Connection between diphoton and triboson channels in new physics searches

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Connection between diphoton and triboson channels in new physics searches

Anastasia Sokolenko

^a,∗

, Kyrylo Bondarenko

^b

, Alexey Boyarsky

^b

, Lesya Shchutska

^c

aDepartmentofPhysics,UniversityofOslo,Box 1048,NO-0371 Oslo,Norway bInstituut-Lorentz,LeidenUniversity,NielsBohrweg2,2333CA Leiden,theNetherlands

cInstituteforParticlePhysicsandAstrophysics,EidgenössischeTechnischeHochschuleZürich,Otto-Stern-Weg5,Zürich,Switzerland

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

Articlehistory:

Received11May2018

Receivedinrevisedform12August2018 Accepted28August2018

Availableonline31August2018 Editor:A.Ringwald

Keywords:

NewphysicsatLHC Axion-likeparticle Background Sensitivity

Photonmisidentification

Diphoton channelprovidesaclean signaturein searchesfor newphysics. Inthispaper, wediscussa connectionbetweenthediphotonchannel(γ γ)andtribosonchannels(Zγ γ,Z Zγ,W Wγ)imposedby theSU(2)L×^U(1)Y symmetryoftheStandardModel(SM)incertainclassesofmodels.Toillustratethis ideawechooseasimplemodelthathasallthesechannels.Inthismodel,thesamephysicscangiverise toγ₊MET insteadofγ γ and 2bosonsplusmissingenergyinsteadof3-bosonchannels.Weanalyze existingconstraintsandprevioussearchesandshowthatchannelsW Wγ andespeciallyZγ₊MET have apotentialtodiscovernewphysicsattheLHC.

©^{2018TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Adiphotonsignal isa goodsignature in thesearchesfornew physics atthe LHC [1–4] and possiblefuture colliders,forexam- ple,theILC [5] orthe FCC [6].The diphoton channel wasone of the first in the Higgs boson discovery [7,8]. More recently, the unconfirmed 750 GeV resonance also appeared in the diphoton channel [9–13].

Inthispaper,wediscusstheconnectionbetweenthediphoton channel(

γ γ

) andthethree-boson channels( Z

γ γ

, Z Z

γ

, W W

γ

) thatisimposedbythe SU(2)L×^U(1)Y symmetryoftheStandard Model(SM) fora certain class of models.The three-boson chan- nels are interesting from experimental point of view because of lowbackgroundandhighdetectionefficiency [14–18].Toillustrate thisidea,we consider thespecific axion-like particlemodel [19].

Similarmodelswerediscussedinthecontextofthe750 GeVres- onancethatwould, inthiscase, beexplainedbymisidentification ofa pair ofphotons createdby a relativistic axion witha single photonduetothefinitegranularityofthedetector [19–27].

The paperis organized asfollows: in Section 2 we introduce asimplephenomenologicalmodelwithaheavyscalars andlight pseudo-Goldstonebosona thatcanproducethecorrespondingsig-

*

Correspondingauthor.

E-mailaddress:anastasia.sokolenko@fys.uio.no(A. Sokolenko).

nal. In Section 3 we calculate constraints on the model coming from Z bosondecays.Wediscussthe3-bosonand2-bosons-plus- missing-energyexperimentalsignaturesinSection4,andconclude inSection5.

2. Themodel

ConsiderasimpleextensionoftheSMwithtwonewscalarpar- ticles,oneofwhichisverylight.Thismodelnaturallycomesfrom the spontaneously symmetry breaking of a global U(1) Peccei–

Quinnsymmetry [28] ofacomplexfieldφ

φ =

^f

+

^s

√

2 e^ia/f

,

(1)

where f is a vacuum expectation value of the φ field, s and a are real scalar fields. Afterthe symmetry breaking one expected themassive particles and themassless particlea (theGoldstone boson).IfthePeccei–Quinnsymmetryisslightlybroken,thefielda becomesmassive,butingeneralmuchlighterthattheheavyscalar particles.Themassiveparticlea iscalledtheaxion.Theinteraction partoftheLagrangianis

Lint

= −

^c1

2 faW_μνⁱ



W^μν,i

−

^c2

2 faB_μν



B^μν

+

^s

(∂

μa

)

²

f

+

Ls

,

(2)

https://doi.org/10.1016/j.physletb.2018.08.067

0370-2693/©^{2018TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Fig. 1. (a):Decayoftheheavyscalars into2axionswithsubsequentdecayinto2 photons.(b):Decayoftheheavyscalarintoaxionand2vectorbosons.

where c1 andc2 are dimensionlesscoupling constants, Bμν and Wμν areⁱ thestrengthtensorsoftheSM U(1)Y and SU(2)L gauge fields correspondingly. W μν^,i and Bμν are tensors dual to the strengthtensors:



F_μν

=

¹

2

ε

_μνσρF^σρ

.

(3)

TheLagrangianLsdescribestheeffectiveinteractionofthes par- ticle withthe SM. The interaction term between s anda comes from the kinetic termof the φ field, therefore it does not have additionalcouplingconstant.

Intermsofthephysicalfields,thestructureofthegaugeinter- actiontermsisthefollowing

Lgauge

=

^a

γ γ ₊

a Z Z

+

^a

γ

Z

+

^aW+W−

+

+

^aW+W−

γ +

^aW+W−Z

,

(4)

wherethepartwith3bosonsisgivenby

LaV V

= −

¹

4 f

^αβγδ

^ (

c1sin²

θ

W

+

c2cos²

θ

W

)

aF_αβF_γδ

+ + (

^c1cos²

θ

W

+

^c2sin²

θ

W

)

a Z_αβZ_γδ

−

−

^{2 sin}

θ

Wcos

θ

W

(

c1

−

^c2

)

aF_αβZ_γδ

+

^2c1aW_α⁺_βW_γ⁻_δ

 .

(5) Inthismodelphoton misidentificationispossibleforthes de- cayshowninFig.1a.Theenergyoftheaxionisatleast M_s/2 so forlow axionmassmathemisidentificationoftwophotos asone happensif

θ >

^12ma

M_s

,

(6)

whereθ isagranularityofthecalorimeter,seeformula (A.3).In thiscase,thischannellookslikeadiphotondecay.

The gauge invariance requires existence of decays s→^{a Z Z ,} s→^{a Z}

γ

, s→^{aW W , that are connected to s}→^aa→⁴

γ

decay.

Fromtheexperimentalpointofview,thesechannelslooklikede- caysinto3bosons:

γ

Z Z ,

γ γ

Z and

γ

W W .Althoughthe3boson channelsshould havesmaller branchingratio than s→^{aa decay,} itispossiblethattheyaremoreexperimentallyfavorable.Wewill discusssuchscenariobelow.

2.1. Decaysoftheheavyscalar

Themaindecaychanneloftheheavyscalarinthemodel (2) is s→^{aa.Thedecaywidthforthischannelis}

Fig. 2. Branchingratiosofthe3bodychannelsfordifferentratiosbetweenc1andc2 couplingconstants:continuouslineiss→^Zγa,dashedlineiss→^{Z Za anddotted} lineiss→W W a channel.Tomakethisplotweusetheconstraintc²₁+c²₂=1.

Fig. 3. Theangulardistributionforthe s particledecayintothreebosons,where ρ=¹

 d

d cosθ ^andθisananglebetweenthevectorbosons( Zγ,Z Z orW W ).



s→aa

=

¹ 32

π

M³_s

f²

.

(7)

From theLagrangian (4) weexpectthe additional3-bosonde- caychannels:decayofs into Z

γ

a, Z Za orW W a (seeFig.1b).The decaywidthsinthelimitM_s^MZ,M_W are



s→^Zγa

= (

^c1

−

^c2

)

²sin²

θ

Wcos²

θ

W

M²_s

16

π

²f²



s→^aa

,

(8)



s→^{Z Za}

= (

^c1cos²

θ

W

+

^c2sin²

θ

W

)

^{2 M}

2s

32

π

²f²



s→^aa

,

(9)



s→W W a

=

^c2₁ ^M2s

16

π

²f²



s→aa

.

(10)

The branching ratiosfor thesechannels depend on the ratiobe- tween thecouplingconstants c1, c2,seeFig.2.Forgenericvalues ofc1, c2allthreechannelshavebranchingratiosofthesameorder ofmagnitude.

All three channels have similar angular distributions for the vector bosons. These distributions are equalto each other in the limit M_s^MZ,M_W.Theangulardistributionforthiscaseispre- sentedinFig.3.Weseethatvectorbosonsprefertoflyinopposite directions.Theaverageanglebetweenthemisθ≈^98◦.

Fig. 4showstheaxion energydistribution 1

 d dEa

forthepro- cess s→^{W W a for 3 different massesof} s particle. At the low axionenergyEa^Msthedistributionscalesas

d



dE_a

∝

E_a³ (11)

andthecut-offenergyisE^max_a = ^M

2 s−^4M2_W

2Ms .

Fig. 4. Theenergydistributionχforthes particledecayintoW W a byaxionenergy Ea,whereχ=¹

 d dEa .

Fig. 5. DecayofZ bosonintoaphotonandtheaxion.Ifaboostedphotonpairis mis-identifiedasasinglephoton,thisdecaywouldlookasZ→γ γexperimentally.

3. Existingconstraintsonthemodel

Thestrongestconstraintsontheparameterscomefromthepre- cisionmeasurementsofZ .InourmodelanewdecaychannelofZ bosonappears(seeFig.5).Thedecaywidthisgivenby



Z→aγ

=

¹

96

π

f²

(

c₁

−

^c2

)

²sin²2

θ

WM³_Z

,

(12) whereweneglectthemassoftheaxion.

Aftertheaxion decay,we have3 photonswithsmallopening angle θZ betweentwo of them, produced fromthe axion. The energyoftheaxionisatleastM_Z/2.Thus,usingformula (A.3) the constraintontheopeningangleis

θ

Z

≤

^12ma MZ

.

(13)

Itisinteresting tomentionthat Z bosondecayintotwo pho- tonsisforbiddenby theLandau–Yangtheorem,mentionedabove.

Nevertheless,theidea that Z boson can produce2 photondecay signaturethroughthelightpseudoscalarparticleisnotnew.There isaSMdecayZ→

π

⁰

γ

withexpectedbranchingratiofrom10⁻¹² to10⁻⁹ [29–38].Thedecayofthistypewassearchedbefore [39], butnotattheLHC.

The measurement of the Z boson decay into 2 photons was performedbytheCDFcollaboration [39] providinganupperbound

BR

(

Z

→ γ γ ) ≤

1

.

5

·

10⁻⁵

.

(14) TheangularresolutionoftheCDFcalorimeterisθCDF≥⁰.1 [40].

Itislowerthanthemaximalopeningangle (13) ifm_a^{750 MeV,} sothemodel (2) wouldproduceadiphotonsignature of Z boson decayinthiscase.The bound (14) constraintsthemodelparame- terstobe

|

^c1

−

^c2

|

f

≤

¹

.

6

·

^{10−4GeV−1}

.

(15) Anotherindependentconstraintcomes fromthefull decaywidth of the Z boson. Value of total decay width of the Z boson is measured as ^exp_Z =².4952(23) GeV [41]. It is equal to the SM

theoreticalprediction^SM_Z =².4960(18)GeV [42,43] withinexper- imentaluncertainties.Weestimate1

σ

deviationfromthe Z decay widthas



_Z

= 



²_Z,exp

+ 

²_Z,SM

=

²

.

9 MeV (16) andrequirethatdecaywidthofnewchannelZ→^a

γ

iswithin2

σ

limit,

|

^c1

−

^c2

|

f

≤

¹

.

8

·

^{10−3GeV−1}

.

(17) Thelastconstraintisweakerthan (15),butitdoesnotdependon thedetectionoftheaxionasonephoton.

4. Results

4.1. Sensitivityofthetribosonvs.diphotonchannels

In thisSection we consider triboson channelsthat arise from s→aV V decays. The experimental signatures in these channels are: Z

γ γ

, Z Z

γ

andW W

γ

,wherethevectorbosonsarenotcol- limated (cf. Fig.3). We analyze thesensitivity to thesechannels, givencurrentconstraintsonthediphotonsearches.

We startwiththe decayscontaining Z boson.The final states of leptonically decaying Z bosons havelower SM background as comparedto thehadronicdecays.Theprobability ofthe Z boson decayintoe⁺e⁻or

μ

⁺

μ

⁻is P_Z→l+l⁻=⁶.7% (wedonottakeinto account Z→

τ

⁺

τ

⁻ becauseit is reconstructed through hadronic

τ

decayswithhighSM background).Thereforeforgeneric values ofc1, c2 thechannel Z

γ γ

ismorefavorable tosearchthan Z Z

γ

. The W boson cannotbe fullyreconstructedintheleptonic decay mode.Thus we concludethat Z

γ γ

channel isthe mostsensitive amongthethreeconsidered.

The main background in the Z

γ γ

channel comes from the non-resonant SM Z

γ

production,which hasquite a low produc- tion cross section in the phase space of interest. Comparing the measured SM backgrounds in papers describing the searches in the Z(l¯_l)

γ

channel [44] andinthediphotonchannel [13],we see that Z

γ

channelhasanorderofmagnitudelowerbackgroundthan diphotonone. Thisbackgroundis evenfurthersuppressed by the requirementofanadditionalenergeticphotonintheevent.There- fore,weexpectthatthischannelisalmostbackground-free.

FromEqs. (7) and(8) andfromtheconstraint (15) wefindthe followinglimitonthebranchingratio

BR

(

s

→

Z

γ

a

) ≤

1

.

5

·

10⁻⁵



Ms

750 GeV



2

.

(18)

Considerthatweexpect1eventinthischannel.Then,takinginto accounttheprobabilityof Z decayintochargedleptons,weexpect

N

≥

¹⁰⁶



750 GeV M_s



₂

(19)

eventsinthediphotonchannel.Thisnumbercannotbecoveredup by anyreasonable SM background,therefore Z

γ γ

channel isless sensitivethanthediphotonone.Theconclusionaboveisalsovalid forW W

γ

and Z Z

γ

channelsifthereisnodegeneracy.

In case of the degeneracy c1≈^c2, the Z

γ γ

channel is sup- pressed and s→W W a=²s→Z Za (see expressions (9) and (10)).

The number of eventsin diphoton channel Nγ γ is connected to thenumberofeventsinW W

γ

channel,

NW Wγ

N_{γ γ}

= 

s→W W a



s→aa

=

^M2sc21

16

π

²f²

.

(20)

Onecan searchfor W W

γ

signature intwo finalstateswhere either only one W boson decays leptonically (W →^e

ν

or W →

μν

), or both W bosons decay to leptons. In the first case, the main SM background comes fromthe W

γ

production withtwo additionaljets,wherethesetwojetsaccidentallyformaW boson mass.Thenumberofbackgroundeventsrapidlydropswiththein- crease of the photon transverse momentum Eγ

T, and is equal to about1eventforEγ

T >300 GeV.Fromthepartonluminosityscal- ingforquark-annihilationprocessesbetweencenter-of-massener- gies of 8 and 13 TeV, the corresponding number of background eventsshouldbeaboutafactorof2largerforthesameintegrated luminosity, andfactor 3 larger forthe integratedluminosity de- liveredby the LHC in2016. Such background ratewouldlead to an upperlimit ona numberofsignaleventsintherangefrom3 (forthe zerobackgroundcase)to6 (foranumberofbackground eventsequalto3)forthemassM_s>1 TeV.Thisconvertsintoand theupperlimitonthesignal crosssectionofabout0.3–0.6 fb.In thisestimate,thebranchingratiocorrectionof0.3istakenintoac- count,andit isassumedthat signalhas100% reconstruction and identificationefficiency.

In the second case, when both W bosons decay leptonically, the main SM backgrounds arise fromtt¯

γ

, Z

γ

, W Z

γ

processes, and processes with a misidentified photon. The SM background becomes negligiblefor Eγ

T >300 GeV,hence wecan conductthe estimatesinazerobackgroundapproximation.Thebranchingratio correctionforthisscenariowouldbe0.06,andthisleadstofactor 5weakerconstraintsonthesignal crosssectionscomparedtothe semileptonicW W

γ

channel.

Letusdiscussthepossibilitytoobserve3-bosonchannelbefore thediphotonone.Thisispossibleifthenumberofthebackground eventsinthediphotonchannelN^bgγ γ ismuchhigherthantheback- groundinthe3-bosononeN^bg_{W W}γ .Theconditioninthecaseofthe Gaussianstatisticsreadsas

NW Wγ N_{γ γ}

>

⎛

⎝

^N

bg W Wγ N^bg_{γ γ}

⎞

⎠

1/2

(21)

Thedataondiphotonbackgroundcanbefoundinthepaper [2]

bytheATLASCollaboration,wheretheboundsonthepeaksearch ofthe diphoton signal are givenat √

s=13 TeV with integrated luminosityofL0=³⁶.7 fb⁻¹.Experimentalanalysisofthe W W

γ

signature has beenperformed by the ATLAS Collaboration atthe center-of-massenergyof √

s=^{8 TeV in the context ofthe mea-} surementoftheSM W W

γ

productionandsearchforanomalous quarticgauge couplings [45].From thispaperwe can extractthe backgroundinthecaseofwhenonlyoneWbosondecayslepton- ically(W→^e

ν

orW→

μν

).Adopting thesebackgroundsforthe samecenter-of-massenergyandthesamebinningwegetestima- tionshownattheFig.6.The backgroundratioisthelargestfora smallmassofthemassoftheheavyscalar.

Theratiointheleft-hand-sideoftheformula (21) dependson parameters of the model. In Appendix B we discuss the simple UV-completionwithNχ heavyfermions.Thenaturalvalueofcon- stantsareM_s∼ ^{f andc}1∼

α

wNχ ,sotheestimateoftheratio (20) isNW W a/_{Nγ γ}∼

α

²_wN²χ/(16

π

²).

4.2. Axionasmissingenergy

Inthediscussionbeforewe havemadeanassumptionthat an axion decays inside thedetector. In thissection we considerthe case, thatan axion could leavethe detector,i.e.thedecaylength l=^c

γ τ

(where

τ

isan axion lifetimeand

γ

is aLorentz factor) is greater than detector length L. The decay length is (see Ap- pendixC)

Fig. 6. Estimationofthenumberofbackgroundeventsforthe√

s=13 andinte- gratedluminosityofL=36.7 fb⁻¹fordiphoton(bluesolidline),W Wγ→W eνγ (greendashedline)andW Wγ→^Wμνγ(reddottedline)channels.(Forinterpre- tationofthecolorsinthefigure(s),thereaderisreferredtothewebversionofthis article.)

l

≈

^{5 m}



100 MeV m_a



4



M_s 1 TeV



f

·

^{10−4GeV−1} c1sin²

θ

W

+

c2cos²

θ

W



2

.

(22) Forthe detectorsize L∼O(^{10 m}) andthecondition todecay outside the detector written as l>100 m we get for the axion mass

m_a

<

47

.

3 MeV



Ms

1 TeV



1/4



 

f

·

10⁻⁴GeV⁻¹ c₁sin²

θ

W

+

^c2cos²

θ

W

 



1/2

.

(23)

Inthiscasetheprobabilityoftheaxiondecayinsidethedetec- toris

Paxion decay

=

¹

−

^e−L/l

≈

^L

l



¹

.

(24)

Instead of comparing diphoton channel with 3-boson chan- nels asin the previous section,we have tocompare thechannel

γ

₊MET [46,47] with Z Z+^{MET, W W} +^{MET and Z}

γ

₊MET channels.Thesearchofthe Z Z+^{MET,W W}+MET signatureswas performedattheLHCfortheSUSYmodels [48,49].Theadvantage ofourmodelcomparedtoSUSYcaseisthat invariantmassofthe decay products should be fixed by the mass of theheavy scalar.

However, thisfactdoesnot givea significantimprovementinthe analysis, because one cannot measure the parallel component of themomentumforthemissingenergy.

Let us consider the channel Z

γ

₊MET, as the dedicated searches were not performed atthe LHC before. Let us check if thenewchannelcanshowasignalbefore

γ

+MET [46,47].Using Eqs. (7),(8) and (24) theratiooftheprobabilitiesofthesignature

Z

γ

₊MET to

γ

+^{MET is} S

=

^PZ→l+l−



s→^Zγa

2Paxion decay



_s→aa

≈

¹

.

9

·

¹⁰⁻⁶



100 MeV m_a



4



M_s 1 TeV



3

×

×



c₁

−

^c2

c1sin²

θ

W

+

c2cos²

θ

W



2

.

(25)

Expression (25) givestheratioofthenumbersofsignalevents.

Taking a conservative assumption that number of background event inboth channels isthe same, we getthe condition to ob- serve Z

γ

+MET signaturebefore

γ

+^{MET as S}>1,whichtrans- latesintothefollowingrequirementontheaxionmass

m_a

<

3

.

7 MeV



M_s

1 TeV



3/4





^c1

−

^c2

c1sin²

θ

W

+

^c2cos²

θ

W

 

^1/2

.

(26) FortheexperimentallyinterestingregionofparametersMs<5 TeV,

f>100 GeV condition (23) holdsifthecondition (26) holds.

Fig. 7. Maximalaxionmass ma forwhich Zγ+MET signaturewillbeobserved beforeγ+MET signatureversustheratioofcouplingconstantsc1,c2.Thescalar massistakenMs=^{1 TeV.}

The region of parameters that satisfies the condition (26) for Ms=^{1 TeV is shown in Fig. 7. We see that for random c}2/c1 ratio the axion mass should be smaller than ∼^{5 MeV to ob-} serve Z

γ

+MET signature before

γ

+^{MET one. In the special} casec₂/c₁≈ −^tan2θW thecondition on m_a isrelaxed andaxion masscan be 100 MeV or bigger.Thus, forsmall axion mass,the Z

γ

₊MET channelisanefficientwaytothesearchfornewphysics attheLHC.

5. Conclusion

Inthispaper,wediscussedthetribosonchannelsasapotential signatureofnewphysics atthe LHCandanalyzethecorrespond- ingsensitivity.Sincesuchsearcheshavenotbeenperformedatthe LHCbynow,wecannotprovideasensitivityprojectionbyreinter- pretingan experimental analysis, butinstead we makeestimates basedonsimilarsignatures.Weshowthatifanewparticledecays tofourphotons,withtwo collimatedphotonsbeingmisidentified asonephotonandhenceleadingtoapickintheobserveddipho- tonevents,thegaugeinvarianceoftheSMdemandstheexistence ofadditionaldecaychannelsthetype Z

γ γ

, Z Z

γ

andW W

γ

.

Toillustratethisideawechoosethesimplemodelwithaheavy scalars and a light pseudoscalara.Wecalculate theparticle de- caywidthsinthismodelandanalyzethekinematicpropertiesof tribosondecays,seeFigs.3,4.

We find that the effective coupling Za

γ

in this model is stronglyconstrainedbythe Z→

γ γ

decaysearches,thereforewe makea specificchoice ofmodelparameters c1=^c2 toavoid this constraint. In this case, one still has significant freedom in the choiceofremainingparameters.

Themainadvantageofthetribosonchannelsisthelowervalue ofexpectedSM backgroundincomparisontothe diphotonchan- nel.Combining thisproperty withthenumber ofdiphoton back- groundeventweconcludethatthischannelcanbehelpfulforthe searchesintheregionoftheinvariantmasseslowerthan500 GeV forthemodelswhereweexpectalargeamountofnewheavypar- ticles.

Anotherinterestingapplicationistosearchforsignatureswith missing energy, namely Z Z +^{MET, W W} +^{MET or Z}

γ

+^MET.

The first two signatures were considered in the context of SUSY searchesat the LHC [48,49]. In our case, unlike the caseconsid- ered in [48,49] we expect a peak in the number of events cor- respondingto theinvariant massequal tothemass oftheheavy scalarM_s.However,thiscannotbe usedtoincrease sensitivityas onlythetransversecomponentofthemissingenergycanbemea- sured.Alternatively,usingthetransversemassofthevisiblesystem could provide means to discriminate the considered modelfrom SMbackgrounds.

Ontheother hand,thededicated searchinthe channel Z

γ

+ MET was not performedatthe LHC. Indeed,in [50,51] the anal- ysis in the channel jets+

γ

+^{MET was reported. However, the} specificationofjetsto Z or consideringleptonic Z decaysshould significantlyincreasesensitivity.Asweshowinsection4.2,thesig- nalinthischannelis notconstrainedby

γ

+MET search [46,47], therefore the signal in this channel can be observed. An advan- tageofthischannel ascomparedto Z Z+^{MET orW W} +^{MET is} the highefficiencyofreconstruction ofhighenergyphotons. The SM background is also expected to be lower. We conclude that dedicated searchesin the Z

γ

₊MET channelhave apotential to discovernewphysicsattheLHC.

Acknowledgements

This research was partially supported by the Netherlands Sci- enceFoundation (NWO/OCW)andthe EuropeanResearchCouncil (grantnumber694896).

Appendix A. Misidentificationoftwophotonsasonephoton

ConsideranultrarelativisticparticlewithenergyE andmassm that decays into 2 photons. Such particle should have spin 0 or 2 (the caseofspin 1 isforbidden because ofLandau–Yang theo- rem [52,53]).

The distribution of photonsin the restframe of the decaying particleisisotropic,whileinthelaboratoryframewiththeLorentz factor

γ

₌E/m,thedistributionofthephotonpairNγ is

dN_γ

d

θ =

¹ 2



γ

²

−

1

cos

(θ/

2

)

sin²

(θ/

2

)



1

γ

²sin²

(θ/

2

) −

¹

,

(A.1)

where θ is the angle between two photons. The minimal angle betweentwophotonsistherefore

θ

min

=

^{2 arcsin}

( γ

⁻¹

) ≈

²

γ

^for

γ 

¹

.

(A.2)

Thedistribution (A.1) issharplypeakingand95% ofalleventshave theanglebetweenthephotonsθmin< θ <3θmin.Thus,theopening anglemostlikelyisintheregion

θ 

^6m

E

.

(A.3)

The mis-identification probability depends on the granularity of thecalorimeterused.

Appendix B. SimpleUVcompletion

Consider the model with N_f heavy vector-like fermion dou- blets

χ

I that are chargedwith respectto the UY(1) and SUL(2) groupsoftheSM,andthecomplexfieldφthatinteractswiththem throughtheYukawainteraction,

Lχ

= ∂

μ

φ∂

^μ

φ

^∗

−

^V

(φ) +

ⁱ

χ ¯

ID

/ χ

I

−

^mχ

χ ¯

I

χ

I

− 

yI J

φ χ ¯

I

χ

J

+

^h

.

c

. 

,

(B.1) where V(φ) is a scalar potential. Aftera spontaneous symmetry breakingandproducesheavy scalars and lightpseudo-Goldstone boson a. These states interact with the SM trough the effective coupling (2) made by the fermionic loop. The expected coupling strength depends on the details of the theory but should be of orderc1,2≈

α

wN_f forYukawa valuesoforderone.Ifthenumber of heavy fermions is smaller than O(³⁰), there is no danger of strongcoupling.

In thissimple theory the mass of the scalar s∼√

λf , where λ is a self-interaction coupling constant of the scalar and f is a scalar’svacuumexpectationvalue. To maximize thenumberof three-bosoneventsascomparedtothediphotononesweconsider λ∼O(¹)(seeEq. (20)).Ontheotherhand,themassoftheheavy fermions are given by their Yukawa couplings, mf ∼^{y f , where} y^{1.Therefore,themassscaleofthescalars andheavyfermions} shouldbeclosetoeachother.Letusdiscussthepossibilitytode- tectthesenewfermions.

Asheavyfermionloopshouldmediatea

γ γ

interactionatleast some of heavy fermions should be electrically charged. Heavy chargedfermionscanbeconstrainedbymonojetssearches [54,55]

(includingcharginosearches [48,56,57])orbystablechargedpar- ticlessearch [58].Thesesearchesputlimitsontheheavy fermion massesbetween0.5 and1 TeV,dependingontheproductionand decaychannels. However, thepresence ofan additionalscalar, as inthemodel (B.1) significantly lowersthe LHCboundsaswell as LEPconstraints(asdiscussede.g. in [59]).Indeed,theextrascalar (thatcouplestofermions

χ

andtotheelectrons)createsdestruc- tiveinterferenceandsuppressestheproduction.Asaresult,based ontheLEPandLHCdatathereisstill apossibilityofexistenceof heavychargedfermionsinthemassrange75÷100 GeV [59].This scenario wouldalsorelax thelimits onheavy fermions fromthe LHC.Thereforewe concludethat currentlythere isstilla number ofpossibilities tointroduce the required heavy chargedfermions withmassesbelow1 TeV.

Appendix C. Decaywidthsofaxionandheavyscalarparticle Fortheaxiona wehavethefollowingdecaywidth



_{a→γ γ}

=

^m3a 16

π

f²



c₁sin²

θ

_W

+

^c2cos²

θ

_W



2

.

(C.1)

Ingeneralcasewithoutdegeneracies, c₁sin²

θ

_W

+

^c2cos²

θ

_W

f

∼ |

^c1

−

^c2

|

f

<

1

.

6

·

^{10−4GeV−1}

.

(C.2) Theestimationforthedecaywidthforsuchvalueis



_{a→γ γ}

=

²

·

^10−13GeV



_m

a

100 MeV



3



c₁sin²

θ

W

+

^c2cos²

θ

W

f

·

^{10−4GeV−1}



2

(C.3) The decay length is given by l=^c

γ τ

, where

τ

_{= ¯}h/ is a lifetime,

γ

is a Lorentz factor. Taking the Lorentz factor as

γ

= M_s/(2m_a)onegets

l

=

^{5 m}



100 MeV m_a



4



M_s 1 TeV



f

·

^{10−4GeV−1} c1sin²

θ

W

+

^c2cos²

θ

W



2

.

(C.4)

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