a 750 gev graviton from holographic composite dark sectors

For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.. For interpretation of the refer-ences to color in this figu

Contents lists available atScienceDirect

www.elsevier.com/locate/physletb

Adrián Carmona

CERN, Theoretical Physics Department, 1211 Geneva 23, Switzerland

Article history:

Received 1 April 2016

Received in revised form 7 July 2016

Accepted 15 July 2016

Available online 19 July 2016

Editor: B Grinstein

We show that the 750 GeV di-photon excess can be interpreted as a spin-2 resonance arising from a strongly interacting dark sector featuring some departure from conformality This spin-2 resonance has negligible couplings to the SM particles, with the exception of the SM gauge bosons which mediate between the two sectors We have explicitly studied the collider constraints as well as some theoretical bounds in a holographic five dimensional model with a warp factor that deviates from AdS5 In particular,

we have shown that it is not possible to decouple the vector resonances arising from the strong sector while explaining the di-photon anomaly and keeping the five dimensional gravity theory under perturbative control However, vector resonances with masses around the TeV scale can be present while all experimental constraints are met

©2016 The Author Published by Elsevier B.V This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/) Funded by SCOAP3

1 Introduction

Thediscovery of theHiggsboson bythe ATLAS andCMS

Col-laborations at the Large Hadron Collider (LHC) marked the

be-ginningof a newera in highenergyphysics Indeed, thefinding

of the long-sought particle offers us the unique opportunity to

starttestingtheoriginofelectroweaksymmetrybreaking(EWSB)

This means that we could be closer than ever to understand

some extremely important unsolved puzzles in particle physics,

like the large hierarchybetween theelectroweak andthe Planck

scales,theoriginoffermionmassesorevenwhatliesbehindDark

Matter (DM) The situation has become even more thrilling

af-terthe announcement by both ATLAS andCMS Collaborations of

a tantalizinghintofa newresonancein di-photonproduction at

masses around ∼750 GeV [1–3] Since the exciting news

awak-ened the feverish imagination oftheorists, we have witnessed a

plethoraofpapersexploringpossibleexplanationsofthereported

anomaly.However, forseveral reasons, the spin-2 possibility has

been largely unexplored (see e.g [4–9]) One of the reasons for

this oblivion is that traditional vanilla explanations in terms of

Kaluza–Klein (KK) gravitons face several problems for such light

masses, since they favor either universal couplings to the

Stan-dard Model(SM)contentorverysmall γ γ branchingratios,which

are not viable phenomenologically In addition, unless large

lo-calizedcurvature terms make thespin-2 resonance much lighter

than the restof the KK spectrum, the constraints resulting from

E-mail address:adrian.carmona@cern.ch.

electroweakprecisiontests(EWPT)clearlyexcludesuch scenarios Moreover, it is known that the presence ofsuch terms can eas-ily turn the radion into a ghost[10,11], questioning the viability

of thesesetups Inthisletter wewill explore an interesting pos-sibility wherethe reported750 GeV resonancemay arisefrom a holographic stronglyinteractingdarksector.Wewillshow thatin modelswherethestrongsectorfeaturessomedeformationof con-formality,parametrizedinthefivedimensional(5D)frameworkby

a modified background,a lightgraviton can naturally explain the observedanomaly whilestillfulfillingallother experimental con-straintsarising fromcollidersearchesorEWPT.Moreover, wewill demonstrate that all this can be done without introducing a too large gapbetweenthemassesofthe KK graviton andthe restof the KK spectrum, which will allow to have perturbativity under controlinthe5Dgravitytheoryandavoidtheemergenceofa ra-dion ghost.Inaddition, we willshow that inthesemodels there

isabeautifulinterplaybetweenthedarksector(possibly explain-ing part of the observed relic abundance) and the collider phe-nomenologyoftheKKvectors.Therefore,measuringtheproperties

ofthehypotheticalparticle,incaseitsexistenceisconfirmed,will definitivelyhelptoanswerifitisrelatedtotheoriginofEWSBor ratherwithotherfundamentalpuzzlesinparticlephysics,likethe originofDM

The article isorganized as follows:in Section 2 we introduce theoriginaltheoreticalmotivationandtheconcrete5Dframework whereallcomputationswillbeperformed Thiswillalsoserveus

to introduce notation andthe input parameters of the theory.In Section 3we willexamineindetailthephenomenological conse-quences of the proposed setups, studying in detail the interplay http://dx.doi.org/10.1016/j.physletb.2016.07.040

0370-2693/©2016 The Author Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Funded by SCOAP 3

betweenEWPT, thedifferentcollidersearchesandrole played by

theDMcandidates.Finally,weconcludeinSection4

2 Theoretical motivation and setup

Tryingtoaddressthehierarchyproblemhasprovidedusa

bet-ter understanding of the SM as well as stimulating theoretical

constructionslikesupersymmetry, composite Higgsmodels,

tech-nicolor or models with warped extra dimensions However, the

multiplication ofnegative resultsfor such theories haspropelled

alternative ways of thinking about new physics, disconnecting it

e.g.fromtheelectroweakscale.Oneparticularexampleisthecase

ofDM,where some of thesetheoretical constructions havebeen

used with the goal of explaining its origin with no deep

con-nectionwiththe electroweakscale,see e.g.[12–17].1 Inthe case

ofmodels with warped extra dimensionsor theirs strongly

cou-pled duals, this more modestand pragmatic approach hassome

advantages, for typical problems associated with these scenarios

are turned into advantages once the hierarchy problem is left

unsolved For instance, in Ref [16] the most minimal examples

wherethe full SM (including the Higgs boson) is extended with

astrongly-interactingcompositesectordeliveringpseudoNambu–

Goldstonebosons(pNGBs)asnaturalDMcandidateswerestudied

Inthisletterwe aregoing toexplorethepossibilitythat thefirst

spin-2resonancearisingintheirholographicconstructionscan

ex-plainthe750 GeV di-photonanomaly.2 Therehave beensome

re-centstudiesonthepossibilityofinterpretingtheputative750 GeV

resonanceasa KKgraviton arisingfromextradimensionalsetups

[4–9] but only Refs [4] and [7] considered the case where the

wholeSM matter content isUV localizedandonly gauge bosons

are allowed to propagate into the bulk However, none of them

consideredtheeffectofthevectorresonances,whichwereignored

orliftedto∼3–4 TeV withoutconsideringtheimplicationsonthe

consistencyofthe5Dtheoryortheradiondynamics.Moreover,we

will studythe more general case where deformations of

confor-malityinthe strongsector areallowed, whichisparametrizedin

the5Dtheorybyamoregeneralwarpfactor.Thiswillincreasethe

generality ofthe approach andwill improvethe agreement with

EWPTandcolliderconstraints

Weconsiderasliceofextradimensionwiththefollowing

met-ric

ds2=e−2 A ( y )ημν dx μ dx ν−dy2, (1)

wherethewarpfactorisgivenby[20–25]

A(y) =ky− 1

ν2log



1− y

ys



and the extra dimension is parametrized by the coordinate y∈

[0,y1],bounded by twofixed points or branes, corresponding to

y=0 (UVbrane)and y=y1 (IRbrane).Ontheotherhand, y s>

y1 represents the position of the singularity responsible for the

deformation ofconformality, withthe AdS5 casebeingrecovered

inthelimitsy s→ ∞or ν → ∞.WeshowinFig 1thewarpfactor

fordifferentvaluesof νforky1=35 andky s=35.1,aswellasfor

theAdS5case.Wetradey sbythecurvatureradiusattheIRbrane,

given(inunitsofk)by

1 All these models explore the possibility of having a strongly coupled sector not

involved in EWSB While in [12–14] and [16] the strong sector only talks to the

SM via gauge interactions, in [15,17] Yukawa interactions are sometimes allowed.

Moreover, Ref [16] focus on the effective holographic description of such scenarios.

2 For other examples of spin-2 resonances arising from strongly interacting dark

sectors, see e.g [18,19].

Fig 1 Warpfactor as defined in Eq (2) forky1=35,ky s=35.1 and different values

ofν We also show the AdS 5 case for comparison, which corresponds to the limits

ν→ ∞orky s→ ∞.

kL1= ν2k(y s−y1)



1−2ν2/ +2ν2k(ys−y1) + ν4k2(ys−y1)2, (3) where 0.1kL11 The value of y1 can be fixed by choosing differentvaluesoftheUV/IRhierarchy A(y1).The AdS5 limit cor-respondstoA(y1) ∼36 andkL1→1

In the transverse-traceless gauge, the spin-2 gravitational ex-citations are parametrized bythe tensor fluctuationsofthe met-ric ημν→ ημν + κ5hμν(x,y), where ∂μhμν=hα α =0 and κ5=

2M−3 2

5 ,withM5 the5D Planckmass.Thegraviton KKexpansion reads

h μν(x,y) = 

n

h ( μν n )(x)f h ( n )(y), (4) where f h ( n )satisfy

(e−4 A ( y ) f ( n )

h (y))+e−2 A ( y ) m ( h n )2f h ( n )(y) =0, (5) and

0= f ( n )

h (0) + κ0k−1m ( h n )2f h ( n )(0) (6)

=e−2 A ( y1) f ( n )

h (y1) − κ1k−1m ( h n )2f h ( n )(y1),

inpresenceofpossiblelocalizedcurvatureterms [10].These pro-filesarenormalized

y1

 0

dy e−2 A ( y ) f h ( n )2[1+ δ(y) κ0

k + δ(y−y1) κ1

k] =1, (7)

insuchawaythat

¯

M2Pl=M35

y1

 0

dye−2 A ( y )[1+ δ(y) κ0

k + δ(y−y1) κ1

where M¯Pl =2.4×1018 GeV is the four-dimensional reduced Planckmass

In the spirit of the models considered in Ref [16], we as-sume that only the SM gauge bosons propagate into the bulk of the extra dimension, with the full SM matter content being lo-calized at the UV brane.3 In addition, we also assume that the

3 Considering some relatively high new physics scale at the UV brane alleviating the hierarchy problem, would not change the picture, provided the light degrees of freedom remain those of the SM (assuming therefore some moderate fine-tuning).

bulk of the extra dimension respects a larger gauge group, like

e.g SU(3) ×SU(3) ×U(1)X or SU(3) ×SU(2)1×SU(2)2×U(1)X,

whichdelivers some dark pNGBs A aˆ(x).We expect therefore

ad-ditionalspin-1KKresonancesinadditiontotheusualelectroweak

vectorones.However,sincetheydonotcoupletotheSM,theywill

play norole in the currentphenomenologicalanalysis The

addi-tionalscalars,ontheotherhand,willhavesizablecouplingstothe

electroweak vector resonances, forthey are all localized towards

theIRbrane,makingthelattertodecayalmostexclusivelytothese

scalars,aswasexplicitlyshowninRef.[16].Atanyrate,theonly

relevantinputfromsuch constructionsinthecurrentstudyisthe

introductionof alarge invisible widthforthe electroweakvector

resonances,that makes the boundsfromcoloroctet searchesthe

leadingones

The KK expansion of the SM gauge bosons reads Aμ(x,y) =



n fA( n )(y) A( n )

μ(x,y) where Aμ=Aμ,Zμ,W±

μ,G a μ. Their profiles satisfythefollowingbulkequationsofmotion

(e−2 A ( y ) f ( n )

andboundaryconditions

f ( n )

A (y1) =0= f ( n )

A (0) = f ( n )

= [∂y−v2

4 (g

2

5+g2

5) ]f Z ( n )



y=0

= [∂y−v2

4 g

2

5]f W ( n )



y=0

.

Inordertobeslightlymoregeneral,wealsoallowforlocalizedUV

gauge kinetic terms (KT), κ2

S y1 and κ2

E W y1, that change the UV boundary conditions above by ∂y→ ∂y+m2

A 2S , E W y1 These KT also change the normalizationconditions for the different gauge

profiles

y1



0

dy fA( n )2(y) +fA( n )2(0) κS2, E W y1=1. (11)

However,inpractice,thesetermsjustbasicallychangethe

match-ingofthe5Dgaugecouplings

g5=g

y1(1+ κ2

E W), g5s=gs

y1(1+ κ2

whereastheratio

g

remains unchanged, forwe havechosen identicalKT for SU(2)L

and U(1)Y Besides the gauge and gravitational kinetic terms

κ2

S , E W and κ0,1,we have five additionalinput parameters inthe

theory M5,A(y1), ν ,k and kL1 We can fix M5 using M¯Pl and

equation(8),whereasm ( h1)=750 GeV allowustoremove e.g. κ1

Forsimplicity,wewillchose κ0=0= κEWleavingusintotalwith

onlyfourparameter{ ν ,kL1,mKK, κ ˜ ,A(y1) },wherewehavetraded

k forthefirstvectorKKmassmKK,anddefinedκ ˜ = 1+ κ2

S TheKK-gravitoninteractionsaregivenby

L ⊃ − κ5

2

∞



n=1

√

gUV UVμν(x)f h ( n )(0)h ( ργ n )(x) ημρηνγ (14)

− κ5

2

∞



n=1

y1



dy√

ge 2 A ( y ) μν( x,y)f h ( n )(y)h ( ργ n )(x) ημρηνγ

g=e−4 A ( y ) and √

gUV=1 are the square root of the determinantofthe 5Dandthe UV-localizedmetrics, respectively, whereas

μν= − √2gδ(

√gL matter)

δg μν = −2δ Lmatter

δg μν

and UV

μν= −2δ LUV

matter

are thebulk andUV-localized stress-energy tensors We can ne-glect the last piece in the stress-energy tensors above, for the gravitonisinourgauge traceless,consideringonly

T μν= −2δ Lmatter

δg μν , T μνUV= −2δ LUV

matter

Weobtaintherefore

T A

μν=e 2 A ( y ) F A

μ β F A

forSU(3)c×SU(2)L×U(1)Y gaugebosons,whereAμ=G a

μ,W I

μ,

Bμ.RegardingtheUV-localizedSMsector,weobtain

T μν G UV= ( ˜ κ2−1)y1F μ G β F νγ G ηβ γ, (19)

forfermions andtheHiggsdoublet H ,where Dμ is theusual

SM covariant derivative and we have defined D[μγν]=Dμγν −

Dνγμ. Sincethe KKgraviton isexponentiallypeakedtowards the

IR brane, the interactions resulting from the above UV-localized terms are negligible compared to the onescoming from(18), so

wewillsafelyneglectthemhenceforth

3 Phenomenological study

One of the first logical concerns of having a 750 GeV KK-graviton (which is not anomalously light comparedwiththe rest

oftheKKspectrum),isthepossibleconflictwithEWPT.However, sincethefullSMmattercontentislocalizedontheUVbraneand the extradimension playsno roleon EWSB,the oblique

parame-ters S and T are zero at treelevel, which alleviatesenormously thepressurefromEWPT.Therefore,theonlyrelevantconstraintin thisregardarethevolumesuppressedW and Y operators[26],

W =g2M2W



W3W3(0), Y= g2M2W



B B(0), (22) whicharegivenby[22]

Y=W =c2W m2Z

y1

y1

 0

e 2 A ( y )(y1−y)2. (23)

Wehaveperformedanup-to-datefittoW=Y ,4andtheallowed valuesat95% C.L.are showninFig 2fordifferentvaluesofmKK

inthe ν–kL1 plane,assuming thebenchmarkvalue A(y1) =37.5, since it will provide the sought cross section for the di-photon anomaly One could wonder of such choice since the hierarchy

4 We thank Jorge de Blas for providing us theχ2 for the EW fit, which includes all the observables considered in the analysis of [27,28], updated with the current experimental values.

Fig 2 Constraintsfrom EWPT at 95% C.L in theν –kL1 plane for different values

ofmKK assumingA ( y1)=37.5 For each value ofmKK , values ofνandkL1 within

the corresponding green region are allowed (For interpretation of the references to

color in this figure legend, the reader is referred to the web version of this article.)

problem is not longer addressed by the extra dimension

How-ever,we still want to havea 5D theory ofgravity with a ∼TeV

KK graviton and, as we will see TeV vector resonances, so it is

not surprising that we end up considering similar values to the

originalRSmodel.Wecanreadilyseefromtheplotthatlarge

de-formationsofconformalityare stronglypreferredbythedata,for

onlysmallvalues ofkL1 areallowed forlow values ofmKK.Still,

oncemKK approaches1 TeV thebulkoftheparameterspaceleads

toagreementwithEWPT.Itisthentemptingtoarbitrarilyincrease

themassesofthevectorresonancesinordertoavoidtheir

exper-imentalconstraints.However, sincethe KK gravitonmass isfixed

at750 GeV, thisisonlypossibleatthepriceofreducing the

per-turbativityinthe5D gravity theory.Indeed,ascan be seenfrom

Fig 3, where we show the regions of the parameter space with

M5L10.4 (sinceforarbitrarysmallvaluesofthisdimensionless

parameterperturbativecontrolinthe5Dgravitytheoryislost)for

differentvaluesofmKK,massesaround2 TeV arealreadyexcluded

for A(y1) =37.5.5 Theseboundscan be relaxed by reducing the

volume factor A(y1),but thiscan not be done indefinitely since

thisalsoreducestheKKgravitoncrosssection,aswewillsee

be-low

Moreover, the size of the required graviton KT to produce a

spectrum wheremKKm h (1) remains another source ofconcern

IntheabsenceofsuchtermsaKKgraviton of750 GeV would

re-quireKKgaugeresonanceswithmasses∼500 GeV,sincetheratio

m h (1)/m g (1) is fixedto ≈1.6 (bothin theRS caseandforsizable

deformationsof conformality) Indeed, as it was alreadypointed

outin[10,11],thepresenceofsuchtermsproduceanegative

con-tribution tothe radion KT,that can at some point turnit into a

ghost.If we perform a similar analysisto theone carried out in

[10]forthemodelathand,weobtainthatthiswillhappenwhen

Z r=1−3κ1/ke−2 A ( y1) F2(y1)X−1

whereF(y)istheradionprofile6 (formoredetailsseee.g.[21,22,

29])andwehavedefined

5 Note that allowing forκ0>0 would increase this tension, since it would

re-sult in smaller values ofM5 with no effect onL1 (see Eq 8 Negative values of

κ0 (which would need to be bigger than some lower bound to avoid a negative

ki-netic term for the massless graviton – in the RS case,κ0>−1), could in principle

increaseM5 However, this effect could only be significant at the price of a

consid-erable fine-tuning arising from the cancellation of the bulk contribution (1+κ0∼0

in RS).

6 We assume∂y( e−2 A ( y ) F ( y ))=0 boundary conditions on both branes.

Fig 3 Excludedregions for losing 5D perturbativity control in theν –kL1 plane for different values ofmKK , assumingA ( y1)=37.5 andM5L10.4 For each value of

mKK , values ofν andkL1 within the corresponding red region are excluded The

RS limitkL1→1 is also excluded formKK=2 TeV (For interpretation of the refer-ences to color in this figure legend, the reader is referred to the web version of this article.)

X F≡

y1

 0

dye−2 A ( y ) F2(y)

× 6+ 362

2β2W2



F

F −2 A2

with

β(φ)W(φ) = −6 √6e ν φ/

√

φ (y) = − √6 νlog[ ν2k(ys−y) ]. (27)

IntheRScase,weget

Z r=1−1

2κ1e 2ky1

⎡

⎣k

y1

 0

dy e 2ky

⎤

⎦

−1

which leads to κ1≤1, after imposing the absence of a radion ghost.Ingeneral,thisboundon κ1 canbetranslatedintoanupper boundon mKK foranyvalueofkL1, ν and A(y1),byusing equa-tion (24).In Fig 4,we show acontour plotforthisvalue, Mmax,

in the ν–kL1 plane for A(y1) =37.5 In the RS case, we obtain

Mmax≈1 TeV.Finding ifsuch boundcan be somehowalleviated

oritisanunavoidableconstraintisaninterestingtheoretical puz-zleper se. However, ifthe appearance ofa 750 GeV resonance is eventually confirmed,itwillbecome amuchmorerelevant ques-tion Since we are not awareof anysolution tothis issueat the moment, we consider the limits from Fig 4 mKK1 TeV to be definitive Therefore, we will consider mKK=0.9 TeV, 0.95 TeV and1 TeV, eventhough the whole parameterspace ofthe latter willbemarginallyexcluded

In the setup at hand,the KK-graviton couples mostly to glu-onsandelectroweakgauge bosons,leadingthereforetodi-photon production via gluon fusion, gg→h (1)→ γ γ, which is favored compared to other production mechanisms when one takes into accountthe8TeVdata[30].Accordingtothecurrentexperimental data,atotalcrosssectionof σ (gg→h (1)→ γ γ ) ∼5 fb isrequired

in order to accommodate the observed anomaly On the other hand, the strongestconstraint dueto thepresence ofthe vector

KK spectrum inthesesetups isdi-jet production[31–33] via the

s-channelexchange ofthe KK gluon pp→g (1)→j j. Weassume

Fig 4 Maximumvalue ofmKK ,Mmax , as a function ofνandkL1 forA ( y1)=37.5.

This value has been obtained requiring the absence of a radion ghost.

Fig 5 Contourvalues ofσ ( gg→h (1)→γ γ )in theν –kL1 plane together with the

exclusion bounds arising from di-jet searches (orange) and from having a radion

ghost (gray) We also show in red contour lines forM5L1∈ {0.3,0.4,0.5} We have

assumedmKK=0.9 TeV,A ( y1) =37.5 and setκ=2.2.t¯t searchesare not

competi-tive enough to constraint this region of the parameter space For completeness, we

also display (in gray) several contour lines for the ratioM5/ ¯ MPl (For interpretation

of the references to color in this figure legend, the reader is referred to the web

version of this article.)

aQCDK-factor κqqg (1)=1.3[34].Thepresenceofelectroweak

vec-torresonancesdonotleadtosignificant colliderconstraintssince

they decayalmost 100% ofthe time tothe darkscalars, forthey

have volume enhanced couplings since they all come from the

stronglyinteractingsector[16].Thiscouldbealsothecaseforthe

KK graviton but, since we are forcedto consider mKK>m ( h1),we

will assume that thepair productionof darkscalars is not

kine-maticallyopenforthespin-2resonance,i.e.m ( h1)/2<mπ<mKK/2

SincethemassesofthepNGBarelinkedtotheKKscalemKK,this

willbealways trueformoderatelylargevaluesofthelatter

Oth-erwise,additionalsources ofbreaking oftheGoldstonesymmetry

would be required We have also considered the bounds arising

fromt t production¯ [35].NotethatduetotheIRlocalizationofthe

KKgraviton, itsdi-leptoncrosssectionwillbemuchsmallerthan

σ (gg→h (1)→ γ γ ) ∼5 fb andthereforewellbeyondcurrent

ex-perimentalsensitivity.In Fig 5, we displaycontour valuesinthe

ν–kL1 plane forthedi-photon crosssection σ (gg→h (1)→ γ γ )

togetherwiththeexcludedregionsarisingfromdi-jetsearches

(or-ange)andthepresenceofaradionghost(gray),formKK=0.9 TeV,

A(y1) =37.5 andκ ˜ =2.2.We alsoshow inredcontourlines for

M L ∈ {0.3,0.4,0.5},tobetterassessthepreferredvalueofM L

giving the desired di-photon cross section Finally, we also dis-play forcompleteness some contour lines (in gray) for the ratio

M5/ ¯MPl.Wehaveexplicitlycheckedthatt¯t searchesarenot com-petitive enough to constraintthisregion of the parameterspace All theseprocesses havebeen computed at the parton level

Feyn-rules v2[37]

In Fig 5,we havechosen the minimal value of κ ˜ that maxi-mizes theallowedregion inthe ν–kL1 plane.Since thecouplings

ggh (1) andqqg¯ (1)scale with1/ κ ˜2 and1/ κ ˜,respectively,the cor-respondingproductioncrosssectionswillbe σ (pp→g (1)) ∝1/ κ ˜2 and σ (gg→h (1)) ∝1/ κ ˜4 On the other hand, the couplings of the KK-graviton to the electroweak gauge bosons donot depend

on κ ˜, making BR(h (1)→ γ γ ) ∝12κ ˜4/(8+4κ ˜4) with good ap-proximation,whereasBR(g (1)→j j)willremain≈5/6.Therefore, increasingthevalueofκ ˜ reducesthedi-photoncrosssection1/ κ ˜2 fasterthanthedi-jetone,moduloafactor3thatcanbegainedvia the enhanced BR(h (1)→ γ γ ) forlarge κ ˜ Tostudy thiseffect in more detailwe show in Fig 6 theaforementioned crosssections

as a function ofκ ˜ forthe AdS5 caseand ν =0.2, kL1=0.1, as-sumingmKK=0.9 TeV and A(y1) =37.5.Forthisparticularpoint

ofthe ν–kL1 planeandκ ˜ =1,theratioinquestionis∼1.5 times bigger thantheone obtainedintheAdS5 case.Thisisduetothe fact that deformations of conformality have a bigger impact on the qqg¯ (1) coupling than in the ggh (1) one, reducing the former slightly more than the latter Since greater values of κ ˜ will de-creasethe di-photoncrosssection fasterthan thedi-jet one,this effectwillbeveryvaluableinordertofulfill currentexperimental boundsandatthe sametime reproducethe di-photonexcess,as canbeseenfromFig 6.7Atanyrate,fromthisfigureonecan read-ilyconcludethattheAdS5 caseisalsoallowedformKK=0.9 TeV andA(y1) =37.5.Inordertoassessfurthertheimpactofκ ˜ onthe parameter space, weshow inFig 7 theequivalent ofFig 5 fora largervalueofκ ˜ =2.5.Wecanseethatregionswithasmaller de-formationofconformalityarenowpreferred,eventhoughsmaller valuesforthedi-photoncrosssectionareobtained

IncreasingmKKto0.95 TeV leadstoaslightlysmallerdi-photon crosssection,whichmoderatelyreducestheallowedregioninthe

ν–kL1 plane, as can be seen from Fig 8, where we show again thecontourvaluesof σ (gg→h (1)→ γ γ )togetherwiththedi-jet and Z r<0 excluded regions, for mKK=0.95 TeV, A(y1) =37.5 and κ ˜ =2.5 Again, we display in red contour lines for M5L1∈ {0.3,0.4,0.5}.Notethat thereisalarger exclusionregioncoming fromthepresenceofaradionghost,whichneverthelessdoesnot overlapsignificantlywiththearealeadingtothecorrectdi-photon cross section.Further increasing mKK to 1 TeV leadsto a notable decreaseoftheallowedparameterspaceforA(y1) =37.5 andκ ˜ =

2.5,asitisshowninFig 9.Notehoweverthat thisvalueofmKK

isanyhowexcludedbythepresenceofaradionghost

4 Discussion and conclusions

Wehaveshownthatthe750 GeV resonance,ifexperimentally confirmed, canbetheKK graviton ofan approximatelyconformal darksector,whichaccountsforthebulkoftheobservedDMrelic abundance.Inthesesetups,theKKgravitoncouplesuniversallyto all SM gauge bosons (modulo possible gauge kinetic terms) and have negligible couplingsto the rest ofthe SM We have explic-itly shown that the massesof the vector resonances can not be

7 One should note however that, for constant values ofM5L1 , larger values of

A ( y1)will be allowed for points with a smaller deformation of conformality There-fore, for fixed values ofM5L1 andmKK , the effect just mentioned will be compen-sated to some extent by the increase inA ( y1), which tends to enhance theggh (1)

coupling with a much smaller effect onqqg (1).

Fig 6 Di-jetcross sectionσ ( pp→g (1)→j j )and the KK-graviton di-photon cross sectionσ ( gg→h (1)→γ γ )as a function ofκ∈ [1,3]forν=0.2,kL1=0.1 and the AdS 5 case In both cases we have assumedA ( y1)=37.5 andmKK=0.9 TeV The horizontal gray line correspond to the upper bound on di-jet production, whereas the vertical gray band corresponds to a di-photon cross section of 3,10]fb.

Fig 7 Contourvalues ofσ ( gg→h (1)→γ γ )in theν –kL1 plane together with the

exclusion bounds arising from di-jet searches (orange) and from having a radion

ghost (gray) We also show in red contour lines forM5L1∈ {0.3,0.4,0.5} We have

assumedmKK=0.9 TeV, A ( y1) =37.5 and setκ=2.5 (For interpretation of the

references to color in this figure legend, the reader is referred to the web version of

this article.)

Fig 8 Contourvalues ofσ ( gg→h (1)→γ γ )in theν –kL1 plane together with the

exclusion bounds arising from di-jet searches (orange) and from having a radion

ghost (gray) We also show in red contour lines forM5L1∈ {0.3,0.4,0.5} We have

assumedmKK=0.95 TeV,A ( y1)=37.5 and setκ=2.5 (For interpretation of the

references to color in this figure legend, the reader is referred to the web version of

this article.)

Fig 9 Contourvalues ofσ ( gg→h (1)→γ γ )in theν –kL1 plane together with the exclusion bounds arising from di-jet searches (orange) We also show in red contour lines forM5L1∈ {0.3,0.4,0.5} We have assumedmKK=1.0 TeV,A ( y1) =37.5 and setκ=2.5 Note that the whole region is in principle excluded by the presence of

a radion ghost (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

taken arbitrarily large if one wants to have perturbativity in the 5Dgravitationaltheoryandatthesametimeexplainthedi-photon anomaly.Moreover,ifavoidingthepresence ofa radionghostfor largeKKmassesprovestobeunachievableoritcomesattheprice

of a large phenomenological impact, the resultant upper bound

mKK1 TeV wouldbeastrongcaseforthesescenariossince, con-trarytoothersetupsexploredrecentlyintheliterature[4–9],they can featurelight enough vector resonanceswithout any theoreti-cal orexperimentalproblem Indeed,arobust predictioninthese scenariosisthepresenceofaO(1)TeV coloroctetresonancewith universalcouplingtofermions,whichareprobedessentiallyby di-jets searches Since the strongly interacting dark sector plays no role inEWSB,light electroweakvector resonancescanbe present without contradicting EWPT andcollidersearches, provided they decay dominantly to the dark scalars, which is a natural expec-tation in these models Our setup also provides a very concrete predictionforthedarkscalarmasses,sincetheKK-gravitonshould not be allowed to pairproduce them,m ( h1)/2=375 GeVmπ

500 GeV.Insummary,wehavepresentedthefirst phenomenolog-icalstudyofsetupsproviding a750 GeV spin-2 excitation where theeffectofthevectorresonancesisnotdecoupled,motivatingit

bytheconsistencyofthefivedimensionaltheoryandexploringin

con-straints

Acknowledgements

IwouldliketothankFlorianGoertzforfruitfuldiscussionsthat

initializedtheproject.IwouldalsoliketothankKaustubhAgashe,

Jose Santiago andMikael Chala for usefulcomments and

discus-sion This research has been supported by a Marie

Skłodowska-CurieIndividualFellowshipoftheEuropeanCommunity’sHorizon

2020 Framework Programme for Research and Innovation under

contractnumber659239(NP4theLHC14)

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