Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Combined
limit
on
the
production
of
a
light
gauge
boson
decaying
into
μ
+
μ
−
and
π
+
π
−
The
KLOE-2
Collaboration
A. Anastasi
f,
c,
D. Babusci
c,
M. Berlowski
c,
w,
C. Bloise
c,
F. Bossi
c,
P. Branchini
t,
A. Budano
s,
t,
B. Cao
v,
F. Ceradini
s,
t,
P. Ciambrone
c,
F. Curciarello
c,
∗
,
E. Czerwi ´nski
b,
G. D’Agostini
o,
p,
E. Danè
c,
V. De Leo
r,
E. De Lucia
c,
A. De Santis
c,
P. De Simone
c,
A. Di Cicco
s,
t,
A. Di Domenico
o,
p,
D. Domenici
c,
A. D’Uffizi
c,
A. Fantini
q,
r,
G. Fantini
d,
P. Fermani
c,
S. Fiore
u,
p,
A. Gajos
b,
P. Gauzzi
o,
p,
S. Giovannella
c,
E. Graziani
t,
V.L. Ivanov
h,
i,
T. Johansson
v,
X. Kang
c,
D. Kisielewska-Kami ´nska
b,
E.A. Kozyrev
h,
i,
W. Krzemien
w,
A. Kupsc
v,
P.A. Lukin
h,
i,
G. Mandaglio
g,
a,
∗
,
M. Martini
c,
n,
R. Messi
q,
r,
S. Miscetti
c,
D. Moricciani
r,
P. Moskal
b,
A. Passeri
t,
V. Patera
m,
p,
E. Perez del Rio
c,
N. Raha
r,
P. Santangelo
c,
M. Schioppa
k,
l,
A. Selce
s,
t,
M. Silarski
b,
F. Sirghi
c,
e,
E.P. Solodov
h,
i,
L. Tortora
t,
G. Venanzoni
j,
W. Wi´slicki
w,
M. Wolke
vaINFNSezionediCatania,Catania,Italy
bInstituteofPhysics,JagiellonianUniversity,Cracow,Poland cLaboratoriNazionalidiFrascatidell’INFN,Frascati,Italy dGranSassoScienceInstitute,L’Aquila,Italy
eHoriaHulubeiNationalInstituteofPhysicsandNuclearEngineering,Mˇagurele,Romania
fDipartimentodiScienzeMatematicheeInformatiche,ScienzeFisicheeScienzedellaTerradell’UniversitàdiMessina,Messina,Italy gDipartimentodiScienzeChimiche,Biologiche,FarmaceuticheedAmbientalidell’UniversitàdiMessina,Messina,Italy
hBudkerInstituteofNuclearPhysics,Novosibirsk,Russia iNovosibirskStateUniversity,Novosibirsk,Russia jINFNSezionediPisa,Pisa,Italy
kDipartimentodiFisicadell’UniversitàdellaCalabria,Rende,Italy lINFNGruppocollegatodiCosenza,Rende,Italy
mDipartimentodiScienzediBaseedApplicateperl’Ingegneriadell’Università“Sapienza”,Roma,Italy nDipartimentodiScienzeeTecnologieapplicate,Università“GuglielmoMarconi”,Roma,Italy oDipartimentodiFisicadell’Università“Sapienza”,Roma,Italy
pINFNSezionediRoma,Roma,Italy
qDipartimentodiFisicadell’Università“TorVergata”,Roma,Italy rINFNSezionediRomaTorVergata,Roma,Italy
sDipartimentodiMatematicaeFisicadell’Università“RomaTre”,Roma,Italy tINFNSezionediRomaTre,Roma,Italy
uENEA,DepartmentofFusionandTechnologyforNuclearSafetyandSecurity,Frascati(RM),Italy vDepartmentofPhysicsandAstronomy,UppsalaUniversity,Uppsala,Sweden
wNationalCentreforNuclearResearch,Warsaw,Poland
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory: Received6July2018
Receivedinrevisedform3August2018 Accepted9August2018
Availableonline13August2018 Editor:L.Rolandi
We searched for the
μ
+μ
− decayofalightvector gaugeboson, alsoknown as dark photon,in thee+e−→
μ
+μ
−γ
ISRprocessbymeansoftheInitialStateRadiation(ISR)method.Weused 1.93 fb−1ofdatacollectedbytheKLOEexperimentattheDANEφ-factory.Nostructureshavebeenobservedover the irreducible
μ
+μ
− background.A 90%CLlimitontheratioε
2=α
/α
betweenthe darkcoupling constantand thefinestructureconstantof3×10−6–2×10−7 hasbeenset inthedarkphoton massregionbetween519MeVand 973MeV.Thisnewlimithasbeencombined withthe publishedresult
*
Correspondingauthors.E-mailaddresses:francesca.curciarello@lnf.infn.it(F. Curciarello),gmandaglio@unime.it(G. Mandaglio).
https://doi.org/10.1016/j.physletb.2018.08.012
0370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
Keywords: e+e−Collisions Darkforces Gaugevectorboson Upperlimits
obtainedinvestigatingthehypothesis ofthedark photondecayingintohadronsine+e−→
π
+π
−γ
ISRevents.Thecombined90%CLlimitincreasesthesensitivityespeciallyinthe
ρ
–ω
interferenceregionand excludesε
2greaterthan(13−2)×10−7.Fordarkphotonmassesgreaterthan600MeVthecombinedlimitislowerthan8×10−7resultingmorestringentthanpresentconstraintsfromotherexperiments.
©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Manygravitationalanomalies observed since thefirst decades ofthe twentieth century, aswell aslarge-scale structure forma-tionintheearlyUniverse,canbe explainedbytheexistence ofa non-baryonicmatterknownasdarkmatter(DM) [1].Darkmatter motivatesextendingtheStandardModelofparticlephysics(SM)to includeadarksectorconsistingoffieldsandparticleswithnoSM gaugechargesandincludingextragaugesymmetries.Theminimal extensionofthe SM consistsofjustone additionalabelian gauge symmetry UD
(
1)
with associateda light vector gauge boson,the darkphoton –knownalsoasU boson,γ
or A–asmediatorof thenewforce,calledforthisreasondarkforce.Inthesimplest sce-nario [2],thecouplingwithSMparticlesarisesfromavectorportal knownaskinetic mixingconsisting inloopsof heavy dark parti-clescharged under both the electromagnetic andthe dark force. TheportalallowsthemixingofthedarkphotonbelongingtotheUD
(
1)
groupwiththeSM photon oftheUem(
1)
symmetry intro-ducingtheLagrangianterm:Lmix
= −
ε
2F em i j F i j dark.
(1)Here
ε
isadimensionlessparameterwhichgovernsthestrengthof themixing(ε
2=
α
/
α
,α
=
α
em, α
istheeffectivedarkcoupling constant)whileFemi j andF i j
darkarethefieldstrengthtensorsofthe SM Uem
(
1)
and dark UD(
1)
gauge groups, respectively. Through theportaltheU bosoncancoupletotheelectromagneticcurrent witha strength proportional to the SM particles electric charge. The process is responsible for both production and decayof the darkphoton inSM interactions thus resulting in anε
2 suppres-sion.Ifthekineticmixingappearsattheone-loop level,ε
canbe estimatedtobeintherange10−2–10−6 allowingvisibleeffectsat highluminositye+e− colliders [3].Duringthelastdecade,thedarkphotonhasbeenthefocusofa world-wideintensive researchbecause consideredaspossible ex-planationofmanyastrophysicalpuzzlingevidences [4].
Inthisworkweinvestigatethesimplesthypothesisofavisibly decaying dark photon looking for resonant production of U
bo-sonfromthecontinuum, consideringasallowed onlydecaysinto SMparticles.The U signal shouldappearasapeak inthe invari-ant mass of the final state particles with a widthmainly domi-natedbytheinvariantmassresolutionsincetheexpectedU -decay
widthcan beconsidered negligible [5].KLOEalreadyinvestigated
e+e−
→
U h(dark Higgsstrahlung) [6], U bosonindecaysof vec-torparticlesto pseudoscalars [7,8],andthevisibledecay hypoth-esis publishing three searches for radiative U production in thee+e−
→
Uγ
process, withthe U boson decayinginto: a)μ
+μ
−[9], using 240 pb−1 of data; b) e+e− [10], using a sample of 1.54 fb−1; c)
π
+π
− [11] analyzing thewholeKLOE dataset cor-respondingto anintegrated luminosityof 1.93 fb−1.Searches for muon andpion pairs, withthe ISR photon selected atsmall an-gle(θ <
15◦, θ >
165◦),coverapproximatelythesameU -bosonmassrangeof520–990MeV,whilefortheelectronpairsthe pho-tonselection was atlarge angle(55◦
< θ <
125◦) allowing toreachalowest U -bosonmassof5MeVandprobingthe
(
g−
2)
μfavored region [12].
InthepresentworkweextendthestatisticsoftheU
→
μ
+μ
−search to the wholedata sample andupdate the analysiswitha newestimateofthebackground,analogoustotheoneusedforthe
U
→
π
+π
− search. The new search confirms no U -bosonsignal inthe dimuoninvariant mass spectrum:a new90% CL exclusion limit inε
2 is estimated. This limit is of comparable magnitude withrespecttothepreviousones,thusacombinedsearchofdark photondecaysintobothmuon andpionpairswouldincrease the sensitivity ofthe single channel searches, particularly, it is more effectivein theregion oftheρ
–ω
interferencewhere thesearch forU→
μ
+μ
−losessensitivity.2. TheKLOEdetector
TheKLOEdetectoroperatesatDA
NE[13],theFrascati
φ
-fac-tory. DANE is an e+e− collider working at a center of mass energy mφ1
.
019 GeV. Positron and electron beams collide at an angleofπ
−
25 mrad,producingφ
mesonsnearlyatrest.The detectorconsistsofalargecylindricaldriftchamber(DC) [14], sur-rounded by a lead scintillating-fiber electromagnetic calorimeter (EMC)[15].A superconductingcoilaroundtheEMCprovidesa0.52 Tmagneticfieldalongthebisectorofthecollidingbeamswhichis takenasthez axisofourcoordinatesystem.The EMC barrel and end-caps cover 98% of the solid angle. Calorimetermodulesarereadoutatbothendsby4880 photomul-tipliers. Energy andtime resolutions are
σ
E/
E=
0.
057/
√
E
(
GeV)
and
σ
t=
57 ps/
√
E(
GeV)
⊕
100 ps,respectively. The driftcham-berhasonlystereowiresandis4 mindiameter,3.3 mlong.Itis builtout ofcarbon-fibersandoperates witha low- Z gasmixture (heliumwith10%isobutane).Spatialresolutionsare
σ
xy∼
150μmand
σ
z∼
2 mm.Themomentumresolutionforlargeangletracksisσ
(
p⊥)/
p⊥∼
0.
4%.ThetriggerusesbothEMCandDCinformation. Events used inthis analysisare triggered by atleast two energy depositslargerthan50 MeVintwosectorsofthebarrel calorime-ter [16].3. e+e−
→
μ
+μ
−γ
dataanalysis3.1. Eventselection
We selected
μ
+μ
−γ
candidates by requiring events with two oppositely-charged tracks emitted at large polar angles, 50◦< θ <
130◦,withtheundetectedISR photon missing mo-mentumpointing–accordingtotheμ
+μ
−γ
kinematics–atsmall polarangles(θ <
15◦, θ >
165◦).Thetracksarerequiredtohave thepointofclosestapproachtothez axiswithinacylinderof ra-dius 8 cm and length 15 cm centered at the interaction point. Inordertoensuregoodreconstructionandefficiency,weselected trackswithtransverseandlongitudinalmomentump⊥>
160 MeV or|
pz|
>
90 MeV,respectively.Thisseparationoftrackandphotonselectionregionsintheanalysis,greatlyreducesthecontamination fromtheresonantprocesse+e−
→ φ →
π
+π
−π
0,fromtheFinal State Radiation (FSR)processes e+e−→
π
+π
−γ
FSR ande+e−→
μ
+μ
−γ
FSR, since theμ
+μ
−γ
cross section diverges at smallFig. 1. Mtrkdistributionsforμ+μ+γ andπ+π−γ.Dataarerepresentedinblack, theMCsimulationsofπ+π−γ and μ+μ−γ channelsareingreenandred, re-spectively,whiletheirsumisinblue;theverticalbacklinerepresentstheselection cutappliedtoseparatethetwochannels.(Forinterpretationofthecolorsinthe figure(s),thereaderisreferredtothewebversionofthisarticle.)
ISR photon angle making FSR processes and
φ
decays relatively unimportant [17–20].Consequently, since ISR-photons are mostly collinear with the beam line, a high statistics for the ISR signal eventsremains. The main background contributions affectingthe ISRμ
+μ
−γ
samplearetheresonante+e−→ φ →
π
+π
−π
0 pro-cess andthe ISR and FSR e+e−→
x+x−γ(γ),
x=
e, π
processes. Their contributions have beenevaluated by applying kinematical cutsintheMtrk,M2π π plane,1 withMππ theinvariantmassofthetrackpairinthepionmasshypothesis.
Aparticleidentificationestimator(PID),L±,basedona pseudo-likelihood function usingthe charged particles time-of-flight and energy depositionsin the five calorimeterlayers is used to sup-pressradiative Bhabhaevents [19,21,22]. Events withbothtracks having L±
<
0 are identified as e+e−γ
events andrejected (see Fig.2).Finally,acutonthetrack-massvariable Mtrk selectsmuonsby requiringMtrk
<
115 MeV asshowninFig.1.Attheendofthe selectiondescribedaboveabout7.16×
106eventssurvive.In order to evaluate the residual background contributions, the sameanalysis chain was applied to simulatedevents forthe
π
+π
−γ
andπ
+π
−π
0 channelswhilethe radiativeBhabha con-tributionhas beenevaluated directlyfrommeasured data. Distri-butionsofthefractionalresidualbackgroundFBGforeachchannel andtheir sumare shownin Fig. 3asa function ofthe invariant massofthetrackpairinthemuonmasshypothesis,Mμμ.Thetotalresidualbackgroundrisesuptoabout9%inthe
ρ
–ω
regionanddecreases downtoabout3%atlowandhighinvariant massvalues.
4. Parametrizationoftheirreducible
μ
+μ
−γ
backgroundTominimizethesystematicuncertaintiesaffectingtheanalysis, weevaluatedtheirreducible
μ
+μ
−γ
backgrounddirectlyfromthe data.InFig. 4,we report thecomparisonbetween dataandesti-1 M
trk is computed from energy and momentum conservation, assumingthe presenceofoneundetectedphotonandthatthetracksbelongtoparticlesofthe samemass: √ s− |p+|2+M2 trk− |p−|2+M2 trk 2 −p++ p−2=0
wherep+(p−)isthemeasuredmomentumofthepositive(negative)particle,and onlyoneofthefoursolutionsisphysical.
Fig. 2. MCL+vs.L−PIDdistributionsforbothtracks.Eventscontainedinthelow leftrectangle(havingbothtrackswithL±<0)areregardedase+e−γ eventsand rejectedintheselection.
Fig. 3. Fractional residual backgrounds as function of Mμμ.
matedbackgrounddistributions(toppanel)andtheirratio(bottom panel),whichareingoodagreementwithinerrors.
We estimated theirreducible
μ
+μ
−γ
background by using a sidebandfittotheobservedspectrum,keeping,foreachiteration, thefitwiththebestreducedχ
2.Thefittosidebandsinthewholemass range has been performed considering sub ranges
±
12σ
wide, where
σ
is thedimuon invariant massresolution ofabout 2MeV[11].ForeachU-masshypothesisaregioncorrespondingto±
3σ
isexcludedfromthefit.Wefitthedatadistributionsby us-ing Chebyshevpolynomials(asinRef. [9])up to6thorderinthe massranges519–757 MeVand811–973 MeV.Inthemassinterval between759and809 MeV,wheretheeffectoftheρ
–ω
interfer-enceispresent[23],weusedanotherparametrization:f
(
x)
=
pol2(
x)
· [
1+
A· (
x−
M)
·
exp(
−
0.
5· ((
x−
M)/λ)
2)
].
(2) The parametrization (2) has beenused because found to best fitthe
μμ
invariantmasssimulatedspectrum(PHOKHARA gener-ator [24–27] with vacuumpolarization correction included anda full descriptionofthe detectorperformedwiththeGEANFI pack-age [28])asshowninFig. 5.As afirststep,thethreecoefficients ofthesecond orderpolynomial pol2(x)andthe parameters A, Mand
λ
arecomputedbyfittingthefunctioninEq.(2) overthefullμ
+μ
−γ
simulatedspectrum:valuesof782.24MeVand6.09MeV wereobtainedfortheparametersM andλ
,respectively.Then,theFig. 4. Toppanel:μ+μ−γ observedspectrum(fullsquares)and estimated irre-duciblebackground(opensquares).Bottompanel:dataandestimatedbackground ratio.
Fig. 5. FitofreconstructedPHOKHARAMCwithvacuumpolarization correction in-cluded.
fitsinthe consideredmassrange(759–809 MeV)ofthe
μ
+μ
−γ
observedspectrumhavebeenperformedbyusingagainthe func-tion (2), keeping the parameters M and
λ
fixed at the values 782.24MeVand6.09MeV,andleavingfreeall theother parame-ters.ExamplesofthefitsperformedbyusingChebyshevpolynomials ortheparametrizationineq. (2) areshowninFig.6.
Thereduced
χ
2 ofthefittosidebandsforboth parameteriza-tionsremainsbelow2inthewholemassrange.Thefitprocedure isstableinthe wholedata rangeandnoanomaly is observedin thefittedbackground.5. Systematicuncertainties
Inthefollowingwe report thesystematicuncertainties affect-ing the analysis, mainly dueto the evaluationof the irreducible
Fig. 6. Examplesoffitsperformedintwosub-rangesoftheμ+μ−γ spectrumby usingChebyshevpolynomials(upperpanel)andparametrization(2) (lowerpanel).
Fig. 7. Bin-by-bin total fractional systematic error of the background estimate.
backgroundandtotheeventselectionappliedtothe
μ
+μ
−γ
can-didates.5.1. Systematicuncertaintiesontheirreduciblebackground
Thefractionalsystematicerrorontheirreducible
μ
+μ
−γ
back-groundisshowninFig.7.Theevaluationofthesystematic uncer-taintieshasbeenderivedforeachmassbinbyestimatingtheerror ofthefit.Thetotalsystematicerrorislessthan1%inmostofthe massrange.The systematic error dueto the side bands fit procedure has been also evaluated by varying the range of the fit interval of
±
1σ
andcomputingthemaximumdifferencebetweennominalfitFig. 8. Global efficiency as function of Mμμ.
Table 1
Summaryofthesystematicuncertainties.
Systematic source Relative uncertainty (%)
Mtrkcut 0.4 Acceptance 0.6–0.1 as Mμμincreases Trigger 0.1 Tracking 0.3–0.6 as Mμμincreases Generator 0.5 Luminosity 0.3 PID negligible Total 0.98–0.94 as Mμμincreases
andthefitderived bychangingthefitinterval.Itscontributionis
<<
1%andthereforeresultsnegligibleinthewholemassrange.5.2. Systematicuncertaintiesoftheglobalefficiency
Fig.8showstheglobalanalysisefficiencythathasbeen evalu-atedfromafull
μ
+μ
−γ
simulation.Thisefficiencyincludes con-tributions from kinematic selection, trigger, tracking, acceptance andPID-likelihoodefficiencies.Table 1 lists all the systematic errors affecting the
μ
+μ
−γ
analysis. We evaluated the corresponding uncertainties by using the same procedures described in Ref. [9]. These systematic un-certaintiesdonotaffecttheirreduciblebackgroundestimationbut enterin thedetermination oftheselection efficiencyandthe lu-minositymeasurement.
6. LimitsonU -bosonproductionin
μμγ
eventsThe
μ
+μ
−γ
observed spectrum doesnot reveal thepresence of any visible structure (see Fig. 4) within the mass-dependent systematicuncertainties.Forthisreason,aprocedurehasbeen ap-plied to evaluate the statisticalsignificance of theobserved data fluctuationsandeventually set a limit on the e+e−→
Uγ
,
U→
μ
+μ
− process. The following subsection describesthe results of thelimitextractionprocedure.6.1. Upperlimitextractionon
ε
2Toextractthe upperlimit(UL) on
ε
2 weused theConfidence LevelSignal(CLS)technique [29].Theprocedurerequiresasinputs theinvariantmassdataspectrum,thebackground(theirreducibleμ
+μ
−γ
background),theU -bosonsignalandthesystematic frac-tional uncertainties on the background estimation foreach Mμμbin.ThesignalhasbeengeneratedwithatoyMCinstepsof2MeV fortheU -bosonmass.Ateachstep,aGaussiandistributionisbuilt
withawidthcorrespondingtotheinvariantmassresolutionofthe dimuonsystemofabout2 MeV.Thesignalisthenintegratedover
Mμμ around MU.Thenumberof signalevents,givenasinput to
theprocedure,isinitiallyarbitraryandveryhigh(abouttentimes the square rootof the estimatedbackground value inthe corre-spondingmassbin)andtheniterativelyscaleduntiltheconfidence levelCLS reaches0.1within
±
0.01.Theintegralofthesignal cor-respondingtothedefinedlevelofconfidencerepresentsthelimit on the numberof U -bosoneventsexcluded at 90%CL. Since the limit isstronglydependent ontheirreduciblebackground evalua-tion,thelimitextractionaccountsforthesystematicuncertainties of the background estimate. The limit extraction procedure uses the total bin-by-bin fractional systematicuncertainty, reportedin Fig. 7, to perform a Gaussian smearing of theμ
+μ
−γ
expected backgroundgivenasinput.TheULonthekinetic mixingparameterhasbeenextractedby using,foreachU -bosonmassvalue,thefollowingformula [9–11]:
ε
2=
α
α
=
NCLSeff
·
L·
H·
I (3) where NCLS is thelimit on thenumber ofevents,eff represents the global efficiency (shown in Fig. 8), L is the integrated lumi-nosity (1.93 fb−1 with an uncertainty of 0.3% [18,19]), H is the radiator function calculated at QED next-to-leading-order correc-tionswithanuncertaintyof0.5% [25–27,30] andgivenby: H
=
dσ
μμγ/
dMμμσ
(
e+e−→
μ
+μ
−,
Mμμ)
.
(4)Here d
σ
μμγ/
dMμμ is the differential cross section of e+e−→
μ
+μ
−γ
,σ
(
e+e−→
μ
+μ
−,
Mμμ)
isthetotalcrosssectionofthee+e−
→
μ
+μ
− process.InEq. (3), I isgivenbythefollowing in-tegralaround MU:I
=
σ
Uμμd√
s,
(5)where
σ
Uμμ=
σ
(
e+e−→
U→
μ
+μ
−,
s)
isthetotalcrosssectionof U -bosonproductiondecaying inthe
μ
+μ
− channelwhen thekineticmixingparameter
ε
isequalto1,s=
M2U.Theuncertainties
on H ,
eff, L, and I, propagate tothe systematicerror on
ε
2 via eq. (3).The resultinguncertaintyonε
2 islowerthan 1%andhas beentakenintoaccountintheestimatedlimit.The exclusion plot on
ε
2 is shown asa dashed linein Fig. 9 comparedwiththeexistinglimitsinthemassrangebelow1 GeV. Our90%CLULrangesfrom3×
10−6 to2×
10−7 inthe519–973 MeVmassinterval.7. CombinedlimitonU -bosonproductionin
μμγ
andπ π γ
events
Inthissectionwepresentthecombinationprocedureofthefull statistics
π
+π
−γ
andμ
+μ
−γ
limits. As forthe previous analy-ses, weuse theCLS technique toestimate a 90%CL limit forthee+e−
→
Uγ
ISR,
U→
μ
+μ
−, π
+π
− process. Toextract the limit, weusethealreadyestimatedbackgroundandobservedspectrafor bothπ π γ
[11] andμμγ
channels in a combined way. A total systematicerrorontheirreduciblebackgroundestimate,givenby the combinationofthecorresponding estimateduncertainties for bothU -bosondecaymodes,isalsogivenasinputtotheprocedure. A combinedU -bosonsignal isgeneratedforboth decaychannels taking into account the differences in global efficiencyand rela-tive branching ratio [3]. Thesignal inputsare generatedwiththe same toy MC procedure performedfor theμ
+μ
−γ
limit extrac-tion,then,eachsignalisintegratedandnormalized tothenumberFig. 9. 90%CLexclusionplot forε2 as afunctionofthe U -boson massfor the e+e−→Uγ process.The U→μ+μ− limit(dashedline), theU→π+π− [11] constraint(dotted line),and the U→μ+μ−,π+π− combination (solidline) at fullKLOE statistics,arepresentedincomparisonwiththe competitivelimits by BaBar [31],NA48/2 [32],andLHCbexperiments[33].
of events estimated from Eq. (3), for a given hypothesis of the kinetic mixingparameter
ε
2. Thelimit computation proceeds ac-cordingtothefollowingsteps:itmakesahypothesisoftheε
2 ki-neticmixingparameter,startingfromanarbitraryverylowvalue; thecorresponding numberofeventsforπ π γ
andμμγ
channels aregeneratedaccordingtoEq. (3) inordertobuild thesignal in-puthistogram, then, the procedure runsas before by comparing data andexpected irreducible background. The search procedure endswhentheestimatedCLS becomescloseto 0.1within±
0.01, providingdirectlythecorrespondingexclusiononε
2.Thecombinedupperlimit,obtainedafteraveraging the statis-ticalfluctuationsby asmoothingprocedure,excludesvaluesof
ε
2 greaterthan(
13−
2)
×
10−7 intheU -massrange519–987 MeV. ItisshowninFig.9,comparedtothemostcompetitivelimits.The other existing limits [7–10,34–37] are not reported to make the figure more readable. The combined limit is represented by the blue area and is more stringent with respect to the already set limitsinthemassregion600–987 MeV,whileitiscomparableto BaBarandLHCbresultsformasseslowerthan600 MeV.8. Conclusions
We analyzed 1.93 fb−1 of KLOE data to investigate the hy-pothesis ofa light vector gauge boson decaying into muonsand pions by means of the ISR method in the e+e−
→
Uγ
ISR,
U→
μ
+μ
−, π
+π
− process.No U -bosonevidencehasbeenfound and acombinedlimitat90%CLusingthetwoU -decaymodeshasbeen extractedonthekineticmixingparameterε
2 intheenergyrange between519and987 MeV.Thenewcombinedlimitismore strin-gent than the alreadyset constraints in the region between600 and987MeVbyexcludingvaluesofε
2 higherthan(
8−
2)
×
10−7. AcknowledgementsWe warmly thank our former KLOE colleagues for the
ac-cess to the data collected during the KLOE data taking
cam-paign.WethanktheDA
NEteamfortheir effortsinmaintaining
low background running conditions and their collaboration dur-ing all data taking. We want to 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 hiscontinuous attentiontothegassystemanddetectorsafety;A. Balla, M. Gatta, G. Corradiand G. Papalino for electronics main-tenance; C. Piscitelli for his help during major maintenance pe-riods. This work was supported in part by the Polish National
Science Centre through the Grants Nos. 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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