Matter-parity as a residual gauge symmetry: Probing a theory of cosmological dark matter

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Matter-parity

as

a

residual

gauge

symmetry:

Probing

a

theory

of

cosmological

dark

matter

Alexandre Alves

a

,

Giorgio Arcadi

b

,

P.V. Dong

c

,

Laura Duarte

d

,

Farinaldo

S. Queiroz

b

,

∗

,

José W.F. Valle

e

a_{DepartamentodeFísica,UniversidadeFederaldeSãoPaulo,Diadema,SP,09972-270,Brazil} b_{Max-Planck-InstitutfürKernphysik,Saupfercheckweg1,69117Heidelberg,Germany}

c_{InstituteofPhysics,VietnamAcademyofScienceandTechnology,10DaoTan,BaDinh,Hanoi,VietNam} d_{UNESP,CampusdeGuaratinguetá,DepartamentodeFísicaeQu ´mica,Guaratinguetá,SP,Brazil}

e_{AHEPGroup,InstitutodeFísicaCorpuscular–C.S.I.C./UniversitatdeValenciaEdificiodeInstitutosdePaterna,C/CatedraticoJoséBeltran,2E-46980} Paterna (Valencia),Spain

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received14June2017

Receivedinrevisedform20July2017 Accepted25July2017

Availableonline3August2017 Editor:A.Ringwald

We discuss a non-supersymmetric scenario which addresses the origin of the matter-parity symmetry, PM= (−1)3(B−L)+2s, leading to a viable Dirac fermion dark matter candidate. Implications to electroweak

precision, muon anomalous magnetic moment, flavor changing interactions, lepton flavor violation, dark matter and collider physics are discussed in detail. We show that this non-supersymmetric model is capable of generating the matter-parity symmetry in agreement with existing data with gripping implications to particle physics and cosmology.

©2017 The Author(s). 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

Thenatureofdarkmatterisoneofthemostchallenging prob-lems inscience, requiringphysics beyond theStandard Model as well as a new symmetry capable of making the corresponding particlestableoncosmologicalscales.R-parityisasymmetry im-posed by hand in supersymmetry in order to avoid fast proton decay,leading alsototheexistenceofa stableWeaklyInteracting MassiveParticle(WIMP),oneofthemostcompellingdarkmatter candidates[1].Evenifimposed byhand,R-parity maystillbreak through high dimension operators [2–4] or spontaneously [5,6]. Whilethe second case leads to an attractive neutrinomass gen-erationscheme[7],one losestheWIMPdarkmatter scenario[8]. Generally,some sort ofsymmetry should be invoked inorder to stabilize the dark matter candidate, and it is desirable that this stabilityarisesfromgaugeprinciples

[9–13]

.Forexample,an alter-nativetoR-parityinnon-supersymmetricschemesisto imposea discreteleptonnumbersymmetrytostabilizetheWIMPdark mat-terparticle[14–16].

Inthis work, we discussa non-supersymmetric model where dark matter stability results from the matter-parity symmetry

*

Correspondingauthor.

E-mailaddress:queiroz@mpi-hd.mpg.de(F.S. Queiroz).

PM

= (−

1

)

3(B−L)+2s, naturally arising as a consequence of the

spontaneous breaking of the gauge symmetry inspired by the works done in [17,18]. In orderto implement thisidea we con-sideranextensionofthestandardmodelbaseduponanextended SU

(

3

)

c

⊗

SU

(

3

)

L

⊗

U

(

1

)

X

⊗

U

(

1

)

Nelectroweaksymmetrybrokenby

Higgs triplets preserving B

−

L. Note that the SU(3)L symmetry

is well-motivated due to its ability to determine the number of generations to matchthat of colors by the anomaly cancellation requirement[19–21].matter-paritysymmetry PM

= (−

1

)

3(B−L)+2s

arises in our model as a result of spontaneous gauge symmetry breaking, and the stability of the lightest RP-odd particle leads

to aviable DiracfermionWIMP darkmatter candidate.Wework out the expected rates for direct detection experiments, flavor changing neutral currents, lepton flavor violation processes such as

μ

→

e

γ

, as well as high energy collider signatures. We also comment on possible connections to cosmological inflation and leptogenesis.

2. Themodel

Our non-supersymmetric model is based on the SU

(

3

)

c

⊗

SU

(

3

)

L

⊗

U

(

1

)

X

⊗

U

(

1

)

N gauge group, in which the matter

gen-erationsarearrangedinthefundamentalrepresentationofSU

(

3

)

L

asfollows, http://dx.doi.org/10.1016/j.physletb.2017.07.056

0370-2693/©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Table 1

TheX andN chargesofthevariousmultiplets.GaugefieldshaveX=N=0 andarenotlisted.

Multiplet laL νaR eaR NaR qαL q3L uaR daR UR DαR η ρ χ φ

X −1/3 0 −1 0 0 1/3 2/3 −1/3 2/3 −1/3 −1/3 2/3 −1/3 0

N −2/3 −1 −1 0 0 2/3 1/3 1/3 4/3 −2/3 1/3 1/3 −2/3 2

Leptons 1-2nd Generations 3th Generation

laL

=

⎛

⎝

ν

eaa Na

⎞

⎠

L qαL

=

⎛

⎝

₋

dα_uα Dα

⎞

⎠

L q3L

=

⎛

⎝

ud33 U

⎞

⎠

L

ν

aR

,

eaR

,

NaR uαR

,

dαR

,

DαR u3R

,

d3R

,

UR Scalars

η

=

⎛

⎝

η

0 1

η

−₂

η

0 3

⎞

⎠

ρ

=

⎛

⎝

ρ

+ 1

ρ

0 2

ρ

₃+

⎞

⎠

χ

=

⎛

⎝

χ

0 1

χ

₂−

χ

0 3

⎞

⎠ , φ

where we have adopted the generation indices a

=

1

,

2

,

3 and

α

=

1

,

2.We emphasize thatall leptons are placed inthe funda-mentalrepresentationof SU

(

3

)

L,along withthethird generation

ofquarks.However,thefirst andsecond generationofquarksare arrangedintheanti-fundamentalrepresentationofSU

(

3

)

L to

can-cel the gauge anomalies. Models based on thisgauge group can featuredifferentrealizationsandfermioncontents

[22–40]

.

ThegeneratorsoftheAbelianU(1)X andU(1)N groupsobeythe

followingrelations, Q

=

T3

−

1

√

3T8

+

X

,

B

−

L

= −

2

√

3T8

+

N

,

(1)

where Ti

(

i

=

1

,

2

,

3

,

...,

8

)

, X and N arethe charges of SU

(

3

)

L,

U(1)X andU(1)N,respectively

[17,18,41–45]

. Theexoticquarks U

andD have electriccharge 2

/

3 and

−

1

/

3 respectively. The quan-tumnumbers associatedto the U(1)X andU(1)N symmetriesare

collectedin

Table 1

.

GaugesymmetrybreakingbytheseSU(3)Higgstripletsand sin-glet addresses the origin of matter-parity conservation and dark matterstabilitybypreserving B

−

L.Indeed,afterthescalar

φ

de-velopsavacuumexpectationvalue (VEV)atscale

,the continu-ousU(1)N symmetryisspontaneouslybrokendowntothediscrete

matter-paritygivenasPM

= (−

1

)

3(B−L)+2s

= (−

1

)

−2 √

3T8+3N+2s_. We emphasize that this is the only plausible way to embed theB

−

L symmetryinthemodelandnaturallyexplaintheorigin ofthe matter-parity, since SU

(

3

)

L and B

−

L symmetriesneither

commute nor close algebraically as shown in detail in [18]. We alsonotethattheexoticfermionshavethefollowing B

−

L

quan-tum numbers,

[

B

−

L

](

Na

,

Dα

,

U

)

=

0

,

−

2

/

3

,

4

/

3, and hence are

RP-odd.ThenewAbeliangaugegroupsgiverisetotwonew

neu-tralgaugebosonswithmassesproportionaltotheB-LandSU

(

3

)

L

symmetrybreakingscales,respectively.Unlessotherwisestatedwe will assume that the B-L symmetry is broken at very high en-ergyscales, implying thatonly one newneutralgauge boson, Z, willbephenomenologicallyrelevant.Concerningtheexoticquarks they aresufficiently heavy since their massesareproportional to

w

=



χ

0 3



,theVEVofthe

χ

0

3 field,takentobelargerthan10 TeV.

Note that in our model the NaR are truly singlets under the

gaugegroup,incontrasttothe

ν

aR whichtransformunderU(1)N,

so they have Dirac masses h_abNw proportional to w

=



χ

₃0



. For allcases, Na canbemadethelightest oddparticleunder

matter-parity,andthereforeitisaDiracdarkmattercandidate(see Sup-plementalMaterial foralternativeassumptions).Inwhatfollows,we willinvestigatethephenomenologicalconsequencesofourmodel. Westartbyaddressingelectroweaklimits.

3. CKMunitarity

Quantum loop correctionsto the quark mixing matrix result-ing from additionalneutral gauge bosons induce deviationsfrom unitarity of the CKM matrix. Other new particles such as right-handed neutrinoscan alsogive rise toviolationofCKM unitarity butthese aresuppressed by themass-mixing withactive neutri-nos andforthisreasonwe neglectthem

[46–48]

.These contribu-tions appear asbox-diagramsinvolving W -gauge bosons andthe

Z gaugebosonleading tohadronic

β

-decay,wheretheCKM ma-trixcanbeextractedfrom.Suchcontributioncanbeparametrized by



CKM

=

1

−



q=d,s,b

|

Vu,q|2 [49]. Applying thisto theneutral

currentwefind,



CKM

= −

0

.

0033 M2 W M2_Z ln

M2 W M2_Z

(2)

whichimpliesintoMZ



200 GeV.

4. Electroweakprecisiontests

New physics contributions tothe

ρ

-parametercome fromthe mixing among the neutral gauge bosons, which is evaluated by

[18],



ρ

≡

M2W c2_WM2_Z 1

−

1



(

c2Wu 2

₋

_v2

₎

2 4c4_W

(

u2

₊

_v2

₎

_w2

+

t4 W

(

u2

+

v2

)

36

2

,

(3)

whereu

,

v

,

w,and

aretheVEVsof

η

1

,

ρ

2

,

χ

3,and

φ

,

respec-tively.Here Z1isthelightestofthemassiveneutralgaugebosons,

i.e.theStandardModelZbosoninthelimitwherethescale w is

sufficientlyhigh.Byenforcingtheexperimentallimit



ρ

<

0

.

0006

[50],we find the boundssummarizedin Table 3,takinginto ac-countthatu2

₊

_v2

₌

_v2

S M

,

vS M

=

246GeV,s 2

W

=

0

.

231,

α

=

1

/

128,

and g2

=

4

π α

/

s_W2 .We havechecked that one-loop newphysics corrections to the

ρ

-parameter dominantly arise from the new non-Hermitian gaugebosons,buttheyare muchsmallerthanthe tree-levelone.

A more robust bound,insensitive to theVEV hierarchy, stems fromthe amazingprecision achievedby LEP. Thisstill provides a goodtestfornewneutralgaugebosons thatcoupletoleptonsvia the e+e−

→

Z

→

f

¯

f productionchannel with Z beingoff-shell. Theboundcanbeobtainedusingtheparametrization

[51]

,

L

=

g2

c2_WM2_Z

[¯

e

γ

μ

(

ae_LPL

+

aeRPR

)

e

][ ¯

f

γ

μ

(

aLfPL

+

aRfPRf

]

(4)

wherea_Lf

= (

g_Vf

+

g_Af

)/

2 anda_Rf

= (

g_Vf

−

g_Af

)/

2.

UsingtheLEP-IIresultsforfinalstatedileptonsweget

[52]

,

g2 cos2

_(θ

W

)

⎡

⎢

⎣

cos

(

2

θ

W

)

2



3

−

4 sin2

(θ

W

)

⎤

⎥

⎦

1 M2_Z

<

1

(

6 TeV

)

2 (5)

Table 2

ThecouplingsofZwithfermions.

f gVf g f A νa c2W 2  3−4s2 W c2W 2  3−4s2 W ea 1−4s 2 W 2  3−4s2 W 1 2  3−4s2 W Na − c2 W  3−4s2 W − c2 W  3−4s2 W uα − 3−8s2 W 6  3−4s2 W − 1 2  3−4s2 W u3 3+2s2 W 6  3−4s2 W c2W 2  3−4s2 W dα −(3−2s 2 W) 6  3−4s2 W − c2W 2  3−4s2 W d3  3−4s2 W 6 1 2  3−4s2 W Table 3

Boundsonthew symmetrybreakingscalefromelectroweak measurementsontheρ-parameter.Thisboundcanbe trans-latedintolimitsonthegaugebosonmassesM2

Z g2_c2 Ww2 3−4s2 W andM2 W= g2_(v2 S M+w2) 4 . u/v 0 1 ∞ w [TeV] 6.53 1.5 3.51 MZ[TeV] 2.58 0.593 1.4 MW[TeV] 2.12 0.494 1.14

5. Muonmagneticmoment

Any fundamental charged particle has a magnetic dipole mo-ment (g) which is parametrized in terms of a

= (

g

−

2

)/

2. In the case of the electron the SM prediction agrees quite well with the experimental observation, constituting a capital exam-ple of the success of quantum field theory. On the other hand, forthemuon, there isa long standing discrepancybetween the-ory and measurement of about 3

.

6

σ

[53]. This translates into



aμ

= (

287

±

80

)

×

10−11 [54,55].Theongoing g

−

2 experiment atFERMILABwillshedlightintothisproblemand,shouldthe cen-tral value remain intact, a 5

σ

evidence for new physics would result,with



aμ

= (

287

±

34

)

×

10−11.Themodelpresentedhere cannotaccount for g

−

2, sincetherequired gaugeboson masses wouldbetoosmalltofulfillcurrentexperimentallimitsfromhigh energycolliders(seebelow).Henceonecanonlyrequiretheir con-tribution tolie within the errorbars. Using Table 2,and current (projected)sensitivities on themuon magneticmoment we find,

MZ

>

180GeV

(

273GeV

),

MW

>

100GeV

(

145GeV

)

.

6. Flavorchangingneutralcurrent

Mesons are unstable systems, but if their lifetime is suffi-ciently long we can observe them at colliders. The K0 meson, a bound state of d

¯

s, is necessarily different from its antiparticle due to strangeness. As a result of CP violation in weak interac-tions, these mesons decay differently, and their mass difference has been used as a sensitive probe for flavor changing interac-tions

[56]

.Similardiscussionholdsforthe B0

s

− ¯

B0s mesonsystem.

DefiningVCKM

=

U†LVL,withUL

(

VL

)

beingthematrixrelatingthe

flavorstatestothemass-eigenstatesofpositive(negative)isospin, onecanfindthatthe contributionto themassdifferencefor me-sonsystemsis

[18]

, K0

− ¯

K0

_:

g 2

(

3

−

t2_W

)

M2_Z

[(

V∗_L

)

31

(

VL

)

32

]

2

<

1

(

104_TeV

₎

2

,

(6) B0_s

− ¯

B0s

:

g2

(

3

−

t2 W

)

M2Z

[(

V∗_L

)

32

(

VL

)

33

]

2

<

1

(

100 TeV

)

2

.

(7)

Theboundderivedonthemassofthe Zgaugebosonisrather sensitive to the parametrization used for the V matrix that di-agonalizes theCKMmatrix.In

[57]

twopossible parametrizations were considered, that yieldeither optimistic orconservative lim-its,whilekeepingtheCKMmatrixinagreementwithdata.Inthe optimistic one, one finds V31

=

0

.

43, V32

=

0

.

089, V33

=

0

.

995,

with the K

− ¯

K0 _{system producing the strongest limit, M} Z

>

14 TeV.Taking aconservativeapproach,one finds V31

=

0

.

00037,

V32

=

0

.

052,V33

=

0

.

998,withtheB0s

− ¯

B0s systemofferinga

bet-ter probe, implying the lower bound MZ

>

1

.

95 TeV. Thus it is

clear that meson systems can be powerful testsfor newphysics effects, although suffer from sizeable uncertainties. In this work wewilladopttheconservativebound,butbearinmindthatmore stringentlimitmaybe applicable.See

[58–70]

forcomplementary studiesonflavorchanginginteractions.

7. DileptonresonancesearchesattheLHC

Dilepton resonance searches are the gold channel for heavy neutral gauge bosons with un-suppressed couplings to leptons

[71]. Since signal events are peaked at the Z mass, the use of cuts on the dilepton invariant mass is a powerful discriminating tool.ThebackgroundcomesmainlyfromDrell–Yannprocessesand iswellunderstood

[72,73]

.Using13 TeVcenter-of-energywith in-tegratedluminosityof

L

=

36

.

1fb−1,andapplyingthecuts,

•

ET

(

e1

)

>

30GeV,ET

(

e2

)

>

30GeV,

|

η

e|

<

2

.

5,

•

pT

(

μ

1

)

>

30GeV,pT

(

μ

2

)

>

30GeV,

|

η

μ

|

<

2

.

5,

•

500GeV

<

Mll

<

6000GeV,

with Mll denoting the dilepton invariant mass, one can find a

boundonthe Zmass

[74]

.1Wehavegeneratedeventswith Mad-Graph5

[78,79]

,adoptingthe CTEQ6Lpartondistributionfunction

[80] andefficiencies/acceptancesasdescribed in

[74]

.The result-ing limit was found to be MZ

>

4

.

25 TeV,superseding previous

studies

[75–77,81–84]

.Keepingasimilardetectorresponsewe ex-pectthatupcomingLHCrunswith

L

=

100

(

1000

)

fb−1 willprobe

MZ

=

4

.

9

(

6

.

1

)

TeV,respectively.

8. Chargedlepton

+

METattheLHC

Thepresenceofachargedgaugeboson(W)isafeatureshared among all models based on the SU

(

3

)

L gauge group. In order

to constrain themass of thischargedgauge boson one looks for hightransverse masssignal events[85,86].Here one canuse the lepton plus missingenergy data,via the pp

→

W

→

l

ν

produc-tionchannelattheLHCwith

L

=

13

.

3 f b−1 _{and13TeVcenterof}

mass energy.No significant excess above StandardModel predic-tionswasseen,leadingtoMW

>

4

.

74 TeV

[86]

.Inthismodel,the

chargedcurrentcontains,

L

⊃ −

√

g 2



¯

eaL

γ

μNaL



W_μ

.

(8)

Since this charged gauge boson will be assumed to be much heavierthanthelightest N (i.e.odd fermioninour case),we ex-pectthat thesignal eventswillhaveapproximately thesamecut efficiencies observed in the ATLAS study. Giventhat the interac-tionsoftheLagrangian inEq.(8)issimilartotheoneconsidered in W searches, thebound above is expectedto beapplicable to

Fig. 1. Regionofparametersyielding4.2×10−13_<Br(μ

_→

_eγ)<4×10−14_inblue, overlaidwithboundsfromLEP(dashedred),B0

s− ¯B0s mixing(dashedpink),

dilep-tondatafromLHC(solidgreen),andl+METdatafromLHCingray.Theupperblue lineintheregionrepresentsthecurrentlimitBr(μ→eγ) <4.2×10−13_.(For in-terpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredto thewebversionofthisarticle.)

ourmodel.This limit isrepresentedby the grayregion in

Fig. 1

. We alsolooked attheprospects forfuturerunsfrom theLHC at 13 TeV,with

L

=

100

(

1000

)

fb−1whichturnouttobesensitiveto

MW

=

5

.

8

(

7

)

TeV.

9. Leptonflavorviolation

In the Standard Model lepton flavor is conserved and neutri-nosaremassless.However,neutrinosexperienceflavoroscillations

[87–89]whichis adirectconfirmation thatleptonic flavoris vio-lated.Anobservationofchargedleptonflavorviolationwouldhave enormousimpact on our understandingof the lepton sector and couldhaveimportantimplicationsfornewphysics.Indeed,the ex-istenceoflepton flavorviolationinneutrinopropagationsuggests that it should alsoexist in the charged lepton sector, leading to decays such as

μ

→

e

γ

. Unfortunately the connection is highly model-dependent[90].Inourmodel,thepresenceofright-handed neutrinos(i.e.oddfermions),withthelightestoneconstitutingthe darkmatter, can mediatea fastdecay

μ

→

e

γ

via W exchange, withabranchingratiofoundtobe

[55]

,

Br

(

μ

→

e

γ

)

=

6

.

43

×

10−6



1 TeV MW



4



f

(

gf e∗gfμ

)

2

,

(9) withgf e

=

g UNe∗

/(

2

√

2

)

andgfμ

=

g UNμ∗

/(

2

√

2

)

.

Current(projected) sensitivityasreportedbythe MEG Collab-oration[91] impliesthat Br

(

μ

→

e

γ

) <

4

.

2

×

10−13

(

4

×

10−14

)

. Thus one can translate this bound into a limit on the product

UNe∗UNμ asfunction of the W mass asshown in Fig. 1. There wehaveoverlaidtheaforementionedconstraintsaltogetheras in-dicatedinthecaption.There wehaveconvertedthelimitsonthe

ZmassintoboundsontheWknowingthattheirmassare deter-minedbyacommonenergyscalew.Weconcludethatdepending on the value for the product UNe∗_UN_{μ the}

_μ

_→

_e

_γ

_{search may}

outperform collider probes. We nowinvestigate the feasibility of thismodelconcerningdarkmattersearches.

10. WIMPDiracdarkmatter

Inourmodel,onecanhaveeitheraDiracorMajoranafermionic darkmatter[30,92–99],thoughinthisworkwefocusontheDirac possibility,sincetheMajoranacaseisalreadyexcludedby combin-ingtheexistingconstraints(seeAppendix A).

The Dirac dark matter candidateis the neutral fermionN. As we discussedearlier the darkmatter mass can be regarded asa free parameter.The currentdarkmatter relicdensityand scatter-ingrateatundergrounddetectorsaredictated,respectively,bythe s-channel andt-channel Z-induced interactions that resultfrom the neutralcurrent. The vectorandaxial-vectorcouplings are ex-hibitedinTable IIIof

[18]

.The Wbosonalsomediatest-channel interactions, which are nevertheless subdominant, and thus ne-glected in our computations. The s-channel Z mediated process induces the dark matter annihilation into SM fermions, whereas the t-channeldiagram accountsfortheannihilation intoZ pairs. Therelicdensitycalculationinthecontextofvectormediatorshas beenperformed(see

[100]

).Ourfindings fullyagreewiththeir re-sultandtheyread,

σ

v



NN

¯

→

f

¯

f



≈

nc



1

−

m 2 f M2 N 2

π

m4 Z



4M2 N

−

m2Z



2

×



g2_{f a}



2g2_χvm4_Z



M2_N

−

m2_f



+

g2_χam2_f



4M2_N

−

m2_Z



2



+

g2_χvg2_{f v}m4_Z



2M2_N

+

m2_f

 

,

(10)

where v is therelativevelocity oftheannihilatingDMpair,nc is

the number of colors of the final state SM fermions. E.g. nc

=

3

for quarks. Sufficiently near resonance, the Z must be included inEq.(10).Anyhow,ifMN

>

mZ,then N mayalsoself-annihilate

intoon-shellZbosonsyielding,

σ

v



NN

¯

→

ZZ



≈

1 16

π

M2_Nm2_Z

1

−

m 2 Z M2_N

3/2

1

−

m 2 Z 2M2_N

−2

×



8g2_χvg2_χaM2_N

+



g4_χv

+

g_χ4_a

−

6g2_χvg2_χa



m2_Z



.

(11)

WehavehandledournumericalcalculationswithinMicromegas wheretheZwidthisproperlyaccountedfor

[101,102]

.

SincetheWIMPmightannihilateintoSMfermionsorZpairs, which have differentannihilation crosssections asshown above, therelicdensitycurverepresentedinred in

Fig. 2

features differ-entdependencesonthedarkmatterandmediatormass(MN and

mZ). Weenforcedthe darkmatterrelicdensityto be27% ofthe

universebudgetasindicatedbyPLANCKdata

[103]

.

The WIMP-nucleonscatteringcross section whichis mediated by a t-channel Z exchange is spin-independent andthus suffers fromstringentlimitsfromXENON1Texperiment

[104]

.Itreads,

σ

S I

_≈

μ

2Nn

π



_{Z f} p

+ (

A

−

Z

)

fn A



2 (12) where, fp

≡

1 m2_Z

(

2guV

+

gdv

) ,

(13) and

Fig. 2. Regionofparametersthatyieldstherightrelicdensity curveinred.The existinglimitsfromthenon-observationofdarkmattermatter-nucleonscattering bytheLUXCollaboration areindicatedinlightblue[105].Theprospectsforthe XENON1Texperimentwith2-yearsexposure[105],aswellastheprojected sensitiv-ity oftheLZdarkmatterexperimentarealsoindicated[106].Currentlimitsaswell asprojectedsensitivitiesfromLHCsearchesofdileptonresonancesforluminosities of100fb−1and1000fb−1arealsoshown.(Forinterpretationofthereferencesto colorinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

fn

≡

1 m2_Z

(

guV

+

2gdV

) ,

(14)

where gu V andgdV aretheNcouplings toup- anddown-quarks

whichare simplythe productofthe Z

−

q

−

q with N

−

N

−

Z

couplings, where q

=

u

,

d given in Table III of [18].

μ

χn is the

WIMP-nucleonreducedmass,andwhere Z and A arethe atomic numberandatomicmassofthetargetnucleus,respectively.

InFig. 2we delimitcurrentexclusionlimit ofXENON1T [104]

with34days-Tonexposure,inblue theprojectedexclusionbounds fromXENON1T

[105]

with2-years-tonexposure andLZ

[106]

ex-periments inpink and purple respectively. It isclearthat current limitsfrom the LHC and dark matter direct detection are rather complementary;inparticularLHCcantesttheWIMPparadigmfor highervaluesofthe darkmattermass. Itis nevertheless exciting toobserve that next generation direct detectionexperiments, i.e. XENON1T andLZ,areexpected toprobe themodel for Z mases upto10 TeVoutperformingtheLHC.

InconclusionwehaveshownthatthisUVcompletedark mat-termodeladdresses theorigin ofmatter-parity fromfirst princi-ples is amenableto a variety of constraintswith gripping impli-cationto cosmology, andadditionally offers a viabledark matter candidateformZ

>

4 TeVanddarkmattermassesof2–5 TeV.

11. Conclusion

Issummary,wehavediscussedan elegantsolutionto the ori-gin of a matter-parity symmetry, PM

= (−

1

)

3(B−L)+2s, and

con-sequently the stability of the dark matter particle, in a non-supersymmetricmodel.Thefact thatthe B

−

L symmetry is pre-servedathighscalesplays akeyroleinaccountingfortheorigin ofmatter-parityconservation.ThelightestPM-oddparticle

consti-tutesaviabledark mattercandidate,whosestability follows nat-urallyfromthebreaking ofthegaugesymmetry. We haveshown thattheschemeoffersgoodprospectsfordarkmatterdetectionin nuclearrecoilexperiments,aswellasflavorchangingneutral cur-rentsintheneutralmesonsystemsK0

_{− ¯}

_K0_andB0

_{− ¯}

_B0_,searches

Fig. 3. InviabilityofMajoranadarkmatter:theplot showshowexistingdilepton eventsearchlimitsprecludeaviableMajoranadarkmattercandidate.

for lepton flavor violating processes such as

μ

→

e

γ

,as well as dileptonandl

+

MET eventsearchesattheLHC.

Acknowledgements

A.A.acknowledges supportfromBrazilianagenciesCNPq (pro-cess 307098/2014-1), and FAPESP (process 2013/22079-8); JWFV fromSpanishgrantsFPA2014-58183-P, MultidarkCSD2009-00064, SEV-2014-0398(MINECO)andPROMETEOII/2014/084(GVA);P.V.D. fromVietnamNationalFoundationforScienceandTechnology De-velopment (NAFOSTED)undergrant number103.01-2016.77;and L.D.fromCAPES.

Appendix A. InviabilityofMajoranadarkmatter

In the model discussed thus far the neutral fermions have a Lagrangian termhN

¯

lL

χ

NR wherehN isthe relevantYukawa

cou-pling. After

χ

develops a nonzero VEV



χ

= (

0

,

0

,

w

)/

√

2 one obtains three heavy Dirac fermions N, withmasses at the large symmetry breaking scale



χ

. Notice however, that one can also addabaremasstermNRNR proportionaltoamassparameter

μ

.

For

μ

→

0 we have Diracfermions, whilefor

μ



w the global symmetryenforcingDiracnessisonlyapproximate,andtheNR

be-comequasi-Diracfermions[107].Ontheotherhand,forarbitrary

μ

∼

w theyaregenericMajoranafermions.

Such a model would be perfectly consistent except that the dark matter interpretation would no longer be viable. Indeed, if thelightestoftheNa isaMajoranafermionitsvectorialcoupling

withthe Zgaugebosonvanishes,affectingitsrelicdensity calcu-lationaswellitsdirectdetectionrates.In

Fig. 3

weshowthefinal resultofhaving Na asMajoranafermionsafterimplementing

col-lider andspin-dependent directdetectionlimits. Onesees that a Majoranadarkmatter fermionisalreadyexcluded inview ofthe currentlimits.

Thishighlightsthetestabilityofthemodel,sincethecouplings are all fixed by gauge symmetry. Therefore, the bare mass term must be suppressed,making the Na (mainly) Diracfermions and

Appendix B. Neutrinoseesawmechanism,leptogenesisand cosmologicalinflation

HerewenotethattheneutrinoshaveYukawaLagrangianterms givenby

L

⊃

hν_ab

¯

laL

ην

bR

+

1 2f ν ab

ν

¯

c aR

φ

ν

bR

+

H

.

c

.

(15)

After the scalars develop nonzero vacuum expectation values,



η

= (

u

,

0

,

0

)/

√

2 and

φ = /

√

2, this leads to

mν

 −

mDm−R1mTD

∼

u2

/

, wheremD

= −

hν u

/

√

2. Since



u

thelightneutrinomassesarenaturallysmallthankstothe canon-icaltype-Iseesawmechanism.Ontheotherhandtheheavy right-handedneutrinos

ν

R havelargeMajoranamassesmR

= −

f ν

/

√

2, attheU(1)N breakingscale.

HerewenotethattheU(1)N breakingthatdefinesR-paritycan

notonlyleadtoneutrinomasses,butalsopotentiallyleadto lepto-genesis,andcosmologicalinflation,incertaincorrelationsto dark matter.

TheleptogenesismechanismisgovernedbyCP-asymmetric

ν

R

decays which, besides the usual mode

ν

R

→

e

η

2 include a new

mode

ν

R

→

N

η

3 to RP-oddstates.Thischannel transforminginto

the dark sector is enhanced with respect to the former. We ex-pect there is a link between the fermionic dark matter and the matter-antimatterasymmetry.Notealsothattheeffectivepotential of

φ

whichhas

ν

R,Higgstriplets,andU(1)N gaugefield

contribu-tions, may easily satisfy slow-roll conditions requiredfor cosmic inflation.Inflationwouldendseeminglyduetoan instability trig-geredby

φ

whenitreachesa criticalvalue definedby thelargest Higgstripletmass.Theinflatoneventuallydecaysintooddscalars,

φ

→

η

3

η

3,whilethechannelintofermionicdarkmattersis

loop-induced. This would ensure that fermionic darkmatter particles arethermallyproduced.

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