

Higgsstrahlung

in

e

+

e

−

→

μ

+

μ

−

and

missing

energy

events

with

the

KLOE

experiment

KLOE-2

Collaboration

A. Anastasi

a

,

f

,

D. Babusci

f

,

G. Bencivenni

f

,

M. Berlowski

s

,

C. Bloise

f

,

F. Bossi

f

,

P. Branchini

p

,

A. Budano

o

,

p

,

L. Caldeira Balkeståhl

r

,

B. Cao

r

,

F. Ceradini

o

,

p

,

P. Ciambrone

f

,

F. Curciarello

g

,

b

,

E. Czerwi ´nski

e

,

G. D’Agostini

k

,

l

,

E. Danè

f

,

V. De Leo

p

,

E. De Lucia

f

,

A. De Santis

f

,

P. De Simone

f

,

A. Di Cicco

o

,

p

,

A. Di Domenico

k

,

l

,

R. Di Salvo

n

,

D. Domenici

f

,

A. D’Uffizi

f

,

A. Fantini

m

,

n

,

G. Felici

f

,

S. Fiore

q

,

l

,

A. Gajos

e

,

P. Gauzzi

k

,

l

,

G. Giardina

g

,

b

,

S. Giovannella

f

,

E. Graziani

p

,

∗

,

F. Happacher

f

,

L. Heijkenskjöld

r

,

W. Ikegami Andersson

r

,

T. Johansson

r

,

D. Kami ´nska

e

,

W. Krzemien

s

,

A. Kupsc

r

,

S. Loffredo

o

,

p

,

G. Mandaglio

g

,

b

,

M. Martini

f

,

j

,

M. Mascolo

f

,

R. Messi

m

,

n

,

S. Miscetti

f

,

G. Morello

f

,

D. Moricciani

n

,

P. Moskal

e

,

F. Nguyen

p

,

∗

,

1

,

A. Palladino

f

,

A. Passeri

p

,

V. Patera

i

,

f

,

E. Perez del Rio

f

,

A. Ranieri

a

,

P. Santangelo

f

,

I. Sarra

f

,

M. Schioppa

c

,

d

,

M. Silarski

f

,

F. Sirghi

f

,

L. Tortora

p

,

G. Venanzoni

f

,

W. Wi´slicki

s

,

M. Wolke

r

a_{INFNSezionediBari,Bari,Italy} b_{INFNSezionediCatania,Catania,Italy}

c_{DipartimentodiFisicadell’UniversitàdellaCalabria,Cosenza,Italy} d_{INFNGruppocollegatodiCosenza,Cosenza,Italy}

e_{InstituteofPhysics,JagiellonianUniversity,Cracow,Poland} f_{LaboratoriNazionalidiFrascatidell’INFN,Frascati,Italy}

g_{DipartimentodiFisicaeScienzedellaTerradell’UniversitàdiMessina,Messina,Italy} h_{InstituteforTheoreticalandExperimentalPhysics(ITEP),Moscow,Russia}

i_{DipartimentodiScienzediBaseedApplicateperl’Ingegneriadell’Università“Sapienza”,Roma,Italy} j_{DipartimentodiScienzeeTecnologieApplicate,Università“GuglielmoMarconi”,Roma,Italy} k_{DipartimentodiFisicadell’Università“Sapienza”,Roma,Italy}

l_{INFNSezionediRoma,Roma,Italy}

m_{DipartimentodiFisicadell’Università“TorVergata”,Roma,Italy} n_{INFNSezionediRomaTorVergata,Roma,Italy}

o_{DipartimentodiMatematicaeFisicadell’Università“RomaTre”,Roma,Italy} p_{INFNSezionediRomaTre,Roma,Italy}

q_{ENEAUTTMAT-IRR,CasacciaR.C.,Roma,Italy}

r_{DepartmentofPhysicsandAstronomy,UppsalaUniversity,Uppsala,Sweden} s_{NationalCentreforNuclearResearch,Warsaw,Poland}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received27January2015

Receivedinrevisedform9June2015 Accepted9June2015

Availableonline10June2015 Editor: L.Rolandi

Keywords:

Darkmatter

WesearchedforevidenceofaHiggsstrahlungprocessinasecludedsector,leadingtoafinalstatewith

adarkphotonU andadarkHiggsbosonh,withtheKLOEdetectoratDANE.Weinvestigatedthecase

ofh lighterthanU , withU decayingintoamuonpairandh producingamissing energysignature.

Wefoundnoevidenceoftheprocessandsetupperlimitstoitsparametersintherange2mμ<mU< 1000 MeV,mh<mU.

©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense

(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

*

Correspondingauthor.

E-mailaddresses:enrico.graziani@roma3.infn.it(E. Graziani),federico.nguyen@cern.ch(F. Nguyen). 1 _{Presentaddress:ENEAUTMEA-TER,CasacciaR.C.,Roma,Italy.}

http://dx.doi.org/10.1016/j.physletb.2015.06.015

0370-2693/©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Darkforces Uboson Upperlimit Higgsstrahlung

1. Introduction

Astrophysicaldata revealin a moreandmoreconvincing way that our knowledge of the Universe is limited to about 4–5% of thetotalmatter–energycontent:thisisgenerallyinterpretedasan evidence of the existence of dark matter and dark energy com-ponents. In recent years, several astrophysical observations have failed to find a common interpretation in terms of standard as-trophysicalorparticle physics sources [1–11].Although thereare alternative explanations for some of these results,they could all beexplainedwiththeexistenceofadarkmatterweakly interact-ing massiveparticle,WIMP,belongingto asecludedgauge sector

under which the Standard Model (SM) particles are uncharged

[12–21].In aminimal model,a newabelian U

(

1

)

S gauge field is

introduced,theUbosonordarkphoton,withmassneartheGeV scale,coupledtotheSMonlythroughits kineticmixingwiththe SMhyperchargefield.The kineticmixingparameter



isexpected tobe ofthe order10−4–10−2 [13–22],so thatobservable effects canbedetectedate+e−colliders

[22–26]

oratfixedtarget exper-iments workingin the GeV region [27–30]. The existence ofthe U boson, through its mixing with the ordinary photon, can also

accommodate the observed discrepancy in the measured muon

anomalous magnetic momentaμ withrespect to the SM

predic-tion [31]. Several searches ofthe U bosonhave been performed inrecentyearswithnegative results,settingupperlimitsto



:A1

[32,33], APEX [34], WASA[35], HADES [36],KLOE [37,38], BaBar

[39].

Since the U boson needs to be massive, one can implement,

incloseanalogywiththeSM,aspontaneousbreakingmechanism ofthe U

(

1

)

S symmetry, thus introducing aHiggs-like particle,h

ordarkHiggs,whosemasshierarchywiththedarkphoton isnot constrainedbythetheory

[23]

.

The U boson can be produced at e+e− colliders via different processes:e+e−

→

U

γ

,e+e−

→

U h(darkHiggsstrahlung)andin decaysofvector particles topseudoscalars. Inthiswork the Hig-gsstrahlungprocesse+e−

→

U hisstudied,usingdatacollectedby theKLOE experimentatthe e+e− colliderDA



NEattheFrascati laboratory, both at a center of mass energy of

∼

1019 MeV, the massof the

φ

meson(on-peaksample),and ata centerofmass energyof

∼

1000 MeV(off-peaksample).Theprocesse+e−

→

U h, withU decayingintoleptonorhadronpairs,is aninteresting re-actiontobe studiedatane+e− collider,beinglesssuppressed,in terms ofthe mixing parameter, than the other final states listed above. There are two very different scenarios depending on the massesofthedark photonmU andofthedarkHiggs bosonmh.

Formh largerthan2mU,thedarkHiggsbosonwoulddecay

dom-inantlyandpromptly to aUboson pair, thusgiving riseto a six chargedparticlefinalstate (thescenariowithmh larger thanmU

butsmallerthan2mU issimilar, withonedarkphoton offshell):

this case was recently investigated by the BaBar [40] and Belle

[41]experiments.Ontheotherside,Higgsbosonslighterthanthe darkphoton wouldhave, inmostof theparameter spaceregion, suchalargelifetimetoescapedetection,showingupasamissing energysignature. We confinedthe search onlyto the lattercase,

mh

<

mU,theso-called “invisible”darkHiggsscenario.

The lifetime of the dark Higgs boson dependson the kinetic mixingparameter



,thebosonmassesmh andmU andthe dark

couplingconstant

α

D [23]. Forbosonmassesoftheorder of100

MeVand

α

D

=

α

em,thedarkHiggsbosonlifetimewouldbe

∼

5 μs

for



∼

10−3_{,corresponding,fortheenergyrangeexploredinthis} analysis,toadecaylengthof

∼

100 m.ThedarkHiggsbosonwould bethusinvisibleupto



∼

10−2_–10−1_{,dependingontheh}_mass.

Inthisworkthesearch islimitedtothedecayoftheUboson inamuonpair:thefinalstatesignatureisthenapairofopposite charge muonsplus missingenergy.Themeasurementisthus per-formed in the range2mμ

<

mU

<

1000 MeV with theconstraint

mh

<

mU.

TheproductioncrosssectionofthedarkHiggsstrahlungprocess isproportionaltotheproduct

α

D

×



2 anddependsontheboson

masses

[23]

.Valuesashighashundredsoffbarereachableinthis model. Comparedto the B-factory case[40,41], KLOE benefits of the1/sfactorandoftheresonance-likebehaviourexpectedforthe productioncrosssection

[23]

.The branchingratiooftheUboson into muon pairs is predicted to be justbelow the 50% level for massesslightly above thekinematicalthreshold mU

=

2mμ, then

todecreaseuptoaminimumaround5%,formassescorresponding tothe

ρ

resonance(duetotheconcurrentdecayintohadrons),and thentoincreaseto

∼

30–40% uptomU



1 GeV[23].

2. TheKLOEdetector

DA



NE, the Frascati

φ

-factory,isan e+e− colliderworkingat the center of massenergy,

√

s

∼

m_φ

=

1

.

0195 GeV [42].Positron and electronbeams collideat an angleof

π

−

25 mrad,

produc-ing

φ

mesons nearly at rest. The KLOE detector is made up of

a large cylindricaldrift chamber (DC)[43],surrounded by a lead scintillatingfiberelectromagneticcalorimeter(EMC)[44].A super-conductingcoilaround theEMC providesa 0.52Tmagneticfield alongtheaxisofthecollidingbeams.

The EMCconsistsofbarrelandend-capmodulescovering 98% ofthesolidangle.Thecalorimetermodulesaresegmentedintofive layers indepthandreadoutatbothendsby4880 photomultipli-ers.Energyandtimeresolutionsare

σ

E

/

E

=

0

.

057

/

√

E

(

GeV

)

and

σ

t

=

57 ps

/

√

E

(

GeV

)

⊕

100 ps,respectively.Thedriftchamber,with

only stereo sense wires, 4 m indiameter and 3

.

3 m long, has a mechanicalstructureincarbon-fiberandoperateswithalow-mass gas mixture (90%helium, 10% isobutane). The spatial resolutions are

σ

xy

∼

150

μ

m and

σ

z

∼

2 mm.Themomentumresolutionfor

large angle tracks is

σ

p_⊥

/

p⊥

≈

0

.

4%. The trigger [45] uses both EMCandDCinformation.Dataarethenanalysedbyanevent clas-sification filter

[46]

,whichselects andstreamsvarious categories ofeventsindifferentoutputfiles.

3. Eventselection

The analysis of the process e+e−

→

U h, U

→

μ

+

μ

−, h in-visible (e+e−

→

U hin the following), has been performedon a data sample of1.65 fb−1 _{collected ata centerofmass energyof}

∼

1019 MeV,correspondingtothemassofthe

φ

meson(on-peak sample inthe following), andon adata sample of 0.206 fb−1 at a centerof mass energy of

∼

1000 MeV (off-peak sample in the following),wellbelowthe

φ

resonance.

The MonteCarlosimulationofthesignal processe+e−

→

U h

hasbeenproducedusinganad hocgenerator interfacedwiththe standard KLOEsimulationprogram

[46]

.Thegeneratorwas based onthecrosssectionformulaineq. (11)ofRef.[23],complemented withprivate communications

[47]

withthe authors,asfaras dif-ferential cross sectionsas afunction of the productionangle are

Fig. 1. Distributionofthepolarangleofthemuonpairmomentumforthesignal

e+e−→U h (blackline)andfor e+e−→μ+μ−γ (redline).Herethe two pro-cessesarenotnormalisedandareshownonlyinordertocomparetheshapesof thedistributions.AllthegeneratedsamplesatvariousmUandmhareincludedin thesignaldistribution.(Forinterpretationofthereferencestocolorinthisfigure, thereaderisreferredtothewebversionofthisarticle.)

concerned. Signal samples have beengenerated for various pairs ofmh–mU valuesalongagridwithstepsof

∼

30 MeVtocoverall

theallowedkinematicregion.Theinvariantmassresolutionvaries

between0.5and2MeVforthemuonpair(Mμμ),andbetween3

and17 MeV forthe eventmissing mass(Mmiss). The signal

pro-cesssignature would thus be the appearance ofa sharp peak in thebidimensionaldistributionMμμ–Mmiss.Moreover,the

distribu-tionofthepolarangledirectionofthemuon pairmomentum,

θ

, contrarilyto most of the dominant background processes,is ex-pected to prefer large angles. The differential cross section has two dominant terms proportional to sin

θ

and sin3

θ

[23], with relative weights smoothly dependent on the boson masses. This angular distribution allows to reject most of the background of QED processes with a simple geometrical selection and implies thatthemissingmomentumdirectionpreferably pointsto avery well equipped region of the KLOE detector, where the best effi-ciencyisachieved.

Fig. 1

showsthedistributionsofthemuonpair polarangle directionforthe signal e+e−

→

U h (black line) and thee+e−

→

μ

+

μ

−

γ

background (redline),where allthe gener-atedsamples at various mU andmh massesare includedin the

signalsample.

Asafirststepoftheanalysis,apreselectionwasperformedby requiring:

•

events withonly two opposite charge tracks withassociated EMC clusters,withpolarangles

|

cos

θ

1,2

|

<

0

.

8 andmomenta

below 460 MeV, that form a reconstructed vertex inside a

cylinderof30cmlength,4cmradius,centeredatthe interac-tionpoint(IP);

•

thesumofthemomentaofthetwotrackstobegreaterthan

450MeV;

•

thepolarangleofthedimuonmomentumtobeinthebarrel acceptance:

|

cos

θ

|

<

0

.

75;

•

themodulusofthemissingmomentumtoexceed40MeV.

Afterthisselection,mostlyaimedatrejectingbackgroundsfrom QED processes,the hermeticity andtightness ofthe electromag-netic calorimeter was used as a veto to avoid the presence of photonsintheeventby requiringno prompt EMCclusters unas-sociated totracks.The calorimetervetoinefficiency asa function oftheenergywasstudiedwithasampleofradiativeBhabha

scat-teringeventse+e−

→

e+e−

γ

andfoundtorangebetween10%at 20 MeVand0.1%atabout200 MeV.

Theeventselectionthenproceededbyapplyingaparticle iden-tification(PID)algorithmtothetwotracks,basedontheexcellent

energy and time resolution of the EMC. A set of feed-forward

neural networks, organised for different valuesof track momen-tumandtrackpolarangle,was trainedonsimulatedMonteCarlo samples to perform muon to electron discrimination. The neural networks used five input variables (cluster time, energy to mo-mentum ratio and three variables related to energy depositions in calorimeter layers) and produces one output. The PID perfor-manceswere checkedon selecteddatasamplesofe+e−

→

e+e−,

e+e−

→

μ

+

μ

−, e+e−

→

π

+

π

−: the fraction of events where bothtrackswere identifiedasmuonswasmeasured tobe85% in

e+e−

→

μ

+

μ

−events,10−4ine+e−

→

e+e−eventsand

∼

50%in

e+e−

→

π

+

π

−events(showersproducedbymuonsorpionshave similarpropertiesatlowenergies).

After missing energy and PID selections, a large background from

φ

→

K+K−,K±

→

μ

±

ν

eventssurvivedintheon-peak sam-ple. This happens when both kaons decay leptonically close to the IP. Charged kaons have an average decay length of

∼

90 cm inKLOE.The reconstructedvertexofthemuon tracksis thus ex-pectedtobedisplacedfromtheIPandwithabadfitquality.Cuts on theradial (

ρ

vtx

<

0

.

5 cm) andz (

|

zvtx

|

<

3 cm) projectionsof

thedistancebetweenthe reconstructedvertexandtheIP andon the

χ

2 _ofthefit(

_χ

2

vtx

<

3)allowed toreducebyafactor

∼

80the

φ

→

K+K−, K±

→

μ

±

ν

background, with a signal efficiency of

∼

65%.

Eventssurvivingall thedescribedselectionswere organised in

bidimensional histogramswiththemuonpairmass Mμμ andthe

eventmissingmassMmissonthetwoaxes.Thebinningwaschosen

tokeep mostofthesignal insidea singlebin.For Mμμ a5MeV binwidthwasenoughoveralltheplane;whileforMmissavariable

binningof15,30and50MeVwidthswaschosen.Accordingtothe simulation,afractionof90–95%ofthesignalwascontainedinone singlebin.Thesignatureoftheprocesswouldthusbethe appear-anceofanexcessinasinglebinintheMμμ–Mmissplaneoverthe

background.Thesignalselection efficiency,estimatedfromMonte CarloonthegeneratedpointsofthemU–mh grid,wasfoundtobe

between15% and 25%,depending onthe masses, withmost

fre-quent values of

∼

20%. The efficiency for a generic point on the

Mμμ–Mmissplanewasthenevaluatedbylinearinterpolation.

4. Results

Afterallthedescribedselections,15 278eventssurvivedinthe on-peak sample(Fig. 2,left plot)and783inthe off-peaksample (Fig. 2,rightplot).Intheleftplotof

Fig. 2

(on-peaksample)several sourcesofbackgroundscanbedistinguished:

• φ →

K+K−, K±

→

μ

±

ν

(quadrangular region at the left of thepopulatedpartofthedistribution);

• φ →

π

+

π

−

π

0_{(quasi-horizontalband,correspondingtoevents} in which both photons from the

π

0 _{decay are undetected),} partlyintersectingthe

φ

→

K+K−,K±

→

μ

±

ν

region;

•

e+e−

→

μ

+

μ

− ande+e−

→

π

+

π

− eventsinthecontinuum

(diagonalandhorizontalbandsstartingfromtheright-bottom partofthedistribution);

•

e+e−

→

e+e−

μ

+

μ

−ande+e−

→

e+e−

π

+

π

−(photon–photon interactions,toptriangularpartofthedistribution,forMmiss

>

350 MeV), withe± inthe final state being scatteredatvery smallanglesinthebeampipe.

Fig. 2. Results for on-peak sample (left plot, 1.65 fb−1_{integrated luminosity) and off-peak sample (right plot, 0.206 fb}−1_{integrated luminosity).}

Fig. 3. Data–MonteCarlocomparisonfortheon-peaksample(topplots)andoff-peaksample(bottomplots).ProjectionsalongtheMμμaxis(leftplots);projectionsalong

theMmissaxis(rightplots).Alsoshownarethevariouscontributingbackgrounds.

Inthedistributionintherightplotof

Fig. 2

(off-peaksample) allthebackgroundsfromthe

φ

decaysarestronglysuppressedand onlythoseinthecontinuumremainvisible.

Monte Carlogenerators fullyinterfaced with the KLOE detec-torsimulationprogramwere availableforallthebackground pro-cessesbutforthee+e−

→

e+e−

μ

+

μ

− ande+e−

→

e+e−

π

+

π

−. Forthese two processes the Courau generator program [48] was

used andthe results smeared to keep into account the detector effects(fastsimulation,seeSection5).

As most of thesignal is expectedto populate a single bin of themassdistributions,a5

×

5 binmatrixintheMμμ–Mmissplane

wasbuiltandmovedslidingallalongthevastmajorityofthe dis-tributionsof

Fig. 2

bothondataandMonteCarlo.Intheperipheric regions, foratwobinwide contour,thematrixwas reducedto a

3

×

3 one.Thepresenceofapossiblesignalwascheckedbyusing thecentralbin,whiletheotherswereusedforbackground evalua-tion.Thiswasdonebycomputingadata–MonteCarloscalefactor

k based onthesumofthe contentsofthe 24(8)bins surround-ingthe centralone forthe 5

×

5 (3

×

3)matrix indata(DT24or

DT8)andMonteCarlo(MC24orMC8):k

=

MCDT2424

(

DT8

MC8

)

.The predic-tionforthebackgroundinthe centralbinis thensimplydefined astheproduct ofthecentralbincontentinMonteCarlorescaled byk (fortheoutermostbincontourtheeffectivenumberofusable binsmaydecreaseto5).ThespecialcasesinwhichDT24(DT8)or

MC24(MC8) arezerowere solved bysettingk tothe meanvalue ofits distribution (separately for on-peak andoff-peak samples). The usage of the described scaling procedure allowed to reduce thesystematicuncertaintiesduetothebackgroundevaluation(see Section5).

Fig. 3

showsthedata–MonteCarlocomparisonafterthe scalingcorrectionfortheon-peakandoff-peaksamples,projected alongthe Mμμ and Mmiss axes,together withtheindividual

con-tributionsofthedifferentbackgroundprocesses.Theagreementis satisfactoryalloverthepopulatedregionsofthedistributions,with theexceptionofthefirsttwobinsoftheMmissone,forwhich

spe-cialcarewasgiveninthesystematicerrorestimate(seeSection5).

5. Systematicerrors

Systematicuncertainties affect the signal efficiencyevaluation andthebackgroundestimate.Severalsourcesofsystematic uncer-taintiesinthesignalefficiencyevaluationfromMonteCarlowere takenintoaccount.

UncertaintiesfromthePIDprocedurewereestimatedby select-ingsamplesofe+e−

→

μ

+

μ

−

γ

indataandMonteCarlo,applying thePIDalgorithmstooneofthetwotrackstoincreasethepurity oftheselectionandstudyingontheoppositetrackthedata–Monte Carlodifferences of the PID efficiencyas a function ofthe track momentum.Thetotaleffect,definedastheaverageproductof in-dividualeffectsonthesingletracks,wasfoundtovarybetween2% and3%,depending onthebosonmasses.Asimilarprocedurewas applied to evaluate the correction factors and systematic uncer-taintiesofthePIDalgorithms forpionidentification,whichaffect thebackgroundevaluation,withatotaleffectbetween1%and4% onthebackgroundestimate.

The same e+e−

→

μ

+

μ

−

γ

samples selected in data and in thesimulationwereused toevaluatetheeffectofthecut onthe vertex–IPdistance.AcorrectiontotheMonteCarlosignal efficien-ciesoftheorderof15%,weaklydependent oncos

θ

,was derived andapplied.Anassociatedsystematicerrorof0.5%wasestimated andaddedonthesignalefficiencyevaluation.

Thesystematic uncertaintydue to theusage of the EMC veto was evaluated by selecting samples of

φ

→

K+K−, K±

→

μ

±

ν

in data and Monte Carlo. In this case, the cut on the vertex–IP distancewas slightlyrelaxed, inorderto increase thesize ofthe sample.A2% data–MonteCarlodifferencewas observedandused bothtocorrecttheMonteCarloefficiencyandtoquotea system-aticuncertaintyduetothissource.

Thesystematicuncertaintyduetothekinematicalpreselections of the analysis was estimated by varying track angles and mo-mentawithintheirmeasurementerrorsbyonestandarddeviation: a1%effectwasascribedtothissource.

Thesystematicuncertaintyduetothebinningchoicewas esti-matedbyevaluatinginthesimulationthebinomialstatisticalerror onthefractionofthesignalcontainedinonebin.Thisturnedout tobeoftheorderof0.3%,onaverage.

Finally,an average

∼

1% uncertaintywas estimateddueto the linear interpolation procedure in the signal efficiency evaluation process.

The total systematic uncertainty on the signal efficiency was then evaluated as the quadratic sum of all the above effects. It neverexceeded4%,withanaveragevalueof3.5%,verysmallwhen compared to the statistical uncertainties affecting this measure-ment.

Mostofthe systematicuncertaintiesin thebackground evalu-ation cancelinthescalefactorratiok. Allthesystematicsources considered forthe signal efficiency evaluation, but those related tothelinearinterpolationprocedure,weretakenintoaccountand theireffectonthebackgroundestimatecomputed.

Additional effects were taken into account. The uncertainties

on the background process cross sections were varied within

their theoretical and measurement errors. A further 1%

uncer-tainty was added for those related to the photon–photon final

states, for which no full simulation was available: samples of generatede+e−

→

μ

+

μ

−

γ

,e+e−

→

π

+

π

−

γ

,e+e−

→

π

+

π

−

π

0 events were weighted in order to reproduce the mostimportant photon–photon final states distributions and then fast simulated andfullsimulatedresultswere compared.The uncertaintyonthe integratedluminositywasestimatedtobe0.3%.

Anadditional contributiontothesystematicuncertainties was added for the very low Mmiss region, for which the data–Monte

Carloagreementisnotfullysatisfactory(see

Fig. 3

).Thefull differ-encebetweenthedataandtheMonteCarlopredictionforthefirst twobinsoftherightplotsin

Fig. 3

wasthuscomputed(separately forthe on-peakandoff-peak samples)andused asan additional contributiontothesystematicerror.

Thetotalsystematicuncertaintyonthebackgroundwas evalu-atedasthequadraticsumofalltheaboveeffects.Ithasanaverage valueof5.5%withaverysmalltailextendingupto10% (and be-yondfortheverylow Mmissregion,seepreviouspoint).

6. p0valuesandupperlimits

In order to evaluate the compatibilityof the observed results withthebackgroundonlyhypothesis(p0 value)andtoderive up-per limits to the parameters of the dark Higgstrahlung process, a Bayesian procedure was set up. Foreach position of the 5

×

5 (3

×

3)binmassmatrix,alikelihoodfunctionwasdevisedbasedon uniformprior probabilities of thecounting variables(constrained tobenon-negative)andonfourPoissoniandistributions represent-ingtheprobabilitiesrelatedrespectivelytothenumberofobserved eventsinthecentralbinoftheslidingmatrix,thenumberof pre-dicted backgroundeventsinthe samebinfromMonte Carlo,the number ofobserved and predictedevents inthe surrounding 24 (8)bins(DT24orDT8andMC24orMC8,enteringinthescalefactor ratiok).Thisproceduretakesthusintofullaccountthefluctuations duetothe dataandMonteCarlostatistics. Thesystematic uncer-tainties on the signal efficiency andon the background estimate were takenintoaccountby convolvingthefourPoissonian distri-butionswithtwocorrelatedGaussiandistributions,withvariances set equal to the estimatedsystematic errors.Whenever the dark Higgsstrahlungprocesswassearchedfor,thesmallfractionof sig-nalexpectedoutsidethecentralbinofthe5

×

5 slidingmatrixwas explicitlytakenintoaccountinthelikelihoodexpression.

The p0 distributions for the on-peak, off-peak and combined samplesareshownin

Fig. 4

,left plot.

Fig. 4

,rightplot,showsthe computed p0 valuesas a function of Mμμ–Mmiss massesfor the

combined sample. There are three values exceeding the thresh-old corresponding toa 3

σ

excessinthe combinedsample, while 4.2wereexpectedonprobabilistic base.Theexcesssignificanceof thosepoints (see Fig. 4)are atthelevelof3

.

1

σ

,3

.

2

σ

and3

.

4

σ

. In the on-peak andoff-peak samples the most significant values exceedingthe3

σ

thresholdareatthelevelof3

.

9

σ

and3

.

8

σ

re-spectively (see Fig. 4, left plot). These excesses, even though at

Fig. 4. Left:p0valuedistributionfortheon-peaksample(redline),off-peaksample(blueline),combinedsample(blackline).Right:p0valuesforthecombinedresult.(For interpretationofthereferencestocolorinthisfigure,thereaderisreferredtothewebversionofthisarticle.)

Fig. 5. 90% CL upper limits inαD×2for the on-peak sample (left plot) and off-peak sample (right plot).

quiteinterestinglevel,arethenlostinthecombinationofthetwo samples, becoming fluctuationsof average size. In order to cope withcasesinwhich apossible signalis locatedjustatthe inter-sectionoftwoormoreadjacentbins(thuslikelylosingthefeature ofshowingupasasinglebinexcessoverthebackground)thefull procedurewasrepeatedbasedondistributions whicharehalfbin shifted (both in Mμμ and Mmiss directions) with respect to the

onesin

Fig. 2

.Norelevantdifferencewasfound.

Asno evidenceofthedarkHiggsstrahlung processwas found,

90% confidence level Bayesian upper limits on the number of

events were derived bin by bin in the Mμμ–Mmiss plane,

sepa-rately forthe on-peak andoff-peak samples,andthen converted interms of

α

D

×



2.They are shownin Fig. 5. Fig. 6showsthe

on-peakandoff-peak90%CLupperlimitsprojectedalongthemU

andmhaxesafteraslightsmoothingtomakethemmorereadable.

ThedifferentcurvesinmU (mh) correspondtodifferentvaluesof

mh (mU). These results were then combined by taking into

ac-countthedifferentintegratedluminositiesofthetwosamplesand therespectivesignalefficienciesandcrosssections.Thecombined

results are almost everywhere dominated by the on-peak

sam-ple, because of the larger available statistics, with the exception ofsomeverynoisy backgroundregions. Theyareshownin

Fig. 7

. Theselimitsarelargelydominatedbythedatastatistics.Valuesas

lowas10−9

_÷

₁₀−8_oftheproduct

_α

D

×



2areexcludedat90%CL

foralargerangeofthedarkphotonanddarkHiggsmasses.

7. Conclusions

A search for the dark Higgsstrahlung process e+e−

→

U h,

U

→

μ

+

μ

−,hinvisible,hasbeenperformedbyKLOEintherange 2mμ

<

mU

<

1000MeVwithmh

<

mU.Noevidenceforsignalhas

beenobservedandupperlimitsontheproductofthekinetic mix-ingparameter



andthedarkcouplingconstant

α

D havebeenset

intherange10−9_–10−8 _in

_α

D

×



2.Withthearbitraryhypothesis

α

D

=

α

em thesemeasurements translateintolimitsonthekinetic

mixingparameter



intherange10−4–10−3.

Acknowledgements

We warmly thank our former KLOE colleagues for the access

to the data collected during the KLOE data taking campaign.

We thank the DA



NE team for their efforts in maintaining low

background running conditions and their collaboration during

all data taking. We want to thank our technical staff: G.F.

For-tugno and F. Sborzacchi for their dedication in ensuring

Fig. 6. Topplots:90%CLupperlimitsinαD×2asafunctionofmUfordifferentvaluesofmhfortheon-peaksample(top,left)andoff-peaksample(top,right).Bottom

plots:samelimitsasafunctionofmhfordifferentvaluesofmU fortheon-peaksample(bottom,left)andoff-peaksample(bottom,right).

Fig. 7. Combined 90% CL upper limits inαD×2as a function of mU for different values of mh(top plot) and as a function of mhfor different values of mU(bottom plot).

his continuous attention to the gas system and detector safety;

A. Balla, M. Gatta, G. Corradi and G. Papalino for

electron-ics maintenance; M. Santoni, G. Paoluzzi and R. Rosellini for general detector support; C. Piscitelli for his help during

ma-jor maintenance periods. This work was supported in part by

the EU Integrated Infrastructure Initiative Hadron Physics Project

under contract number RII3-CT-2004-506078; by the European

Commission under the 7th Framework Programme through the

‘Research Infrastructures’ action of the ‘Capacities’ Programme, Call:FP7-INFRASTRUCTURES-2008-1,GrantAgreementNo.227431;

by the Polish National Science Centre through the Grants No.

02641, 2011/01/D/ST2/00748, 2011/03/N/ST2/02652, 2013/08/M/ ST2/00323,andby theFoundationForPolish Science throughthe

MPDprogrammeandtheprojectHOMINGPLUSBIS/2011-4/3.

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