Scrutinizing right-handed neutrino portal dark matter with Yukawa effect

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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Scrutinizing right-handed neutrino portal dark matter with Yukawa effect

Priyotosh Bandyopadhyay

^a

, Eung Jin Chun

^b

, Rusa Mandal

^c^,^d^,^∗

, Farinaldo S. Queiroz

^e

aIndianInstituteofTechnologyHyderabad,Kandi,Sangareddy-502287,Telengana,India bKoreaInstituteforAdvancedStudy,Seoul130-722,RepublicofKorea

cTheInstituteofMathematicalSciences,HBNI,Taramani,Chennai600113,India dIFIC,UniversitatdeValència-CSIC,Apt.Correus22085,E-46071València,Spain

eInternationalInstituteofPhysics,UniversidadeFederaldoRioGrandedoNorte,CampusUniversitário,LagoaNova,Natal,RN59078-970,Brazil

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

Articlehistory:

Received24July2018

Receivedinrevisedform6November2018 Accepted2December2018

Availableonline4December2018 Editor:G.F.Giudice

Keywords:

Right-handedneutrino Darkmatter

Directandindirectdetection

AnalyzingtheneutrinoYukawaeffectinthefreeze-outprocessofagenericdarkmattercandidatewith right-handedneutrinoportal,weidentifytheparameterregionssatisfyingtheobserveddarkmatterrelic density aswell as the currentFermi-LATand H.E.S.S.limits and the future CTA reachongamma-ray signals.InthisscenariothedarkmattercouplestotheHiggsbosonatone-looplevelandthuscouldbe detectedbyspin-independentnucleonicscatteringforareasonablerangeoftherelevantparameters.

©²⁰¹⁸^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The smallness of neutrino masses may be explained by the presence of right-handed neutrinos (RHNs) with large Majorana mass realizing the seesaw mechanism [1]. It is conceivable that adarkmatter(DM)candidatecouplestoaRHNandthusitspair- annihilation to a RHN pair is responsible for the DM freeze-out.

SuchasituationcanberealizedspeciﬁcallywhenRHNs areintro- ducedinassociationwithanextended(B−^L)^gauge^symmetry^[2, 3].Inthisscenario,an interesting featurearisesintheprocess of DM thermalfreeze-out. Due to a tiny neutrino Yukawa coupling of a RHN with lepton and Higgs doublet, the RHN may not be fullythermalizedandthus the observedDM relicdensitycan be achievedbythe DMannihilationratedifferentfromthestandard freeze-outvalue[2,3].Suchafeaturehasbeenrealizedalsoinvar- iousscenarios[4–6].

TheRHNasaportaltoDMwassuggestedinasimplesetupas- sumingthecouplingN

χ

φwhereafermion

χ

orascalarφcanbe aDMcandidate [7],andstudiedextensivelyinRefs. [8–14].Inthis

*

Correspondingauthor.

E-mailaddresses:[email protected](P. Bandyopadhyay),[email protected] (E.J. Chun),Rusa.Mandal@iﬁc.uv.es(R. Mandal),[email protected] (F.S. Queiroz).

paper,weexploretheenlargedparameterspaceincludingtheRHN Yukawaeffecttoinvestigatehowitis constrainedby thethermal DM relic density, direct andindirect detections. We will assume that DMisthefermionﬁeld

χ

,andthusthenucleon-DMscatter- ingarisesatone-loopthroughtheφ–φ-Higgscoupling.

The restof the paper is organized as follows.In Sec. 2, after describing the RHN portal structure with a fermionic DM candidate, we discuss the impact of neutrino Yukawa couplings to the thermalfreeze-outcondition oftheDMpair-annihilationtoa RHN pair. This allows usto identify parameter regions satisfying the observed DMrelicdensity, whichare constrainedby indirect detection experiments.Applying thelatest Fermi-LATandH.E.S.S.

data ongamma-ray signals, produced by RHNdecays inour scenario,weputcombinedconstraintsonthemodelparameterspace in Sec. 3. In Sec. 4, we consider a direct detection process aris- ingfromone-loopinducedDM–DM-Higgscouplingandlimitsfrom therecentdataandfuturesensitivityonspin-independent(SI)DM scatterings.FinallyweconcludeinSec.5.

2. DMfreeze-outincludingneutrinoYukawaeffect

Let us consider the simplistic scenario for a RHN-portal DM basedontheType-Iseesaw.TheLagrangianofsuchconstructwill containthefollowingnewterms

https://doi.org/10.1016/j.physletb.2018.12.003

0370-2693/©²⁰¹⁸^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

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Fig. 1.TheFeynmandiagramsfortheDMparticleχannihilationtoRHNNpair(a) andthedecayofNtoSMparticles(b),(c)areshown.

−

L

⊂

¹

2m²₀

φ

²

+ κ φ

²

|

H

|

²

+

₁

2m_χ

χ χ +

¹ 2mNN N

+

^yNL H N

+ λ

N

χ φ +

^h.c.

.

(1)

Here L and H are theSM SU(2)L doublets and N is aMajorana fermion(RHN).Therearetwonewﬁeldsinthedarksector:areal scalarφ andaMajorana fermion

χ

whicharesinglets underthe SMgaugegroup.ForthestabilityofaDMcandidate,weassigned, e.g.,a Z₂ parityunderwhichthe darksector ﬁeldsare odd.After theelectroweaksymmetry breaking, H=(v+^h)/√

2,we getthe scalarmassm²_φ=^m²0+

κ

v² andtheh–φ–φcoupling

κ

v.

Therearetwocouplingsλand

κ

whichconnectthedarksector (φ and

χ

) tothe visiblesector. When φ is a thermalDMcandi- date,theHiggsportalcoupling

κ

plays an importantrole.Inthis case,theparameterspaceishighlyconstrainedbyvariousconsid- erationsincludingthelatestXENON1Tresult [15].TheRHN-portal process,φφ→^{N N} ^through^the^t-channel ^exchange^of

χ

,canalso beoperativetoproducetherightthermalrelicdensity.Noticethat a similar situation was studied in Ref. [2] where φ corresponds toaright-handedsneutrinoDM.Inthispaper,weconcentrateon thefermion

χ

asa DMcandidate.Ourresultson theRHN-portal propertycanalsobe appliedto thecaseofthescalarφ asaDM candidate.

When

χ

is lighter thanφ,it becomes a viableDM candidate.

FormN<mχ,the DMparticle

χ

canannihilate to the RHNpair viaat-channelexchangeofφ(Fig.1(a)).Thethermalaveragean- nihilationcrosssectionisgivenby,

σ

v

χ χ→N N

= λ

⁴

m_χ

+

^mN

2

16

π

m²_χ

+

^m²_φ

−

^m²_N

₂

1

−

^m²^N m²_χ

1/2

.

(2)

There are other relevant annihilation processes like φφ →

χ χ

(N,N),φφ→^SM^particles^andco-annihilationchannel

χ

φ→ N→^SM ^particles ^which ^can ^contribute ⁱⁿ^the êvaluationôf^DM numberdensity. We quote these expressions in Appendix A. We noticethattheco-annihilation channelis suppressedbytwo rea- sons;firstlythe tinyYukawa coupling yN, secondlythe choiceof parameterspaceaway fromtheresonant N production,andthus hasinsignificanteffectinthefreezeoutmechanism.Westartwith thecoupledBoltzmannequationswrittenintermsofthevariable Yi≡ⁿi/s,describingtheactualnumberofparticlei percomoving volume,wheren_ibeingthenumberdensity,sistheentropyden- sity ofthe Universe, and the variable x≡^mχ/T. The Boltzmann equationsrelevantforourstudyare

dY_χ dx

= −

¹

x² s

(

m_χ

)

H

(

m_χ

) σ

v

χ χ→^{N N}

⎛

⎝

Y_χ²

−

Y_χ^eq

Y_N^eq

2

Y_N²

⎞

⎠

+

¹ x²

s

(

m_χ

)

H

(

m_χ

) σ

v

φφ→χ χ

⎛

⎝

Y_φ²

−

Y_φ^eq

Y_χ^eq

2

Y_χ²

⎞

⎠ ,

(3)

dY_φ dx

= −

¹

x² s

(

m_χ

)

H

(

m_χ

) σ

v

_φφ→χ χ

⎛

⎝

Y_φ²

−

Y_φ^eq

Y_χ^eq

2

Y_χ²

⎞

⎠

−

¹ x²

s

(

m_χ

)

H

(

m_χ

) σ

v

φφ→N N

⎛

⎝

Y_φ²

−

Y_φ^eq

Y_N^eq

2

Y_N²

⎞

⎠

−

¹ x²

s

(

m_χ

)

H

(

m_χ

) σ

v

φφ→^SM

Y_φ²

−

^Y_φ^eq²

,

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dY_N dx

=

¹

x² s

(

m_χ

)

H

(

m_χ

) σ

v

χ χ→N N

⎛

⎝

Y_χ²

−

Y_χ^eq

Y_N^eq

2

Y_N²

⎞

⎠

+

¹ x²

s

(

m_χ

)

H

(

m_χ

) σ

v

φφ→^{N N}

⎛

⎝

Y_φ²

−

Y_φ^eq

Y_N^eq

2

Y_N²

⎞

⎠

−

H

(

m_χ

)

^x

YN

−

^Y^eq_N

.

(5)

TheentropydensitysandHubbleparameterHattheDMmassis s

(

m_χ

) =

²

π

²

45 g_∗m³_χ

,

H

(

m_χ

) = π

√

90

√

g_∗ M^r_plm²_χ

,

whereM^r_pl=².44×¹⁰¹⁸^{GeV is}^the^reduced^Planck^massând^Y_Nêq istheequilibriumnumberdensityofi-thparticlegivenby Y_iêq

≡

ⁿ

eq i

s

=

⁴⁵ 2

π

⁴

π

8

g_i

g_∗ m_i

T

3/2

e⁻^mi^T

0

.

145

_g

i

100 m_i m_χ

3/2

x³^/²e⁻

mi mχx

.

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HereinthelastlineofEq. (6) weusetheeffectivenumberofrel- ativisticdegreesoffreedom g_∗ 100 andtheinternal degreesof freedom gχ,N=^{2 for}^the^two^Majorana^particles

χ

,N andgφ=¹ forφbeingtherealscalar.Theﬁrsttermsontheright-handsideof Eqs. (3) and(5) denotetheforwardandbackwardreactionsof

χ χ

to N N throught-channel φexchangeshowninFig.1(a).Itcanbe seenfromEq. (1) thattheYukawainteractionoftheright-handed neutrinoallowsittodecaytoSMparticlesviathemixingwiththe SM neutrinos proportional tothe coupling y_N.The third termof Eq. (5) describes thedecay andthe inversedecayof N shownin Fig.1(b)and(c)wherebeingthetotaldecaywidthofN.Below wequotetheexpressionsofthepartialdecaywidthsofN tothree possiblechannelsh

ν

,^±W^∓ andZ

ν

,respectively.

(

N

→

^h

ν ) = (

N

→

^h

ν ¯ )

=

^y²^N^m^N 64

π

1

−

^m²^h

m²_N

2

,

(7)

(

N

→

⁻W⁺

) =(

^N

→

⁺W⁻

)

=

^y²^N^m^N 32

π

1

−

^m²^W

m²_N

2

1

+

²^m²^W

m²_N

,

(8)

(

N

→

^Z

ν ) = (

N

→

^Z

ν ¯ )

=

^y²^N^m^N 64

π

1

−

^m²^Z

m²_N

2

1

+

²^m²^Z

m²_N

.

(9) TherelicabundanceoftheDMcandidate

χ

canbeevaluatedby,

h²

=

^m^χ^s⁰^Y^χ

(∞)

ρ

c

/

h²

,

(10)

(3)

Fig. 2.Theactualnumberofχ, φandNpercomovingvolumeareshowninbluedashed,greendot-dashedandreddottedcurves,respectively.Thepanelsfrom(a)to(d) areobtainedbysolvingthecoupledBoltzmannequations(Eqs. (3)–(5))withthetotaldecaywidthofNas10⁻¹⁰GeV,10⁻¹⁵GeV,10⁻²⁰GeV and0 GeV,respectively.The effectofdecaytermisprominentfromtheplots.Themassesofχ,N,φareassumedtofollowmχ=nmN=1/nmφwithn=1.2,mN=300 GeVandthecouplingsλ=0.4, κ=1.Theobservedrelicdensityissatisﬁedinpanel(b)with=10⁻¹⁵GeV.

wheres0=^{2890 cm}⁻³ îs^the^currentêntropy^densityôf^theÛni- verse and

ρ

c/h²=¹.05×¹⁰⁻⁵ ^GeV/cm³ ^is ^the ^critical ^density.

Yχ(∞)istheasymptoticvalue oftheactualnumberof

χ

percomoving volume obtained from numerical solutions of the above Boltzmannequations.Weillustratetheeffectofdecayandinverse decayof RHN in the evaluationof DM density,for a benchmark case,inFig.2.Itcanbeseenthat,inthiscase,thecontributionof scalarDM φ to relicdensityis negligiblecompared to theMajo- ranafermion

χ

.

Dependingontheflavor structureoftheYukawacoupling yN, theRHN decays differentlytoeach lepton flavor, which willlead toadifferentpredictionforindirectdetection.Forouranalysisof indirectdetection,wewillassumeN decayingequallytothreelep- tonflavors.

3. Indirectdetection

Here we would like to mention that the RHN-portal models canbeprobedbyindirectdetectionexperiments.Theannihilation ofDMpairtoRHNs, whichthendecaythrough weakinteractions inducedbyactive-sterileneutrinomixing,leadstogamma-raysig- nals that can be probed by experiments such as Fermi-LAT and H.E.S.S. telescopes [12,13]. In our work we employed the receipt describedin [12] toﬁndthe H.E.S.S.boundsandtheresultsfrom [16] fortheFermi-LATboundonthedarkmatterannihilationcross section for the

χ χ

_→N N process which is depicted in Fig. 3.

We emphasize that H.E.S.S. and CTA limits rely on the current

(projected)sensitivitytogamma-ray emissionstemmingfromthe GalacticCenter.Sincenoexcesshasbeenobserved,stringentcon- straints have been placed on the dark matter annihilation cross section.ItisclearfromtheﬁgurethattheCTAlimit ismorecon- straining and this is a direct result of the CTA array containing Large, Medium andSmall-Sized Telescopes that will signiﬁcantly strengthen CTA sensitivity to darkmatter models [17]. We focus our discussion on the benchmark scenario where mχ=ⁿ^mN = 1/nm_φ.

The left panel of Fig. 3 in the

σ

v−^mχ plane shows the lines satisfying observed relic abundance by Planck data h²= 0.1199±⁰.0027 [18] achieved for different values of the cou- plingλ.Thegreenandyellowshadedregionsdepict90%C.L.limit on annihilation cross section from Fermi-LAT [16] and 95% C.L.

bound fromH.E.S.S. data [12], respectively.Theright-panelshows thecorrespondingsituationinthem_N−^yN plane.Onecanobserve an importantfeature that given a ﬁxed value of λ, the observed reliccanbeobtainedforquiteextendedrangesoftheDMmassmχ by changingtheneutrinoYukawacoupling yN,vizcontrollingthe decay width.Thisparameter spaceis currentlyallowed by the limitsfromindirectdetectionexperimentshowevercanbeprobed bytheprojectedboundfromCTAinfuture.Thesystemofthecou- pledBoltzmannequations,(3) and(5),reducestotheconventional onewheretheRHNisassumedtobeinthermalequilibrium.This isrealizedwhen

σ

v ²×¹⁰⁻⁹^GeV²^and^the^result^becomes^in- dependentof yN,whichisnicelydepictedintherightpanel. The gray shaded region isforbidden by theperturbativity limit on λ.

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Fig. 3.Theleftandrightpanelsshowtheallowedparameterspaceintheplaneof(mχσv⁾^and^(mN,yN),respectively.TheobservedrelicdensityisobtainedfortheDM couplingλ=0.4 (dashed),0.6(dot-dashed),0.8(dotted),1.0(long-dashed)and√

4π (solid).ThegreenandyellowshadedregionsareexcludedbyFermi-LAT(at90%C.L.) andH.E.S.S.(at95%C.L.)data,respectively.ThebluesolidcurverepresentsfutureboundfromCTAwheretheregionabove(below)willbeexcludedat90%C.L.forleft(right) panel.Thegrayregionisforbiddenbyperturbativitylimit.Themassesofχ,N,φareassumedtofollowmχ=nmN=1/nmφwithn=1.2,κ=1,andtheRHNisassumed todecayequallytoeachleptonﬂavor.

Fig. 4.The interaction of the DMχwith the Higgshinduced at one-loop level.

Forhighervaluesofn,theparallellinesfor yN≥¹⁰⁻⁷ ⁱⁿ^the^left panelofFig.3wouldbesatisﬁedforhighervaluesofλforagiven m_N.This isdueto thefact thatan increase inn decreases

σ

v^, whichcanbereadfromEq. (2).

4. Directdetection

Notice that the model contains no tree-level coupling of the fermionicDMtotheHiggsboson,butaneffectiveh–

χ

–

χ

coupling arisesfromtheone-loopdiagramshowninFig.4:

−

Lhχ χ

= κ

h

χ χ ¯

where

κ

_≡ ^λ

2

κ

v 16

π

²

m_χc1

(

x

) −

mNc0

(

x

)

m²_φ

,

(11)

andc1,0(x)areloop-functionsofx≡^m²N/m²_φgivenby

c1

(

x

) =

¹

−

^4x

+

^3x²

−

^2x²^ln^x 2

(

1

−

^x

)

³

,

c₀

(

x

) =

¹

−

^x

+

^x^ln^x

(

1

−

^x

)

²

.

Theinduced h–

χ

–

χ

coupling

κ

(Eq. (11))controlsthe SInucle- oniccross-section

σ

SI

=

⁴

π μ

_r²

κ

g_nnh m²_h

2

,

(12)

where

μ

r=^mχmn/(mχ+^mn) is the reduced mass and gnnh ≈ 0.0011 is thenucleon-Higgs coupling.Themeasurements ofDM- nucleonSIcrosssectionconstraintheeffectiveHiggs-DMcoupling stringentlyand the result is depicted inFig. 5 which showsthe latestboundfromXENON1T 2018result[19] and thefuturelim- itsfromLZ[20] andXENONnT [21] experiments.Theregionabove thementionedcurvesareexcludedat90%conﬁdencelevel.

Fig. 5.Thecontourplotfordirectdetectioncross-sectionthroughaloopinduced h–χ–χ couplingisshowninmχ− |λ²κ|^plane.^The²⁰¹⁸^XENON1T ^{bound [19]}

isshownbythered-dashedcurve.Thegreen- andorange-dottedcurvesarethe expectedboundsfromLZ [20] andXENONnT [21] experiments,respectively. The regionabovethementionedcurvesareexcludedat90%conﬁdencelevel.

It canbe seenthat thelatest datafromXENON1T experiment excludes|λ²

κ

_|_≥O(1)formχ≤^{150 GeV}^and^the^futuresensitivity ofXENONnT canruleout suchvalue of|λ²

κ

_|upto 600 GeV DM mass.Asthedirectdetectionprocessarisesatone-looplevelwith an additionalcoupling

κ

irrelevantfortheDMannihilation,there remains a wide range of parameter space to be probed by both directandindirectdetections.

5. Conclusion

The darksector maypossiblybe connectedto thevisiblesec- torthroughheavyMajoranaRHNswhichareintroducedtoexplain the observed neutrinomassesand mixing. Assuming afermionic DMcandidatewhichpair-annihilatestoaRHNpair,weperformed a comprehensiveanalysisofthe parameter spaceconsidering the neutrinoYukawaeffectinthethermalfreeze-outprocessandim- posing the current results of indirect and direct detection experiments. When the neutrino Yukawa coupling is too small to maintaintheRHNinfullthermalequilibrium,theDMannihilation cross-sectionneedstobelargerthanthestandardfreeze-outvalue toobtaintheobservedrelicdensity.However,theallowedparam- eterregionisquitelimitedandwellbelowthecurrentlimitsfrom Fermi-LATandH.E.S.S.telescopesdetectinggammaraysignals.The

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CTA willbe ableto probea largepartof theregion asshown in Fig. 3. In this scenario, a DM-Higgs coupling arises at one loop andthuscouldbeprobedbydirectdetectionexperimentsthrough spin-independentscattering.The2018XENON1Tboundandfuture limitsareillustratedinFig.5.

Acknowledgements

We thank Christoph Weniger for the discussion and encour- agement.EJCissupported bythe NRFgrant fundedby theKorea government (MSIP) (No. 2009-0083526) through KNRC at Seoul NationalUniversity.FSQ thanks theﬁnancial support fromUFRN, MECandICTP-SAIFRFAPESPgrant2016/01343-7.TheworkofRM hasbeensupportedinpartby GrantsNo. FPA2014-53631-C2-1-P, FPA2017-84445-P and SEV-2014-0398 (AEI/ERDF, EU) and by PROMETEO/2017/053(GV,ES).

Appendix A

In this section we provide the expressions for cross sections involved in the coupled Boltzmann equations (Eqs. (3)–(5)). The scalarDM particleφ can annihilate to

χ

(N)pair viaa t-channel exchange of N(

χ

) and the thermally averaged cross section is given in Eq. (13) ((14)). The φ pair can also annihilate to the SM particles where the dominant channels are φφ →^hh ^and φφ→^h→^t¯t, W W, Z Z wherehistheSMHiggsboson.Thepro- cessφφ→^hh^combines^threecontributionsasshowninEq. (15);

contact4-pointinteraction (ﬁrst term), s-channel Higgsexchange (second term) and t-channel φ exchange (third term). All three channels written in Eq. (16) proceed through a s-channel Higgs exchangeandhencearelessdominantfarfromtheresonantHiggs production. We use these expressions in solving the Boltzmann equations(Eqs. (3)–(5))inSecs.2and3.

σ

v

φφ→χ χ

= λ

⁴

m_χ

+

^mN

2

π

m²_φ

−

^m²_χ

+

^m²_N

2

1

−

^m

2χ m²_φ

3/2

,

(13)

σ

v

φφ→^{N N}

= λ

⁴

m_χ

+

^mN

2

π

m²_φ

+

^m²_χ

−

^m²_N

2

1

−

^m²^N

m²_φ

3/2

,

(14)

σ

v

_φφ→hh

=

1

−

^m²^h m²_φ

1/2

1 64

π

m²_φ

×

2

κ ₊

⁶

κ

m²_h

(

4m²_φ

−

^m²_h

) (

4m²_φ

−

^m²_h

)

²

+

^m²_h

²_h

2

+ κ

⁴v⁴ 2

π

m²_φ

2m²_φ

−

^m²_h

₂

,

(15)

σ

v

φφ→h→SM

=

√

2

κ

²v²G_F

π (

4m²_φ

−

^m_h²

)

²

+

^m_h²

²_h

×

3m²_t

1

−

^m²^t

m²_φ

3/2

+

2m²_φ

1

−

^m²^W m²_φ

1/2

+

^m²φ

1

−

^m²^Z

m²_φ

1/2

.

(16)

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