A SUSY inspired simplified model for the 750 GeV diphoton excess

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

A

SUSY

inspired

simplified

model

for

the

750

GeV

diphoton

excess

E. Gabrielli

a

,

b

,

c

,

K. Kannike

c

,∗

,

B. Mele

d

,

M. Raidal

c

,

e

,

C. Spethmann

c

,

H. Veermäe

c

a_{Dipart.diFisicaTeorica,UniversitàdiTrieste,StradaCostiera11,I-34151Trieste,Italy} b_{INFN,SezionediTrieste,ViaValerio2,I-34127Trieste,Italy}

c_{NICPB,Rävala10,Tallinn10143,Estonia}

d_{INFN,SezionediRoma,c/oDipart.diFisica,UniversitàdiRoma“LaSapienza”,PiazzaleAldoMoro2,I-00185Rome,Italy} e_{InstituteofPhysics,UniversityofTartu,Estonia}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received28December2015

Receivedinrevisedform29February2016 Accepted29February2016

Availableonline3March2016 Editor:A.Ringwald

Theevidenceforanewneutralscalarparticlefromthe 750 GeVdiphotonexcess,and theabsenceof anyothersignal ofnewphysics attheLHCsofar, suggeststhe existenceofnew coloured scalars.To studythispossibility,weproposeasupersymmetryinspiredsimplifiedmodel,extending theStandard Modelwithasingletscalarandwithheavyscalarfieldscarryingbothcolourandelectriccharges–new scalarquarks.Toallowthelattertodecay,andtogeneratethedarkmatteroftheUniverse,wealsoadd aneutralfermiontotheparticlecontent.Weshowthatthismodelprovidesatwo-parameterfittothe observeddiphotonexcessconsistentlywithcosmology,whiletheallowedparameterspaceisboundedby theconsistencyofthemodel.Inthecontextofoursimplifiedmodelthisimpliestheexistenceofother supersymmetricparticlesaccessibleattheLHC,renderingthisscenariofalsifiable.

©2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

The discovery ofthe Higgs boson atthe LHC [1,2] completed the observation ofall fundamental degreesof freedom predicted bytheStandard Model(SM) ofparticleinteractions.Nevertheless, it is widely believed that the SM suffers froma series of short-comings, relatedtothestability of theelectroweakscale andthe absenceofa candidateforthedarkmatter (DM)ofthe Universe, for instance. Solutions to these problems require extending the presenttheoreticalframeworktoincludenewdegreesoffreedom, possibly relevant at the energyscales probed by colliders in the nearfuture.

TheLHC Run2at13TeVcollision energyprovides the poten-tialtoprobephysicsatshorterdistancescomparedtoLHCRun1at 7 TeVand8 TeV.Theexplorationhasjuststartedwithabout4 fb−1

of integrated luminosity delivered to the ATLAS and CMS exper-iments, beginning in June 2015. Searchingfor two-particle reso-nancesisanespeciallyadequatewaytolookfornewphysics man-ifestationswhennewthresholdsincollisionenergiesarereached. Both ATLAS and CMS are presently analysing the new data sets, andtryingtogetthemostoutoftheveryfirstrunat13TeV.

*

Correspondingauthor.

E-mailaddress:kannike@cern.ch(K. Kannike).

In a recent CERN seminar both ATLAS [3,4] and CMS [5,6]

presented a photon pair excess with an invariant mass at about 750 GeV, with a local significance varying (depending on the narrow- or wide-width assumption) in the range 2.6 to 3.9

σ

. Thesignal alsoexhibits some compatibilitywiththe photon-pair studies of Run 1 data by the CMS. Assuming that the observed diphotonexcessisdueto anewresonance,CMSprovidesa com-bination of Run 1 plus Run 2 data for its production cross sec-tiontimesbranching fractionintophotonsto be4

.

5

±

1

.

9 fb [5]. The corresponding ATLAS resultfor 13 TeV was estimated to be 10

.

6

±

2

.

9 fb[7]. While further data will be neededin order to clarifywhethertheobserved excessisrobust,it isexcitingto as-sumethat thedi-photonexcessisreallypointingtotheexistence ofnew physics below a scale of1 TeV, and to try to determine whichkindofSMextension canpredict suchan effect.Presently, noanomalyinanyotherfinalstatehasbeendetected[3,5],which severelyrestrictsanyrealisticexplanationoftheexcess.

Themostnaturalinterpretationoftheobserveddiphotonexcess isdue to the decaysof a singlet scalar S intophotons, S

→

γ γ

[7–26].1Theexistenceoflightscalarsmuchbelowthecut-offscale oftheSM (suchasthePlanckscale)requiressomemechanismto protecttheirmassesagainstradiative correctionsfromthecut-off

1 _{Solutionswithpseudoscalarshavealsobeenconsideredin[7,27–31].}

http://dx.doi.org/10.1016/j.physletb.2016.02.069

scale.Byfarthemostpopularsolutiontothehierarchyproblemis supersymmetry.However, inrecentyearssupersymmetry haslost someofitsappealbecauseofthesevereexperimental constraints fromtheLHC[3,5].

Inthe context ofthe diphotonexcess theconventional super-symmetricmodels,suchastheMinimalSupersymmetricStandard Model(MSSM),haveseveralshortcomings.Firstly,theexcess can-not be explained within the MSSM alone [7,12,32,16], and the framework must be extended to accommodate the new signal. Assuming that the new state is a scalar singlet, the supersym-metrictheory itisembedded incouldbe, forexample,the Next-to-MinimalSupersymmetricStandardModel(NMSSM)ratherthan the MSSM. Secondly, mostof the diphoton excess studies so far haveassumedtheexistenceofheavycolouredvectorlikefermions that, at one loop, induce singlet scalar couplings to gluons and photons[13,11,27,12,32,16,15,14,19,20,33–36,23].Inaddition,new coloured fermions are severely constrained by LHC searches and must be very heavy [3,5]. Therefore, extending the non-minimal supersymmetricmodelsfurtherwithchargedandcoloured vector-likefermions impliesthatthe modelthat issupersymmetrisedis not theSM. Themodelbecomes unnecessarily complicated with-outanyobviousneedforthesespecificnewparticles.

Inthisworkwearguethatthediphotonexcesshintsatthe ex-istenceofrelativelylightcolouredandchargedscalars.First,these particles, thesquarks, do exist in any supersymmetric extension of the SM and there is no need to extend the model with new

adhoc particles. Second, the LHC constraints on coloured scalar massesare much lessstringent than on coloured fermions, such asgluinos.2 _{These argumentsallow forrelatively light squarksin} the loops generating gg

→

S

→

γ γ

that are potentially observ-ableat theLHC in comingyears, renderingthis scenariodirectly testable. Third, one ofthe favourable features ofsupersymmetric modelsistheexistenceofdarkmatter(DM)thatcomesforfreeas thelightestneutralsuperpartnerofgaugebosonsandscalars.We usetheseargumentstoaddresstheLHCdiphotonexcess.

Motivatedbytheabovementionedgoodfeaturesof supersym-metrictheories, wepropose a supersymmetryinspired simplified modelthatisabletoexplainthediphotonexcessconsistentlywith allotherLHCresultsandwiththeexistenceofDM.Although min-imal by construction,andthereforenot supersymmetricby itself, thismodelusestheparticlecontentoftheNMSSMandcanbe em-beddedintothelatter.3 Therefore,themassspectrumofthistype ofsupersymmetric models must be very differentfrom the ones predictedbysimplesupersymmetrybreakingscenarios.

Westudythiseffectivemodel carefullyandshow that the re-quirementofaphysical,chargeandcolourconservingvacuum re-strictstheallowedmassparameterstobeconstrainedfromabove, renderingthemodeltestableorfalsifiablebycolliderexperiments. Inthecontext ofthesimplified modelthisstatementmeans that theeffectivetheorybreaksdownandthenewsupersymmetric de-greesoffreedommustappeartocurethemodel.Therefore,if ver-ified,ourframeworkpredicts theexistenceofnewsupersymmetric particlesatthereachofthenextcolliderruns.Thusthedi-photon excess may change our present understanding of the supersym-metrybreakingpatternsandtheroleofscalarsinsupersymmetric models.

2 _{Theonlyexceptionarestronglycoupledscalardiquarks[37],exoticscalars} cou-pledtotwovalencequarks,thatshouldproducequark–quarkresonancesatthe LHCandwhosemassesare,therefore,constrainedtobeabove6 TeV[38]The mod-elswithcolouredscalarsinthelooppresentedinRef.[11]arebasedondiquarks thatarenotsuperpartnersofquarks.Also,theirmodeldoesnotcontaindarkmatter candidates.

3 _{Alternatively,thesingletcouldbeasgoldstino[39–41],thesuperpartnerofthe} supersymmetrybreakinggoldstone.

Fig. 1. Leading order contributions to the main decay modes of S. 2. TheSUSYinspiredsimplifiedmodel

We constructa supersymmetryinspired simplifiedmodelthat produces a narrowscalar resonance gg

→

S

→

γ γ

.As shownin

Fig. 1, its interactions withphotons andgluonsare therefore in-ducedatlooplevelbyanotherscalarfield Q that

˜

iscolouredand carrieshypercharge,whichweassumetobeq_Q˜

=

2

/

3. Q is

˜

there-foreidenticaltothewellknownright-handedup-typesquarkthat transforms in the fundamental representation of SU

(

3

)

but is a singletunder SU

(

2

)

.ToavoidanyconflictwithLHC phenomenol-ogy and cosmological and astrophysical observations, the squark

˜

Q isrequiredtobeunstable.Asinthesupersymmetricextension ofthe SM,we takeit todecayintoa quarkanda neutralino-like fermion

χ

0,whichisthedarkmattercandidateinourscenario.

ThusweconsideraminimalextensionoftheSMwiththereal singlet scalar field S, three generations of ‘squarks’ Q

˜

i and the

‘neutralino’

χ

0. Obviously,themodelwiththisparticle-contentis

by itself not supersymmetric, butrequires embedding into a su-persymmetrictheory.ThegeneralLagrangianforthegivenparticle sectorcontainsthefollowingterms

L

kin

= |

DμQ

˜

i

|

2

+

1 2

(∂

μS

)(∂

μ_S

₎

−

M2_˜ Q

| ˜

Qi

|

2

₋

1 2M 2 S0S2

+

1 2

χ0

¯

(

/

∂

−

mχ0

)

χ0

,

(1)

L

dec

=

1 2yχS

χ

T 0

χ0

+ (

yiQ

˜

i †

χ

₀TUi R

+

h.c.

),

(2)

L

scalar

= −

μ

Q˜S

| ˜

Qi

|

2

−

μ

S 3 S 3

₋

λ

S 4 S 4

− λ

SQ˜S2

| ˜

Qi

|

2

− λ

Q˜

| ˜

Qi

|

2

| ˜

Qj

|

2

− λ

_Q˜

( ˜

Q_i†Q

˜

j

)( ˜

Q†jQ

˜

i

),

(3)

L

H

= −(

μH

S

+ λ

H SS2

)

H†H

− λ

HQ˜

( ˜

Qi †

_˜

Qi

)(

H†H

),

(4)

withthecovariantderivative Dμ

= ∂

μ

+

gsTaGaμ

+

eqQ˜Aμ,where

Ga

μ isthegluonand Aμ isthephotonfield,andwesumoverthe

generationindicesi for Q

˜

i.Weassumeaflavoursymmetryto

for-bidanyothertermsinvolvingQ

˜

i.Eq.(3)containstheinteractions

among thetwo scalars, mostimportantlythe firstterm withthe coupling

μ

Q˜ whichhasdimensionsofmass.

We require that Mχ

,

M_Q˜

>

MS

/

2 to forbid tree level decays

ofthe S resonance.Also,instabilityof Q dictates

˜

that M_Q˜

>

Mχ .

This choice hasthe benefit ofproviding a darkmatter candidate – the neutralino

χ

0. It has recently been shown [10,9] that in

Tosatisfy the observation



DMh

∼

0

.

1,theneutralino mass must

be

O(

300

)

GeV [10,9], implying a somewhat compressed spec-trum.

The latter means that the model is less constrained by LHC searchesforsquarkpair productionforthefinal stateoftwo jets andmissingenergy,sincethetransversemomentaoftheresulting final jets(which arethe only visibleobjects in theevent) are in thiscasenaturallysuppressed.Inourmodel,thescalarquarkscan beaslightas400 GeV.In[42] theATLAScollaboration presented search results for various SUSY decaychains following squark or gluinopairproduction.Fordirectlyproducedsquarkswithmasses above 400 GeVwhichdirectlydecaytoquarks andinvisible neu-tralinos,neutralinomassesabove350 GeVarenotexcludedbyall presentsearches.

The couplings of the Higgs to the new scalars in Eq. (4) are added forcompleteness andare constrained by electroweak pre-cision observables and by the properties of the SM Higgs boson as measured atthe LHC. These couplings can be made arbitrar-ily small without affecting our conclusions about the 750 GeV resonance inthis model,thus contradictionswith previous mea-surementscanalwaysbeavoided.

As we have already commented, our model does not fit into theMSSMbutrequiressomeextendedsupersymmetricmodel,the NMSSMbeingthesimplestofthem.We notethatthemass spec-trumofsuch amodelmust featurelight scalarswhilethe gluino mustbeheavy tocomplywiththeLHCbound.Sinceourstudyis phenomenological, we just assume this supersymmetry breaking pattern.

3. Conditionsforaphysicalvacuum

Weconsidertheconditionsforthevacuumofthemodelnotto breakcolourandelectriccharge.Weneedtoensurethefollowing: 1. Thepotentialisboundedfrombelowinthelimitoflargefield

values.

2. The squarks Q

˜

i do not get VEVs, which would break colour

andelectriccharge.The truevacuumshould beat S

=

0 and

˜

Q

=

0,therefore thepotential hasto be positiveeverywhere else,4

V

(

S

=

0

, ˜

Q

=

0

) >

0

.

(5) 3. S doesnot get aVEV: anon-zero VEVfor S wouldshift the

massof S awayfromMS.5

Thepotentialmustbeboundedfrombelowinorderforafinite minimumofpotentialenergytoexist.Inthelimitoflargefield val-ues,wecanignorethedimensionfultermsinthescalarpotential. The fullboundedbelowconditionscan befound viaco-positivity constraintsonthequarticpartofthescalarpotential[43]:

λ

S

>

0

,

λ

Q˜

+ θ(−λ

Q˜

)λ

 ˜ Q

>

0

,

λ

H

>

0

,

(6)

¯λ

S Q

≡

2



λ

S

[λ

Q˜

+ θ(−λ

Q˜

)λ

 ˜ Q

] + λ

SQ˜

>

0

,

(7)

¯λ

H Q

≡

2



λ

H

[λ

Q˜

+ θ(−λ

Q˜

)λ

 ˜ Q

] + λ

HQ˜

>

0

,

(8)

¯λ

H S

≡

2



λ

H

λ

S

+ λ

H S

>

0

,

(9) 4 _{TheHiggsportalcouplingsarealreadystronglyconstrained[23]andweneglect} themforphenomenologicalreasons.WealsoassumethatμH0 topreventalarge

decaywidthofS intoHiggsbosons.

5 _{AVEVfor S wouldalsogeneratelargecontributiontothemassofthesquark,} whichwouldneedtobefine-tuned.

Fig. 2.σ(pp→S)×BR(S→γ γ)atthe13TeVLHC.Thecoloured regions corre-spondto4.5±1.9 fb (innerregion)and4.5±3.8 fb (outerregion)corresponding tothe1σand2σregionsforNf=3 degeneratesquarkgenerations.Thehorizontal

axisshowsthemassofthecoloured scalarparticleQ and˜ theverticalaxisthe tri-linearSQ˜Q coupling.˜ Thegreyshadedregionisforbiddenbythepresenceofcolour symmetrybreakingassumingλQ˜= λS= λSQ˜=4π.(Forinterpretationofthe

ref-erencestocolourinthisfigurelegend,thereaderisreferredtothewebversionof thisarticle.)

λ

H S



λ

_Q˜

+ θ(−λ

_˜ Q

)λ

 ˜ Q

+ λ

HQ˜



λ

S

+ λ

SQ˜



λ

H

+

2



[λ

_Q˜

+ θ(−λ

_˜ Q

)λ

 ˜ Q

]λ

S

λ

H

+



¯λ

S Q

¯λ

H Q

¯λ

H S

>

0

,

(10)

where

θ

istheHeavisidestepfunction.Theconditionscanbe satis-fiedbytaking

λ

S

≥

0,

λ

Q˜

≥

0,

λ

Q˜

≥

0,

λ

SQ˜

≥

0,

λ

H S

≥

0,

λ

HQ˜

≥

0.

Thestationarypointequationsforthenewparticlesarethen 0

=

μ

_Q˜

| ˜

Qi

|

2

+ (

M2S

+

2

λ

SQ˜

| ˜

Qi

|

2

₎

_S

+

μS

S2

+ λ

SS3

,

(11) 0

= | ˜

Qi

|(

M2_Q˜

+

2

λ

Q˜

| ˜

Qi

|

2

+

μ

Q˜S

+ λ

SQ˜S2

).

(12) IfQ

˜

i

=

0,weneed

μ

2_S

<

4

λ

SM2S (13)

for S notto get a VEV. We will take

μ

S



0 to get the largest

allowedparameterspaceforthediphotonsignal.However,wenote that a smallbut non-zero

μ

S could always be generated at two

loops.

S and Q

˜

i could also get non-zero VEVs simultaneously. We

needto forbid thisto prevent acoloured vacuum. The forbidden partoftheparameter spaceis foundby requiringthat the vacua whereS andQ

˜

ihavenon-zeroVEV–iftheyexist–arelocal

min-imaofthepotential,thatis,V

>

0.

Note that the bound does not depend on the number of flavours,which cancels out inthe minimisation equations. Espe-cially, the

λ

_˜

Q term does not affect the result, since its minimal

valueiszero.Also,itisplausiblethattheboundwillnotbe weak-enedbymuchiftheflavoursymmetryisabandoned.

Tofit the diphoton signal we need a large

μ

_Q˜ that tends to destabilisetheSMvacuum.Thiseffectcanbecounteredwithlarge quarticcouplings.InFig. 2 weshow theforbiddenregion on

μ

_Q˜ vs. M2

˜

Q plane with gray colour for the least constraining choice

λ

_Q˜

= λ

S

= λ

_SQ˜

=

4

π

.Inthe contextof thiseffectivemodel,that

ofnon-perturbativecouplingssignalsthebreak-downofthe effec-tive model.Thisimpliesthat thesupersymmetricparticles ofthe fullmodelmustappearbelowthescalegivenbythisconstraint. 4. Eventrates

We choose the mass of the singlet to be on the resonance,

MS

=

750 GeV. At this energy scale

α

s

(

MS

)

=

0

.

0894

(

31

)

[44],

whereas for

α

=

1

/

137 weuse the zeromomentum value. From theCMS[5]weknowthat

σ

(

pp

→

S

→

γ γ

)



4

.

5 fb.

Thepartialdecaywidthsofthesinglet S intotwophotonsand intotwogluonsare[45,46]

(

S

→

γ γ

)

=

α

2M3_S

μ

2_˜ Q 1024

π

3_M4 ˜ Q N2_fN2_cq4_˜ Q

|

A0

(

τ

)

|

2

_,

₍₁₄₎

(

S

→

gg

)

=

α

2 sM3S

μ

2_Q˜ 512

π

3_M4 ˜ Q N2_f

|

A0

(

τ

)

|

2

,

(15)

respectively. Nc

=

3 denotes thedimension of the representation

forthe squarks andNf thenumber ofsquarkflavors. Thescalar

loopfunctionisgivenby[45]

A0

(

τ

)

=

τ

(

1

−

τ

f

(

τ

)),

(16)

with

τ

=

4M2_˜

Q

/

M 2

S,andtheuniversalscalingfunctionis

f

(

τ

)

=



arcsin2

√

1

/

τ

τ

≥

1

,

−



arccosh

√

1

/

τ

−

i

π

/

2



2

τ

<

1

.

(17)

Thecrosssectionforproducingthediphotonsignal viathe de-cayofS inthenarrowwidthapproximationis

σ

(

gg

→

S

→

γ γ

)

=

σ

(

gg

→

S

)

BR

(

S

→

γ γ

),

(18) wherethe productioncrosssection isrelated tothe decaywidth intogluonsby

σ

(

gg

→

S

)

=

π

2 8MS

(

S

→

gg

)δ(

ˆ

s

−

M2_S

).

(19) Taking into account that

(

S

→

γ γ

)

 (

S

→

gg

)

 

S, the

branchingratioreads BR

(

S

→

γ γ

)



1 2

α

2

α

2 s N2_cq4_˜ Q



0

.

58%

,

(20)

where we used

α

s

(

MS

)



0

.

09,

α



1

/

137 and assumed the up

type squark with the charge q_Q˜

=

2

/

3. We remark that if the dominantdecaymodeof S is S

→

gg asassumedhere,thecross section forthe resonant productionof diphotons by gluon–gluon fusion is approximately independent of the details of the strong interactionsince

σ

(

gg

→

S

→

γ γ

)



π

2 8MS

(

S

→

γ γ

)δ(

s

ˆ

−

M2_S

).

(21) Atthelevelofprecisionconsideredhere,weassumethatthis can-cellationalsoholdsifhigherordercorrectionsin

α

saretakeninto

account.

To calculate the S resonance production cross section at the LHC,weintegrateEq.(21)numericallyusingtheMSTWparton dis-tributionfunction(pdf)set[47]

σ

(

gg

→

S

→

γ γ

)

=

π

2

8M3_SIpdf

(

S

→

γ γ

),

(22)

where

√

s

=

13 TeV isthecentre of massenergyofLHC proton– protoncollisions,and

Ipdf

=

1



M2_S/s dx x g

¯

(

x

)

g

¯



M2_S sx

≈

5

.

8

,

(23)

is thedimensionlesspdf integral evaluated at

√

s

=

13 TeV. Here

g

(

x

,

MS

)

= ¯

g

(

x

,

MS

)/

x isthepdfofthegluonatmomentum

frac-tionx evaluatedatthescaleMS

=

750 GeV.

Toreproducetheobservedsignal,wefindthatthepartialdecay widthtophotonsis

(

S

→

γ γ

)

≈ (0

.

68

±

0

.

28

)

MeV

.

The parameter space that reproduces the observed decay width forNf

=

3 generationsisdepictedinFig. 2.Accountingfor

unitar-ity andpreserving colour andcharge symmetries, itfollows,that within the 1

σ

band thedata favours Nf

≥

2 generationsof light

squarks withmassesbelowM_Q˜



800 GeV andarelatively large couplingtothescalar S of

μ

_Q˜



2 TeV.Aswasalsonotedin[16]

inthecontextofadifferentmodel,wesimilarlyfindthatthe sig-nal cannot be reproduced by asingle generation oflight squarks within 1

σ

.

Themostimportantresultevident inFig. 2isthat theallowed parameter space of this effective model is bounded to a small region by thedi-photon excessandby theconsistency ofthe ef-fective model.Thisimpliesthatnewparticlesmust bepresentin Natureatthescale

O(

1

)

TeV.

5. Effectivefieldtheoryapproach

We turn to analyse ourscenario in terms ofthe effective La-grangianapproach.Inthecasethesquarkisheavierthanthe sin-glet S,thelattercanacquireeffectivecouplingswithphotonsand gluonsbyintegratingoutthesquarkfield.Forgenericsquarksthis correspondstoaneffectiveLagrangian

L

eff

=

1



γ S FμνFμν

+

1



G S GaμνGa_μν

,

(24) where Fμν andGa

μν arethefieldstrengthsoftheSMgaugefields,

while



i denote theeffectivescaleofthenon-renormalizable

in-teraction. In the simplified model considered above, the condi-tion M_Q˜

MS cannotholdforphysicallyallowedparameters,see Fig. 2. Thus the rates obtained by using the effectiveLagrangian needtoexplicitlyaccountfortheloopfunction A0 (i.e.non-trivial

scaling of



i) toget accurateresults,eveniftheexpansion E

/

i

naivelyseemstobewelldefined.

Nevertheless, theeffective Lagrangianapproach is very useful, since it allows to capture in a model-independent way the cru-cial information concerning the underlying dynamics responsible ofgeneratingtheeffectivecoupling.Iftheeffectiveoperatoris gen-erated perturbatively by integrating out particles running in the loops,itscoefficienthasthegeneralform

1



i

=

αi

4

π

NegQ S˜ m_Q˜ Ci

,

(25)

whereCi isan

O(

1

)

factororiginatingfromloopintegralsand gS

denotes an effective coupling between S andthe mediators and

Ne isthe effectivenumberof degreesoffreedom running inthe

loops. Thecross sectionobtainedfromtheeffectiveLagrangian is roughly

σ

(

pp

→

S

→

γ γ

)

≈

α

2_N2 eg2S 512 m2_˜ Q

.

(26)

NegS

≈

70

×

m_Q˜ MS

.

(27)

As we can see, this would require necessarily a gS



O(

10

)

if

Ne

∼

O(

1

)

. Then, from these results one can naively guess that

this large number of gS points towards either strong dynamics

or a relatively large number ofdegrees offreedom inthe loops. This is, indeed, a justified conclusion if one considers vector-like fermions running in the loop [13,11,27,12,32,16,15,14,19,20, 33–36,23,48],where gS coincideswiththecorrespondingfermion

Yukawacouplingtothescalarresonance.Inthisrespect,we qual-itatively agree with the effective model approach conclusions of Ref.[48]onthelargeproductionrates.

However,aswehaveshownwiththepresentsimplifiedmodel, whenscalar fieldsarepropagating intheloop, theabove conclu-sionsdonotholdanymore.ThecouplinggS canbemadenaturally

(and consistently) very large, even in the framework of weakly coupled field theories,beingrelated tothe ratio gS

=

μ

Q˜

/

mQ˜

∼

O(

10

)

. This is the advantage of having a soft coupling

μ

_Q˜ in theories with scalars. However, thisrequires that the scalar res-onance VEV is stringentlyconstrained, most likely vanishing.We have seen that constraints fromthe colour-charge breaking min-ima could limit the ratio

μ

Q˜

/

mQ˜. This implies that the present

simplified model breaks down and Eq.(25) doesnot correspond tothescaleinEq.(24)anymore.Thecorrectinterpretationwould requiretheknowledgeofthefullsupersymmetrictheory.

6. Discussionandconclusions

Wehaveshownthattherecenthintforthe750 GeV diphoton excess at the LHC can be explained by introducing a new scalar singlet and scalar quarks which can possibly be embedded in a supersymmetrictheoryofNature.However,thecorresponding su-persymmetrictheorymustcontainasingletinadditiontotheSM particle content, and the mass spectrum of the sparticles must be ratherunusual,featuringseverallight scalarswhilethe gluino mustbeheavytosatisfytheLHCconstraints.

To studythe diphoton excess we havepresented a simplified modelthat capturestherequiredpropertiesofthe supersymmet-ric theoryitis tobeembedded in.Asthe result,we haveshown thattheNMSSM-likeparticlecontentissufficienttogeneratelarge enoughgg

→

S andS

→

γ γ

processesatloopleveltoexplainthe observations.In particular,the colouredscalars inthe loopshave an advantageover thefermions toproducethe neededlarge sig-nal because ofthe possibly large dimensionful coupling

μ

_Q˜. We havealsoshownthattherequirementofacolourandcharge con-servingvacuumconstrainstheparameterspaceofthisscenarioso thatthemodelistestable.Inthecontextofthesimplifiedmodel, that by itself is not supersymmetric,this impliesthat the model breaksdownatratherlowenergywherenewsuperpartnersofthe completesupersymmetricmodelmustappeartosavephysics.The concrete prediction of our scenario is the existence of relatively lightsquarkswhichshouldbesearchedforattheLHC.

Weconcludethat,ifthisscenariowillturnouttobethe expla-nation of the diphoton excess, supersymmetry, indeed, was ‘just around the corner.’However, to studythe full the modelandits precisepropertieswouldrequiremorediscoveriesattheLHCorat thefuture100 TeVcollider.

Acknowledgements

TheauthorsthankLucaMarzolaandStefanoDiChiarafor use-ful discussions. This work was supported by the grants IUT23-6, PUT716,PUT799andbytheEUthroughtheERDFCoEprogram.

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