Limit on the production of a low-mass vector boson in $e^{+}e^{-} \rightarrow U\gamma$, $U\rightarrow e^{+}e^{-}$, with the KLOE experiment

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Limit on the production of a low-mass vector boson in e ⁺ e ⁻ → ^U γ ^, U → ^{e + e − with the KLOE experiment}

A. Anastasi

^e,d

, D. Babusci

^d

, G. Bencivenni

^d

, M. Berlowski

^t

, C. Bloise

^d

, F. Bossi

^d

,

P. Branchini

^q

, A. Budano

^p,q

, L. Caldeira Balkeståhl

^s

, B. Cao

^s

, F. Ceradini

^p,q

, P. Ciambrone

^d

, F. Curciarello

^e,b,k

, E. Czerwi ´nski

^c

, G. D’Agostini

^l,m

, E. Danè

^d

, V. De Leo

^q

, E. De Lucia

^d

, A. De Santis

^d

, P. De Simone

^d

, A. Di Cicco

^p,q

, A. Di Domenico

^l,m

, R. Di Salvo

^o

,

D. Domenici

^d

, A. D’Uffizi

^d

, A. Fantini

^n,o

, G. Felici

^d

, S. Fiore

^r,m

, A. Gajos

^c

, P. Gauzzi

^l,m

, G. Giardina

^e,b

, S. Giovannella

^d

, E. Graziani

^q

, F. Happacher

^d

, L. Heijkenskjöld

^s

,

W. Ikegami Andersson

^s

, T. Johansson

^s

, D. Kami ´nska

^c

, W. Krzemien

^t

, A. Kupsc

^s

, S. Loffredo

^p,q

, G. Mandaglio

^e,f

, M. Martini

^d,j

, M. Mascolo

^d

, R. Messi

^n,o

, S. Miscetti

^d

, G. Morello

^d

, D. Moricciani

^o

, P. Moskal

^c

, A. Palladino

^d,∗,1

, M. Papenbrock

^s

, A. Passeri

^q

, V. Patera

^i,m

, E. Perez del Rio

^d

, A. Ranieri

^a

, P. Santangelo

^d

, I. Sarra

^d

, M. Schioppa

^g,h

, M. Silarski

^d

, F. Sirghi

^d

, L. Tortora

^q

, G. Venanzoni

^d,∗

, W. Wi´slicki

^t

, M. Wolke

^s

aINFNSezionediBari,Bari,Italy bINFNSezionediCatania,Catania,Italy

cInstituteofPhysics,JagiellonianUniversity,Cracow,Poland dLaboratoriNazionalidiFrascatidell’INFN,Frascati,Italy

eDipartimentodiFisicaeScienzedellaTerradell’UniversitàdiMessina,Messina,Italy fINFNGruppocollegatodiMessina,Messina,Italy

gDipartimentodiFisicadell’UniversitàdellaCalabria,Rende,Italy hINFNGruppocollegatodiCosenza,Rende,Italy

iDipartimentodiScienzediBaseedApplicateperl’Ingegneriadell’Università“Sapienza”,Roma,Italy jDipartimentodiScienzeeTecnologieapplicate,Università“GuglielmoMarconi”,Roma,Italy kNovosibirskStateUniversity,630090Novosibirsk,Russia

lDipartimentodiFisicadell’Università“Sapienza”,Roma,Italy mINFNSezionediRoma,Roma,Italy

nDipartimentodiFisicadell’Università“TorVergata”,Roma,Italy oINFNSezionediRomaTorVergata,Roma,Italy

pDipartimentodiMatematicaeFisicadell’Università“RomaTre”,Roma,Italy qINFNSezionediRomaTre,Roma,Italy

rENEAUTTMAT-IRR,CasacciaR.C.,Roma,Italy

sDepartmentofPhysicsandAstronomy,UppsalaUniversity,Uppsala,Sweden tNationalCentreforNuclearResearch,Warsaw,Poland

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received2September2015

Receivedinrevisedform25September 2015

Accepted2October2015 Availableonline8October2015 Editor:M.Doser

Keywords:

Darkmatter Darkforces

TheexistenceofanewforcebeyondtheStandardModeliscompellingbecauseitcouldexplainseveral strikingastrophysicalobservationswhichfailstandardinterpretations.Wesearchedforthelightvector mediatorofthisdarkforce,theU boson,withtheKLOEdetectorattheDANEe⁺e⁻ collider.Usingan integratedluminosityof1.54 fb⁻¹,westudiedtheprocesse⁺e⁻→^Uγ^,withU→^{e+e−,usingradiative} returntosearchforaresonant peakinthedielectroninvariant-massdistribution.Wedidnotfindev- idenceforasignal,andseta90% CLupperlimitonthemixingstrengthbetweentheStandardModel photonandthedarkphoton,ε²,at10⁻⁶–10⁻⁴inthe5–520 MeV/c²massrange.

©^{2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

*

Correspondingauthors.

E-mailaddresses:palladin@bu.edu(A. Palladino),graziano.venanzoni@lnf.infn.it(G. Venanzoni).

1 Presentaddress:DepartmentofPhysics,BostonUniversity,Boston,USA.

http://dx.doi.org/10.1016/j.physletb.2015.10.003

0370-2693/©^{2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

The StandardModel (SM)of particlephysics hasreceived fur- ther confirmation with the discovery of the Higgs boson [1–3], however,thereare stronghintsofphysicsit cannotexplain, such asneutrinooscillations[4]andthemeasuredanomalousmagnetic momentof themuon [5].Furthermore, theSM does notprovide adarkmatter(DM)candidateusuallyadvocatedasanexplanation ofthenumerousgravitationalanomaliesobservedintheuniverse.

Manyextensions ofthe SM [6–10] considera WeaklyInteracting MassiveParticle(WIMP)asaviableDMcandidateandassumethat WIMPsarechargedunderanewkindofinteraction.Themediator of the new force would be a gauge vector boson, the U boson, alsoreferredtoasadarkphotonorA^.Itwouldbeproduceddur- ingWIMPannihilations,haveamasslessthantwoprotonmasses, andaleptonicdecaychannelinordertoexplaintheastrophysical observationsrecentlyreportedbymanyexperiments[11–21].

In theminimal theoretical model,the U boson isthe lightest particleofthedarksectorandcancoupletotheordinarySMpho- tononlythroughloopsofheavydarkparticleschargedunderboth SM U(1)Y and dark U(1)D symmetries [6,22–26]. These higher- orderinteractionswouldopenaso-calledkineticmixingportalde- scribedinthetheorybytheLagrangiantermLmix= −^ε₂^F_{i j}^EWF_Dark^{i j ,} where F_{i j}^EW is the SM hypercharge gauge field tensor and F_Dark^{i j} is the dark field tensor. The

ε

parameter represents the mixing strengthandistheratioofthedarkandelectromagneticcoupling constants.Inprinciple,thedarkphotoncouldbe producedinany processinwhicha virtualorrealphoton isinvolvedbuttherate is suppressed dueto the very smallcoupling (

ε

<10⁻²). In this respect,high-luminosityO(^GeV)-energye⁺e⁻collidersplayacru- cialroleindarkphotonsearches[27–29].

We investigated the e⁺e⁻→^Uγ ^{process by} considering the U bosondecayingintoe⁺e⁻.Atthelevelofcouplingaccessibleby KLOEin thischannel theU boson isexpected todecaypromptly leavingitssignalasaresonantpeakintheinvariant-massdistribu- tionoftheleptonpair.Theenergyscanwasperformedbyapplying theradiativereturnmethodwhichconsistsofselectingtheevents inwhicheitherelectronorpositronemitsaninitial-stateradiation (ISR) photon which carries away a part ofthe energy andeffec- tivelychangestheamountoftheenergyavailableforU bosonpro- duction.Theselectedinitial- andfinal-stateparticlesarethesame asintheradiativeBhabhascatteringprocesssowereceivecontri- butionsfromresonants-channel,non-resonantt-channel U boson exchanges, andfroms–t interference. The finite-width effectsre- latedto s-channelannihilationsub-processes,scatteringt-channel and s–t interference are of order of U/m_U for the integrated crosssection andcan be neglected withrespect to anypotential resonancewe wouldobserve; U∼^{10−7–10−2MeV forthe cou-} plingstrengths to which we aresensitive [30].The non-resonant t-channeleffectswouldnotproducea peakintheinvariant-mass distributionbutcould, inprinciple, appearinanalyses of angular distributionsorasymmetries.Wearegoingtoreportexclusivelyon resonants-channelU bosonproduction.

Usingasample ofKLOEdatacollectedduring 2004–2005,cor- responding to an integratedluminosity of 1.54 fb⁻¹, we derived anewlimitonthekinetic mixingparameter,

ε

²,approachingthe dielectronmassthreshold.

Fig. 1. Cross section of the KLOE detector.

2. KLOEdetector

The Frascati φ ^{factory, DA}NE, is an e⁺e⁻ collider running mainlyatacenter-of-massenergyof1.0195 GeV,themassofthe φ ^{meson. Equalenergyelectron andpositronbeamscollideatan} angleof∼^{25 mrad,producing}φ^{mesonsnearlyatrest.}

The KLOE detector consists of a large cylindricalDrift Cham- ber(DC)[31]witha25 cminternal radius,2 mouter radius,and 3.3 mlength,comprising∼^{56,000wiresforatotalofabout12,000} drift cells. It is filled with a low- Z (90% helium, 10% isobutane) gas mixture and provides a momentum resolution of

σ

p_⊥/p_⊥≈ 0.4%. The DC is surrounded by a lead-scintillating fiber electro- magnetic calorimeter (EMC) [32] composed of a cylindrical bar- rel and two end-caps providing 98% coverage of the total solid angle. Calorimeter modules are read out at both ends by 4880 photomultiplier tubes, ultimately resulting in an energy resolu- tion of

σ

E/E =⁵.7%/√

E(GeV) and a time resolution of

σ

t = 57 ps/√

E(GeV)⊕^{100 ps.A}superconductingcoilaroundtheEMC providesa0.52 Tfieldtomeasurethemomentumofchargedpar- ticles.AcrosssectionaldiagramoftheKLOEdetectorisshownin Fig. 1.

The trigger[33]usesenergydeposition inthecalorimeterand drift chamber hit multiplicity.Tominimize backgrounds the trig- gersystemincludesasecond-levelcosmic-raymuonvetobasedon energydeposition inthe outermostlayers ofthe calorimeter,fol- lowedby asoftwarebackgroundfilterbasedon thetopologyand multiplicity of energy clusters and drift chamber hits to reduce beambackground.Adownscaledsampleisretainedtoevaluatethe filterefficiency.

3. Eventselection

Using 1.54 fb⁻¹ of KLOE data we have searched for U boson productionintheprocesse⁺e⁻→^Uγ ^followedbyU→^e+e−.The

Fig. 2. (Coloronline.) Thetrackmassdistributionbeforeeventselectionformea- surementand expectedbackgroundsimulations.Someofthe simulationshad a prescalingforMtrack<80 MeV/c²,whichhasbeenaccountedforinthebackground evaluation.ThemeasurementdatasetwasprescaledforMtrack>85 MeV/c².The trackmassvariablepeaksatthe massofthechargedtrackinthefinalstatefor eventswithtwo chargedtracks and aphoton.The selection regionis Mtrack<

70 MeV/c².

center-of-massenergyofthecollision dependsonthe amountof energycarriedawaybytheinitial-stateradiation(ISR)photon.The irreduciblebackgroundoriginatesfromthe e⁺e⁻→^e+e−γ ^radia- tive Bhabha scatteringprocess, havingthe same three final-state particles. The reducible backgrounds consist of e⁺e⁻→ μ⁺μ⁻γ^, e⁺e⁻→ π⁺π⁻γ^{, e+e−}→ γγ ^{(where one photon convertsinto an} e⁺e⁻ pair), ande⁺e⁻→ φ→ ρπ⁰→ π⁺π⁻π^{0, aswell asother} φ decays.Theexpected U bosonsignal wouldappearasa resonant peakintheinvariant-massdistributionofthee⁺e⁻pair,mee.This searchdiffers fromtheprevious KLOE searches[34–36]in itsca- pabilitytoprobethelowmassregionclosetothedielectronmass threshold.

Weselectedeventswiththreeseparate calorimeterenergyde- positscorrespondingto twooppositely-charged leptontracksand a photon. The final-stateelectron, positron,and photon were re- quired to be emitted at large angle (55^◦< θ <125^◦) with re- spectto the beam axis,such that they are explicitly detected in thebarrelofthecalorimeter,see Fig. 1.The large-angleselection greatlysuppressesthet-channelcontributionfromtheirreducible Bhabha-scattering background which is strongly peakedat small angle.Since we are interested mostly in the low invariant-mass region,weselectonly eventswithahard photon, E_γ>305 MeV, chosen toselecta subsampleofthe eventsgenerated byour MC simulation.Werequired bothlepton tracks tohavea first DChit within a radius of 50 cm from the beam axis and a point-of- closest-approach(PCA)tothebeamaxiswithinthefiducialcylin- der,

ρ

_PCA<1 cm and−⁶<z_PCA<6 cm,entirelycontainedwithin the vacuum pipe eliminating background events from photons converting on the vacuum wall. We eliminated tightly spiralling tracks by requiring either a large transverse or a large longitu- dinalmomentum foreach of the lepton tracks, p_T >160 MeV/c or p_z>90 MeV/c. We require that the total momentum of the chargedtracks is (|p_e+| + |p_e−|) >150 MeV/c to avoid the pres- enceofpoorly reconstructed tracks.Apseudo-likelihood discrim- inantwasusedto separateelectrons frommuonsandpions[37].

A furtherdiscriminationfrommuonsandpionswasachievedusing theM_trackvariable.M_track isthe X massforan X⁺X⁻γ ^finalstate, computed using energy and momentum conservation, assuming m_X+=^mX⁻ [37]. In Fig. 2the Mtrack distributionis reported for measureddataandforall therelevantMC simulatedbackground components. Including the cut M_track<70 MeV/c² we were left with681,196eventsattheendofthefullanalysischain.

Fig. 3. (Coloronline.) Dielectroninvariant-massdistributionfrommeasurementdata withnon-irreduciblebackgroundssubtractedcomparedtothe Babayaga-NLOMC simulation.

4. Simulationandefficiencies

WeusedMCeventgeneratorsinterfacedwiththefullKLOEde- tector simulation,GEANFI[38],includingdetectorresolutionsand beam conditions on a run-by-run basis, to estimate the level of backgroundcontaminationduetoalloftheprocesseslistedinthe previoussection.Excludingtheirreduciblebackgroundfromradia- tiveBhabhascatteringevents,thecontamination fromthesumof residualbackgroundsafterallanalysiscutsislessthan1.5%inthe wholem_ee range,andnoneofthebackgroundshapesarepeaked, eliminatingthepossibilityofabackgroundmimickingtheresonant U bosonsignal.TheirreducibleBhabhascatteringbackgroundwas simulatedusingthe Babayaga-NLO[39–42]eventgeneratorimple- mented within GEANFI (includingthe s-, t-,and s–t interference channels) and is shown in Fig. 3 along with the measured data aftersubtracting the non-irreducible backgroundcomponents.No signalpeakisobserved.

In orderto evaluate theU boson selection efficiency we used a modified version of the Babayaga-NLO event generator imple- mented within GEANFI, such thatthe radiative Bhabhascattering processwas onlyallowed toproceedviatheannihilationchannel, in whichthe U boson resonancewould occur. In orderto create alarge-statisticssampleinourregionofinterestwerestrictedthe Babayaga-NLOgeneratedeventstowithin50^◦< θ_e^MC_+,e−<130^◦and E^MC_γ >300 MeV.Thegenerator-level efficiencyduetothisrestric- tionwasevaluatedusinga Phokhara MCsimulation[43].Thetotal efficiency is evaluated as the product of the generator-level ef- ficiencyand theevent-selection efficiency,containing thecuts in Section 3conditionedto thegenerator-levelrestriction aswell as the triggerefficiency, andisshownin Fig. 4. Thedecrease inef- ficiencyas m_ee→^2me comes from the requirementon the total momentumofthechargedtracks.

5. Upperlimitevaluation

Weusedthe CLS technique[44] todeterminethelimit onthe numberofsignal U bosonevents, N_U,at90% confidencelevelus- ingthemee distribution.Theinvariant-massresolution,

σ

mee,isin therange1.4<

σ

mee<1.7 MeV/c².Chebyshev polynomialswere fit to the measured data (±¹⁵

σ

mee), excluding the signal region of interest(±³

σ

mee). The polynomial with

χ

²/N_dof closest to 1.0 was used as the background.A Breit–Wigner peak with a width of 1 keV smeared with the invariant-mass resolution was used asthe signal. An example of one specific CLS resultis shown in Fig. 5, yielding an upper limit of N_U=215 U boson events at

Fig. 4. Smootheddistributionofthetotalefficiencydefinedastheproductofthe selectionefficiencyfor the e⁺e⁻→Uγ →e⁺e⁻γ finalstateevaluatedusingthe Babayaga-NLOeventgeneratormodifiedtoallowonlythes-channelprocess,and thegenerator-levelefficiencyevaluatedfroma Phokhara MCsimulation.

Fig. 5. (Coloronline.) TheCLSresultat90%CLformU=¹⁵⁵.25 MeV/c²showingthe measureddata,theChebyshev-polynomialsidebandfit,andthesignalshapescaled totheCLSresult.

Fig. 6. Upper limit on the cross sectionσ^e⁺e⁻→Uγ,U→e⁺e⁻ .

mU=¹⁵⁵.25 MeV/c²atthe90%confidencelevel.The

χ

²/Ndofwas 1.09forthisChebyshev-polynomialsidebandfit.

Theupperlimitat90%confidencelevelonthenumberofU bo- son events, UL(N_U), can be translated into a limit on the cross section,

UL



σ ^

e⁺e⁻

→

U

γ,

U

→

e⁺e⁻



=

^UL

(

NU

)

L

eff

,

(1)

whereL istheluminosityand

eff isthetotalselection efficiency.

ThelimitisshowninFig. 6.

Fig. 7. (Coloronline.) Exclusionlimitsonthekineticmixingparametersquared,ε², as afunctionofthe U bosonmass. Theredcurvelabeled KLOE(3) isthe result ofthisarticlewhilethecurveslabeledKLOE(1) andKLOE(2)indicatetheprevious KLOEresults.AlsoshownaretheexclusionlimitsprovidedbyE141,E774,Apex, WASA,HADES,A1,BaBar,andNA48/2.Thegraybanddelimitedbythedashedwhite linesindicates themixinglevelandmU parameterspace thatcouldexplain the discrepancyobservedbetweenthemeasurementandSMcalculationofthemuon (g−2)μ.

We then translated thelimit on NU toa 90% confidencelevel limit on the kinetic mixing parameter as a function of m_ee as in[36],

ε

²

(

m_ee

) =

^NU

(

m_ee

)

_eff

(

m_ee

)

1

H

(

m_ee

)

I

(

m_ee

)

L

,

(2) wheretheradiatorfunction H(mee)wasextractedfrom

d

σ

_eeγ

/

dm_ee

=

^H



m_ee

,

s

,

cos

(θ

_γ

) 

· σ

_ee^QED

(

m_ee

)

usingthe Phokhara MCsimulation[43]todeterminetheradiative differentialcrosssection, I(mee)istheintegralofthecrosssection

σ

(e⁺e⁻→^U→^e+e−), L=¹.54 fb⁻¹ is the integrated luminos- ity, and

eff(mee) is the total efficiency described in Section 4.

Our limit is shown in Fig. 7 along with the indirect limitsfrom the measurements of (g−²)_e and (g−²)_μ at 5

σ

shown with dashedcurves.Limitsfromthefollowingdirectsearchesareshown withshadedregions andsolidcurves:E141 [45],E774 [45],KLOE (φ→ η^U,U→^{e+e−) [34,35], Apex[46],WASA[47],HADES [48],} A1 [49], KLOE (e⁺e⁻→^Uγ^{, U}→ μ⁺μ^{−) [36], BaBar [50], and} NA48/2[51].

6. Systematicuncertainties

The background was determined by Chebyshev-polynomial sidebandfits.Theparametersofthepolynomialswerethenvaried within 1

σ

to determine the maximum variation of the polyno- mial shape. The uncertaintyofeach bin was setto theextent of that variation evaluated atthe bin center.An exampleof theer- ror bars on the Chebyshev-polynomial sideband fits can be seen in Fig. 5. These binuncertainties were taken intoaccount in the CLSprocedure whendetermining NCLS(mee).Since theirreducible backgroundissmoothforeachfitrange,weassumetheChebyshev polynomials sufficiently represent the background with negligi- ble systematic uncertainty. Any uncertainty in the shape of the smearedresonantpeakwasalsotakentobenegligible.

The efficiencyof the e⁺e⁻→^e+e−γ ^{event selection was de-} termined by taking the ratio ofthe set of simulated eventsthat passed the selection criteria to the total simulated sample. We apply a 0.1% systematic uncertainty due to the Babayaga-NLO event generator [39–42], a 0.1% systematic uncertainty for the

Table 1

Summaryofsystematicuncertainties.Theuncertaintiesontheefficiency,radiator function,andcross-sectionintegralvaryasafunctionofmee.Thenumbersquoted herecorrespondtothelargestestimatewithinourmeerange.

Systematic source Relative uncertainty

Background (sideband fit) negl.

eff(mee) 2%

MC generator, 0.1%

Trigger, 0.1%

Software background filter, 0.1%

Event selection, 2%

H(mee) 0.5%

I(mee) negl.

L 0.3%

trigger, anda 0.1% systematicuncertainty for the softwareback- ground filter. All together the uncertainty on the selection effi- ciencyisdominatedby thestatisticaluncertaintyon theselected sample. A Phokhara MCsimulation [43] was performedto eval- uate the generator-level efficiency due to the restriction E^MC_γ >

300 MeV and50^◦< θ_e^MC_+,e−<130^◦.Theselectionefficiencyandthe generator-levelefficiencyarecombinedtogivethetotalefficiency,

eff(m_ee).TheuncertaintyisgivenastheerrorbandinFig. 4,again dominatedbythestatisticaluncertaintiesinthesimulateddataset.

There are two effects that contribute to the uncertainty in theradiator function, H(m_ee). First,since thevalue of H(m_ee) is taken from simulated data, we must take into account the sta- tistical uncertainty on those values. Second, we assume a uni- form0.5%systematicuncertaintyinthe calculationof H(mee),as quotedin[43,52–54].Theuncertaintyintheintegratedluminosity is0.3%[37].Theuncertaintieson H(m_ee),

eff(m_ee),andL,propa- gatetothesystematicuncertaintyon

ε

²(mee)via(2).Asummary ofsystematicuncertaintiesispresentedinTable 1.

7.Conclusions

WeperformedasearchforadarkgaugeU bosonintheprocess e⁺e⁻→^Uγ ^withU→^{e+e−usingtheradiativereturnmethodand} 1.54 fb⁻¹ ofKLOEdatacollected in2004–2005.Wefoundno ev- idenceforaU bosonresonantpeak andseta90% CLupperlimit onthekineticmixingparameter,

ε

²,at10⁻⁶–10⁻⁴ intheU-boson massrange5–520 MeV/c².Thislimitpartlyexcludessomeofthe remaining parameterspacein thelow dielectronmass region al- lowed by the discrepancy between the observed and predicted (g−²)_μ.

Acknowledgments

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 DANE team for their efforts in main- taining low background running conditions and their collabo- ration during all data taking. We want to thank our techni- cal staff: G.F. Fortugno and F. Sborzacchi for their dedication in ensuring efficient operation of the KLOE computing facili- ties; M. Anelli for his continuous attention to the gas system and detector safety; A. Balla, M. Gatta, G. Corradi and G. Pa- palino for electronics maintenance; M. Santoni, G. Paoluzzi and R. Rosellinifor generaldetector support; C. Piscitellifor his help during major 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,GrantAgreement No. 227431; by the Polish National Science Centre through the GrantNos. DEC-2011/03/N/ST2/02641,2011/03/N/ST2/02652,2013/

08/M/ST2/00323,2013/11/B/ST2/04245,2014/14/E/ST2/00262, and bytheFoundationforPolishSciencethroughtheMPDprogramme.

In addition, we would like to thank the Babayaga authors, C.M. Carloni Calame,G. Montagna,O. Nicrosini,andF. Piccinini,for numeroususefuldiscussions andhelp whilemodifyingtheir code forourpurpose.

References

[1]ATLASCollaboration,Phys.Lett.B716(2012)1.

[2]CMSCollaboration,Phys.Lett.B716(2012)30.

[3]CMSCollaboration,J.HighEnergyPhys.06(2013)081.

[4]K.Olive,etal.,Reviewofparticlephysics,Chapter14:neutrinomass,mixing, andoscillations,Chin.Phys.C38(2014)090001.

[5]J.Miller,etal.,Annu.Rev.Nucl.Part.Sci.62(2012)237.

[6]M.Pospelov,A.Ritz,M.Voloshin,Phys.Lett.B662(2008)53.

[7]N.Arkani-Hamed,etal.,Phys.Rev.D79(2009)015014.

[8]D.S.M.Alves,etal.,Phys.Lett.B692(2010)323.

[9]M.Pospelov,A.Ritz,Phys.Lett.B671(2009)391.

[10]N.Arkani-Hamed,N.Weiner,J.HighEnergyPhys.0812(2008)104.

[11]P.Jean,etal.,Astron.Astrophys.407(2003)L55.

[12]O.Adriani,etal.,Nature458(2009)607.

[13]M.Aguilar,etal.,AMSCollaboration,Phys.Rev.Lett.110(2013)141102.

[14]J.Chang,etal.,Nature456(2008)362.

[15]A.A.Abdo,etal.,Phys.Rev.Lett.102(2009)181101.

[16]F.Aharonian,etal.,HESSCollaboration,Phys.Rev.Lett.101(2008)261104.

[17]F.Aharonian,etal.,HESSCollaboration,Astron.Astrophys.508(2009)561.

[18]R.Bernabei,etal.,Int.J.Mod.Phys.D13(2004)2127.

[19]R.Bernabei,etal.,Eur.Phys.J.C56(2008)333.

[20]C.E.Aalseth,etal.,CoGeNTCollaboration,Phys.Rev.Lett.106(2011)131301.

[21]C.E.Aalseth,etal.,CoGeNTCollaboration,Phys.Rev.Lett.107(2011)141301.

[22]B.Holdom,Phys.Lett.B166(1985)196.

[23]C.Boehm,P.Fayet,Nucl.Phys.B683(2004)219.

[24]N.Borodatchenkova,D.Choudhury,M.Drees,Phys.Rev.Lett.96(2006)141802.

[25]P.Fayet,Phys.Rev.D75(2007)115017.

[26]Y.Mambrini,J.Cosmol.Astropart.Phys.1009(2010)022.

[27]R.Essig,P.Schuster,N.Toro,Phys.Rev.D80(2009)015003.

[28]B.Batell,M.Pospelov,A.Ritz,Phys.Rev.D79(2009)115008.

[29]M.Reece,L.Wang,J.HighEnergyPhys.0907(2009)051.

[30]L.Barzè,etal.,Eur.Phys.J.C71(2011)1680.

[31]M.Adinolfi,etal.,Nucl.Instrum.MethodsA488(2002)51.

[32]M.Adinolfi,etal.,Nucl.Instrum.MethodsA482(2002)364.

[33]M.Adolfini,etal.,Nucl.Instrum.Methods492(2002)134.

[34]F.Archilli,etal.,KLOE-2Collaboration,Phys.Lett.B706(2012)251.

[35]D.Babusci,etal.,KLOE-2Collaboration,Phys.Lett.B720(2013)111.

[36]D.Babusci,etal.,KLOE-2Collaboration,Phys.Lett.B736(2014)459.

[37] A.Denig,etal.,KLOEnote192,www.lnf.infn.it/kloe/pub/knote/kn192.ps.

[38]F.Ambrosino,etal.,KLOE-2Collaboration,Nucl.Instrum.Methods534(2004) 403.

[39]L.Barzè,etal.,Eur.Phys.J.C71(2011)1680.

[40]G.Balossini,etal.,Nucl.Phys.B758(2006)227.

[41]C.M.C.Calame,Phys.Lett.B520(2001)16.

[42]C.M.C.Calame,etal.,Nucl.Phys.B584(2000)459.

[43]H.Czy ˙z,etal.,Eur.Phys.J.C39(2005)411.

[44]G.C.Feldman,R.D.Cousins,Phys.Rev.D57(1998)3873.

[45]J.D.Bjorken,etal.,Phys.Rev.D80(2009)075018.

[46]S.Abrahamyan,etal.,APEXCollaboration,Phys.Rev.Lett.107(2011)191804.

[47]P.Adlarson,etal.,WASA-at-COSYCollaboration,Phys.Lett.B726(2013)187.

[48]G.Agakishiev,etal.,HADESCollaboration,Phys.Lett.B731(2014)265.

[49]H.Merkel,etal.,A1Collaboration,Phys.Rev.Lett.112(2014)221802.

[50]J.P.Lees,etal.,BaBarCollaboration,Phys.Rev.Lett.113(2014)201801.

[51]J.R.Batley,etal.,NA48/2Collaboration,Phys.Lett.B746(2015)178.

[52]G.Rodrigo,H.Czy ˙z,J.H.Kühn,M.Szopa,Eur.Phys.J.C24(2002)71.

[53]H.Czy ˙z,A.Grzelinska,J.H.Kühn,G.Rodrigo,Eur.Phys.J.C27(2003)563.

[54]H.Czy ˙z,A.Grzelinska,J.H.Kühn,G.Rodrigo,Eur.Phys.J.C33(2004)333.