Co-genesis of Matter and Dark Matter with Vector-like Fourth Generation Leptons

0.4 MB·English

by  Chiara Arina

Co-genesis of Matter and Dark Matter with Vector-like Fourth Generation Leptons
ChiaraArinaa,RabindraN.Mohapatrab,NarendraSahuc
aGRAPPAInstitute,UniversityofAmsterdam,SciencePark904,1090GLAmsterdam,Netherlands
bMarylandCenterforFundamentalPhysicsandDepartmentofPhysics,UniversityofMaryland,CollegePark,Maryland20742,USA
cDepartmentofPhysics,IITHyderabad,OrdnanceFactoryCampus,Yeddumailaram502205,Medak,AP
Abstract
We discuss aspects of a scenario for co-genesis of matter and dark matter which extends the standard model by adding a fourth
generationvector-likeleptondoubletandshowthatifthefourthneutrinoisamassivepseudo-Diracfermionwithmassinthefew
hundredGeVrangeandmasssplittingofabout100keV,itslightercomponentcanbeaviableinelasticdarkmattercandidate. Its
3
relicabundanceisproducedbytheCPviolatingout-of-equilibriumdecayofthetype-IIseesawscalartriplet,whichalsogivesrise
1
totherequiredbaryonasymmetryoftheUniverseviatype-IIleptogenesis,thusprovidingasimultaneousexplanationofdarkmatter
0
2andbaryonabundanceobservedtoday. Moreover, theinducedvacuumexpectationvalueofthesamescalartripletisresponsible
forthesub-eVMajoranamassestothethreeactiveneutrinos. Astablefourthgenerationofneutrinosiselusiveatcollider,however
n
mightbedetectedbycurrentdarkmatterdirectsearchexperiments.
a
J
Keywords: Darkmattertheory;theoriesbeyondthestandardmodel;baryonasymmetry;neutrinotheory.
0
3

] 1. Introduction tons,probablythemoststringentboundistheZinvisiblewidth
h
measuredatLEP,becauseitprovidesstrongevidenceforonly
p Dark Matter (DM), which constitutes 23% of the total en- three family of light neutrinos. A 4th generation neutrino, if
-
pergy budget of the Universe is currently supported by the ro- present, should be very distinct in nature from the three SM
etation curve of galaxies and clusters, gravitational lensing and neutrinos. Indeeditshouldbeheavierthanatleastm /2,inor-
hlargescalestructureoftheUniverse. Theseindirectevidences dertoavoidconflictwithZ decaywidthmeasuremenZt. There-
[
suggestthattheDMshouldbemassive,electricallyneutraland fore the model of fourth generation leptons we present is dis-

2stableonthecosmologicaltimescale[1].Theonlyinformation tinctfromtheideaofsequentialrepetitionoftheSMfermionic
vabout DM hitherto known is its relic abundance which is pre- families.
5
ciselymeasuredbytheWilkinsonMicrowaveAnisotropyProbe Asiswell-known,insimpleheavyfourthgenerationexten-
3
4(WMAP)[2]andisgivenbyΩDMh2 = 0.11. However,theun- sions of SM, the heavy neutrino (N4), which is part of a lep-
0derlyingmechanismwhichgivesrisetotherelicabundanceis ton doublet L ≡ (N ,E ), does not qualify as a dark matter
4 4 4
1.unknown. since rapid N4N¯4 annihilation to SM particles via Z-exchange
1 Itisusuallypresumedthataweaklyinteractingmassivepar- reduces its relic density to a value far below what is required
2ticle of mass O(100) GeV can be a good candidate for DM as for it to be a viable DM candidate as well as is excluded by
1its annihilation cross-section < σ|v| >≈ 3×10−26cm3/s satis- directDMsearchesduetoitscouplingwiththeZ boson. Our
v:fiestherequirementofrelicabundance,becauseitisproduced modelforthefourthgenerationneutrino N ishoweverdiffer-
4
iby the standard thermal freeze-out mechanism [3]. However, ent: in addition to being part of a vector-like doublet, it has
X
an alternative mechanism has been explored in the literature, twoadditionalfeatures,whichendowitwiththepropertiesthat
arwheretherelicabundanceofDMoriginatesviatheasymmetric makeitaviabledarkmattercandidate. (i)N4isapseudo-Dirac
component rather than the symmetric component of any sta- neutrino, whose Majorana mass arises from the vev (vacuum
ble species. In this case, the relic abundance depends on the expectation value) of a Y = 2 Higgs triplet ∆, acquired below
amount of CP-violation in the theory, in a similar way to the electroweak(wk)phasetransition. Wewillcallthisthetype-II
baryogenesismechanism[4–39]. seesaw Higgs field, which anyway is present in our model to
In this article we study the possibility of adding a vector- make the familiar active neutrinos acquire mass via the type-
like lepton doublet to the standard model (SM) whose neutral II seesaw mechanism. The presence of this Majorana mass
member (to be called fourth neutrino henceforth) could be a makes it an inelastic dark matter [49], that has the advantage
candidateforDM.Indeedafourthgenerationoffermions[40– offittingtheresultsofcurrentDMsearchexperimentsandnot
46]isoneofthesimplestextensionofphysicsbeyondtheSM beingexcludedbyupperlimits. Tokeepthefourthfamilylep-
with rich phenomenology and also extensively searched for at ton doublet stable, we then impose an extra Z symmetry on
2
colliders. Thepropertiesofthenewfamilyaresubjecttotight the model under which the fourth family lepton doublet L is
4
constraints from electroweak precision measurements and by oddandallotherfieldsofthetheoryareeven[50,51]: besides
directsearches[47,48]. Consideringthefourthgenerationlep-
PreprintsubmittedtoPhysicsLetterB January31,2013
thefourthfamilyneutrinobeinglighterthanthecorresponding 2.1. TripletSeesawandSub-eVMajoranaMassesofThreeAc-
chargedlepton,itisdecoupledfromtheotherleptondoublets. tiveNeutrinos
(ii)Secondly,thedecayofthetwotype-IIseesawHiggstriplets In addition to the vector-like lepton doublet, we add two
via their CP violating coupling produces an asymmetry in the scalartriplets∆ withY =2. Sincethehyperchargeof∆is2,
1,2
fourthfamilyleptonnumber,whichislargeenoughsothatthe it can have bilinear coupling to Higgs doublet H as well as to
depletion problem of relic density alluded to above does not theleptondoublets.Thescalarpotentialinvolving∆(fromhere
occur. In fact, this asymmetry is comparable to the ordinary onwedropthesubscriptsforthetwoscalartripletsandreferto
leptonnumbergeneratedinthesamedecaywhichgivesriseto themlooselyas∆)andHcanbewrittenasfollows:
the matter anti-matter asymmetry in the Universe via leptoge-
nesis [50, 51]. Both asymmetries can be comparable to each V(∆,H) = M2∆†∆+ λ∆(∆†∆)2−M2H†H
otherinrealisticmodels. Inotherwords,thetripletmassscale ∆ 2 H
λ
issuperheavysothatitsCPviolatingout-of-equilibriumdecay + H(H†H)2+λ∆HH†H∆†∆
can produce asymmetry simultaneously in the DM and lepton 2
sectorandabovetheelectroweakphasetransitiontemperature, + √1 (cid:104)µ ∆†HH+h.c.(cid:105) . (1)
H
the lepton asymmetry for the familiar leptons gets converted 2
to the baryon asymmetry via SU(2) sphalerons [52]. In this
L Thebi-linearcouplingsofleptonsandHiggstoscalartripletare
case,wewanttoemphasizethatthegeneratedleptonasymme-
givenby:
try in the fourth generation does not get converted to baryon
viasphaleronprocessessinceL beingavector-likedoublet,it 1 (cid:104) (cid:105)
doesnotcontributetotheB+La4nomalyofthestandardmodel. −L⊃ √ fHM∆∆†HH+(fL)α,β∆LαLβ+h.c. , (2)
2
Ontheotherhandthesymmetriccomponentgetsdepletedvia
rapidannihilation,i.e. Z-exchange. Thecommonoriginoftwo where fH = µH/M∆ and α,β = 1,2,3. Below electroweak
asymmetries from the ∆ decay then naturally explain the sim- phasetransitionthescalartripletacquiresaninducedvev:
ilarorderofmagnitudefortheDM-to-baryonratioandbyad- v2
justingthemassesandcouplingsinbothsectors,onecanhave (cid:104)∆(cid:105)=−fH √ , (3)
Ω /Ω ∼ 5. Thus our model provides another example of 2M∆
DM B
co-genesisofmatteranddarkmatter. wherev=(cid:104)H(cid:105)=246GeV.Thevalueof(cid:104)∆(cid:105)isupperboundedto
It is worth mentioning that in this paper we focus on the bearound1GeVinordernottospoiltheSMprediction:ρ≈1.
model building aspects of the co-genesis mechanism with re- The∆L L couplinggivesMajoranamassestothreeflavorsof
α β
specttoRef.[50,51]andtrytoaddresssomeissuesaboutthe activeneutrinosas:
viability of the scenario described above that were left unex-
√ v2
plored. In particular we propose a mechanism to introduce (M ) = 2f (cid:104)∆(cid:105)=−f f √ . (4)
ν αβ αβ L,αβ H
a splitting in mass between the neutral and charged partner 2M∆
of the vector-like doublet and we investigate the survival of Taking M∆ ∼ 1010 GeV, fH ∼ 1 and fL ∼ O(10−4) we get
the asymmetry at electroweak phase transition. Lastly we up-
M ∼ O(eV), which is compatible with the observed neutrino
ν
date the direct detection part with the latest data release by
oscillationdata[58–60].
XENON100[53],investigateifthemodelmightaccommodate
theexcessseenbytheCRESST-IIdetector[54]andifthereis
2.2. TripletSeesawandPseudo-DiracmassoffourthGenera-
acompatibilitywiththeKIMSexclusionbound[55].
tionNeutrino
Our letter is organised as follows. In section 2 we present
TheLagrangianthatgivesthe4thfamilyneutrinoitsmass
the model for a fourth generation of fermions, discussing in
isgivenby:
section4constraintsfromelectroweakprecisionmeasurements
and direct searches at colliders. The phenomenology for gen- f
−L = M L L + √4 Lciτ ∆L +h.c. (5)
eratingtheasymmetriesandthemeasuredDM-to-baryonratio L4−mass D 4 4 2 4 2 4
ispresentedinsection3togetherwiththeconstraintsfromDM
directsearches. Wethensummarizeinsection5. where MD generates the Dirac mass of the N4. Below elec-
troweak phase transition ∆ acq√uires an induced vev and gen-
erates a Majorana mass m = 2f (cid:104)∆(cid:105) for N . Therefore, the
4 4
2. FourthGenerationPseudo-DiracNeutrinoasDM
DiracspinorN canbewrittenassumoftwoMajoranaspinors
4
(N )and(N ). AsaresulttheLagrangian(5)becomes:
Fourthfamilyneutrinohasbeenstudiedasadarkmatterin 4,L 4,R
gaugeextensionsofthestandardmodelbyseveralauthors[42, −L = M (cid:104)(N )((N )+((N )((N )(cid:105)
43,56,57]. Inthisstudy,wefocusonavectorlike4thgenera- L4−mass D 4,L 4,R 4,R 4,L
(cid:104) (cid:105)
tionleptondoublet,L4,whichwillgiveacandidateofinelastic + m (N4,L)c(N4,L)+(N4,R)c(N4,R) . (6)
DM and being vector-like will not need the new set of quarks
This implies that there is a 2 × 2 mass matrix for the fourth
foranomalycancellation.
generation neutrino in the basis {N ,N }. By diagonalising
4,L 4,R
the mass matrix we get the two mass eigenstates N and N
1 2
2
withmasseigenvalues(MD−m)and(MD+m). Thusthemass where X∆ = n∆/s, with s = (2π2/45)g∗T3 the entropy den-
splittingbetweenthetwostatesisgivenby: sity and n∆ the number density of the triplet scalar. ηL, ηL4
√ aretheefficiencyfactorswhichtakeintoaccountthedepletion
δ=2m=2 2f4(cid:104)∆(cid:105). (7) ofasymmetriesduetothenumberviolatingprocessesinvolving
L ,L andH.Atatemperatureaboveelectroweakphasetransi-
Weassumethatthemasssplittingissmall,namelyδ∼O(100) α 4
tiontheleptonasymmetrygetsconvertedtobaryonasymmetry
keV,comparedtothemassscaleofthesestates,whichisofor-
viatheSU(2) sphaleronsas:
der 100 GeV. Therefore, the two mass eigenstates are pseudo- L
DiractypeneutrinoandactasinelasticDM.Thelighterofthem Y =−0.55Y . (11)
B L
is indeed stable, because of the discrete Z symmetry we im-
2
posed. Besides the fourth generation being inert, namely it As noted in [50, 51], the primordial L4 asymmetry is much
does not couple to the three SM families of fermions, it does largerthantheprimordialvalueofthefamiliarleptonasymme-
not couple neither to the Higgs boson, implying that all the trybyafactorof f2/f2(nearly108).Theenhancedannihilation
H L
YukawacouplingstotheSMHiggsfieldarezero. Themasses rateof L4 causesamuchstrongerwash-outof(cid:15)L4 viathepro-
ofthevector-like4thgenerationarethereforenotlinkedtoelec- cesses L4L4 → HH than of the corresponding asymmetry (cid:15)L
troweaksymmetrybreakingandarenotpredictedbythemodel. forfamiliarleptons,whosecouplingsaremuchsmaller. Using
We however suppose them at the electroweak scale and take thisandtheequations(10)and(11),wegettheDMtobaryon
intoaccounttheconstraintsfromLEPdirectsearches. abundance:
Ω 1 m (cid:15) η
2.3. Masssplittingbetweenthechargedandneutralcomponent ΩDM = 0.55 mN4 (cid:15)L4 ηL4 , (12)
B p L L
ofL
4
where m ∼ 1 GeV is the proton mass and η represent the
Animportantpartofthediscussionofdarkmatterneutrino p L4,L
wash out effect. The details of the numerics can be found in
inourmodelisthesplittingbetweenthechargedandtheneutral
references[50,51], whereaphenomenologicalanalysisofthe
memberofthefourthgenerationleptondoublet. Asimpleway
parameterspacesatisfyingΩ ∼5Ω hasbeenrealized. Here
toachievethiswithoutdisturbingotheraspectsofthemodelis DM B
weplotinfigure1aparticularsolutionfortheco-genesismech-
tointroduceanSMsingletlepton N withnearTeVscalemass
M andadditionalHiggsdoubletH(cid:48),withyukawacouplingsof anism:weobservethattheasymmetrygeneratedintheDMsec-
N tor(Y =1.0×10−10)isofthesameorderoftheasymmetryin
theorderofO(0.1−1). TheextrafieldstransformundertheZ DM
asL →−L ,H(cid:48) → H(cid:48) andN →−N. OnceH(cid:48) acquiresavev2 theleptons(YL =1.6×10−10)andhenceinthebaryonicsector.
v(cid:48) ,4theN a4ndN fieldgeta2×2massmatrixoftheform: Theefficiencyinthedarkmatterchannelisalthoughlargerthan
wk 4 the efficiency in the leptonic channel because it should com-
(cid:32) M h(cid:48)v(cid:48) (cid:33) pensate the effect of a large DM mass (see equation 12) and a
M = 4 wk (8)
N4,N h(cid:48)v(cid:48) M small CP asymmetry; the fast channel is the Higgs one. The
wk N
parametersusedforthesolutionoftheBoltzmannequationsas
This lowers the mass of the dark matter neutrino to the value
wellastheabsoluteyieldsaregiveninthecaptionandarerep-
m ≡ M ∼ M −∆m∼ M − (h(cid:48)v(cid:48)wk)2.
N4 DM 4 4 MN resentative of a large portion of the allowed parameter space.
Viablesolutionscanbefindfordarkmattermassesrunningup
3. Pseudo-Diracfourthgenerationneutrinoasdarkmatter toTeVscale,eventhoughtheyaredisfavouredwithrespectto
solutionsatlowerdarkmattermassbecauseofthenaturalness
3.1. Co-genesisofmatteranddarkmatter principle: since the ratio of DM to baryon abundance is close
Sincethescalartripletissuperheavy,itdecaysintheearly tounititismorenaturaltohavelightdarkmatterwiththesame
Universeinaquasi-equilibriumstateinvariouschannels,namely efficiency and CP asymmetries than the visible matter. Larger
∆ → L L ,∆ → L L and∆ → HH. Thedecaychannelscan dark matter masses are allowed because of the compensation
α β 4 4
be easily read from the Lagrangian (2). Since these couplings effectbetweenasymmetriesandefficiencyfactors,asdescribed
are in general complex, charge conjugation (C) and parity (P) byequation12.
are jointly violated through the interference of tree-level and We wish to point out that it is possible to construct theo-
one loop self-energy correction diagrams. As a result the de- ries where the two Higgs triplets couple to the different set of
cayof∆producesasymmetriesinthevisible(i.e. ∆ → LαLβ) leptons(onetofamiliaronesandtheothertoL4)duetotheex-
sectorandintheDMsector(i.e. ∆ → L L ). Theasymmetry istenceofsomesymmetrybutmixwitheachotherwithasmall
4 4
intheHiggsdisappearsafterthelateracquiresavev. However, mixingaftersymmetrybreaking. Inthiscase,thehierarchybe-
theasymmetriesinthevisibleandDMsectorsremainforever. tween fH and fL can be of order 10−2 or so, so that the ratio
Quantitatively,theasymmetriesintheleptonanddarkmat- between (cid:15)L4 is much less than in the model described above.
(cid:15)L
tersectorsareasfollows There can be a larger range of parameters where current dark
matterabundancecanbefitted. However,inthiscasethecon-
YL ≡ nsL =(cid:15)LX∆ηL, (9) ceptofco-genesishastobesacrificedattheleadingorder.
YDM ≡ nLs4 =(cid:15)L4X∆ηL4, (10)
3
0
10−12
H(z)
−1 mN = 1 TeV
10−13 4
m = 100 GeV
N
−2 4
10−14 mN = 45 GeV
4
−3
εg((|Y|/,X)ξ10ii −4 Γ (GeV)LL44 1100−−1165
o
l −5 10−17
−6 10−18
−7 10−19
−8 10−20
−2 −1 0 1 2 102 101 100 10−1 10−2
log10(z) T (GeV)
Figure 1: Absolute value for the Yield of leptons (cyan solid), DM (dotted Figure2: ThescatteringrateoftheprocessL4L4 → ff¯asafunctionofthe
magenta),Higgs(dashedblack),scalartripletasymmetry(solidred)plusscalar temperatureiscomparedwiththeHubbleexpansionrate. Forillustrationpur-
tripletabundance(blacksolid), forasuccessfulpointwithmDM = 60GeV, posewehaveassumedtheMajoranamasssplittingtobe100keVandwehave
BL=0.015,BDM=1.7×10−5,(cid:15)L=3.4×10−7,(cid:15)DM=3.6×10−8,whichleads consideredthreevaluesforthemassofthefourthgenerationneutrinoasla-
toΩDM/ΩB=5.0,YL=1.6×10−10,YDM=1.0×10−10andηDM/ηL=0.48. belled.
Inordertogiveaqualitative“feel”fortheaboveargument,
3.2. Cosmologicalevolutionofdarkmatterbelowelectroweak
we note that the rate for the lepton number depleting process,
phasetransition
Γ(L L → ff¯)viaZ-exchangeisexpectedtobegivenby:
Asemphasizedintheprevioussection,eventhoughthepri- 4 4
lmepotrodnialasLy4m(mDeMtr)y,assytrmomngetwryasish-mouutchefflaercgtievrethaabnovtehethfaemeilleica-r Γ(L4L4 → ff¯)(cid:39) G2F2MπD2 cθW (cid:18)2δT(cid:19)2 nnL4T3, (13)
troweak phase transition epoch T = T , brings them to be of γ
wk
similarmagnitude. Animportantissuearisesafterelectroweak whereGF istheFermicouplingconstant,cθW thecosineofthe
phasetransition,whenthereisthesmallMajoranamassforL WeinbergangleandwehaveusedtheBoltzmanndistributionto
4
whichturnsonbelowTwk. ThissplitstheL4intotwoMajorana accountforthenon-relativisticnumberdensityofN4 particles.
eigenstates N1 and N2 by 100 keV mass. The question to be AsaresultbelowTwk,wefindthatthisleptonnumberdepletion
addressednowis: canthetwostatesannihilatetoreduceΩ ? ratesuffersanexponentialsuppressionandthereforeitisslower
DM
Asithasbeennotedin[50],iftheDMmassis≥ 2TeV, L L¯ thantheexpansionrateoftheuniversefortherangeofmasses
4 4
annihilationfreezesoutbeforeT andnofurtherreductionof weareinterestedin. Hencethisprocessisnotveryeffectivein
wk
Ω takes place. However, what happens for lower masses reducingthedarkmatterasymmetry,asshowninfigure2. We
DM
needs to be discussed, i.e. do we lose the L asymmetry via thereforebelievethatoncethedarkmatterasymmetryhasbeen
4
weakannihilationprocessesbelowTwk. createdaboveTwk,itwillsurvivetillthepresentepoch.
Therearetwopossiblethingsthatcanhappen: thetwoMa- AnotherissueisthepossibleoscillationofN4 → N¯4viathe
joranaeigenstatescanannihilateeachotherviaboththelepton δ/2 [50, 61–63] below the temperature when triplet vev turns
numberconservingandtheleptonnumberviolatingprocesses, on. NotethatiftheMajoranamassturnsonbelowthefreeze-
wherethelatterinvolvestheMajoranamassδ/2. Thedominant out temperature for N4N¯4 annihilation, the oscillations simply
lepton number conserving annihilation only reduces the sym- redistributestherelicdensitybetweenN1 andN2 andwhenN2
metriccomponentbutnottheasymmetricpartwhichwouldre- decaysto N1,thenetrelicdensityremainsunchanged. Thisis
quire the intervention of the small Majorana mass δ/2. Since for example the case when MDM ≥ 2 TeV. If MDM ≤ 2 TeV,
relicdensityofDMisduetotheasymmetricpart,iftheL vi- therearetwopossibilities:
4
olating reaction rates are out of equilibrium, in this range, the (i)UnlikegenericDM,ourDMcandidatehasweakaswell
“turningon”ofδ/2willnotaffecttherelicdensity. Wethere- as magnetic moment interactions with the hot plasma of the
foregiveaheuristicdiscussionofwhetherthisisthecase. We earlyuniverse. Discussionofsuchoscillationsinthepresence
expect the L violating part of the annihilation to be propor- ofdensemediumastheearlyUniverseisnotverysimple[64]
4
tionaltotheparameterδ/2. and it is not clear how to estimate the oscillation rate in such
4
varyinareasonablerangeofvalues,inorderforthescattering
to occur. A Majorana mass of the order of 100 keV accounts
for the DAMA [66] annual modulated signal (shaded region),
whileamuchwiderrangeaccountsfortheeventexcessseenin
CRESST[54](bluenonfilledregion). Howeverthoseregions
are severely constrained by XENON100 [53] and KIMS [55].
KIMSisveryconstrainingbeingascintillatorwithIodinecrys-
tals as DAMA. Our dark matter candidate can explain simul-
taneouslytheDAMAandCRESSTdetection, withamarginal
compatibilityat90 %withXENON100andKIMS,foramass
S
range that goes from 45 GeV up to ∼ 250 GeV. If we give up
theDAMAexplanation,thenitcouldaccountfortheCRESST
excessuptomassesoftheorderof∼500GeV.
The details on the model cross-section are given in [50],
while for the numerical analysis of the latest experimental re-
sultswereferto[65].
4. ElectroweakPrecisionTestsandDirectLimitsonFourth
GenerationLeptons
Nowadays a fourth family of fermions, in particular chiral
Figure3: 2Dmarginalposteriorpdfinthe{δ,mN4}-plane. Theshaded(blue and whose mass is related to electroweak symmetry breaking,
solid)contoursdenotethe90%and99%credibleregionsforDAMA(CRESST) isveryseverelyconstrainedbyLHCwiththeHiggs-likesignal
respectively. Themagentadot-dashedlineistheXENON100exclusionlimit,
at125GeV,flavourviolatingprocessesandelectroweakpreci-
whilethegreendashedlineistheupperboundofKIMSexperiment,at90S%
siontests[67–71],perhapsalmostruledout.Oneofthereasons
confidencelevel[65].Alltheastrophysicaluncertaintiesandnuisanceparame-
tershavebeenmarginalizedover.ThelightgrayregionisexcludedbyLEP. isthatthe4thgenerationofquarksmodifiestheproductionof
theHiggsbosonanddepletestheh→γγdecaychannel,which
goes into contradiction with the experimental data. However
a situation. We therefore assume that such oscillations do not
the constraints on a 4th generation of fermions strongly de-
playanimportantroleindepletingtheN asymmetryforM ≤
4 DM pendontheassumptionsofthemodel[47]. Forexampleithas
2TeV.
beenshownthatvector-likefamiliescanprovidethemeasured
(ii)Secondpossibilityistomodifythemodelsuchthatthe
branchingratioforh→γγandbecompatiblewithelectroweak
Majoranamassarisesduetoatripletvev“turningon”atamuch
precisionmeasurements[42].
lower temperature than T . For example, we could consider
wk IfreallytheYukawacouplingsbetween L and H arezero
4
multi-HiggsdoubletmodelswiththeHiggsfieldsthatcoupleto
as well, as in our model, the only constraints come from the
∆toinducetripletvevsthemselveshavevevsoforderofafew
obliqueparametersSandT[72]andfromdirectmeasurements
GeVs(asinhightanβtwoHiggsmodels). Thiswouldrequire
at LEP. These latter are as follows: the N are pseudo-Dirac
µ∆ (cid:29) M∆ (e.g. µ∆ ∼ 1013 GeVand M∆ ∼ 109 GeV).Insuch neutrinosandarestable,hencelowerbound4edbytheinvisible
models, the Majorana mass δ/2 will turn on around 5 GeV so
Z-decaywidth,whichgivesm > 45GeV. Theboundonthe
thatwecouldallow M ≥ 100GeVandforsuchmasses,by N4
DM masscannotbeloweredfortheMajoranacase[73]becauseit
thetimeδ/2turnson,theN4freeze-outwouldhavetakenplace reliesontheprocessZ → N N¯ whichcontributesonlytothe
4 4
and as we argued before, the relic density will not be reduced
invisiblewidthoftheZboson.However,thechargedpartnerE±
further. 4
canbesearchedforinthecolliderandisrequiredtobeheavier
thanN . Inparticular,thepairproductionofE−E+atLEPwith
3.3. FourthGenerationNeutrinoandDMDirectSearches 4 4 4
subsequent decay to SM particles and missing energy (in the
We now make a few comments on the implications of our formofneutrinoandDM)putsalowerlimitonitsmassscale
modelfordarkmattersearch. Asnoted,thecouplingbetween tobe[48]:
N and∆providesasmallMajoranamasstothe4thgeneration
4
ofneutrinos. Inthemassbasis,N1hasanoffdiagonalcoupling mE4 >101.9GeV and mE4 −mN4 ≡∆m>15GeV. (14)
withtheZ boson,preventingittobeexcludedbydirectdetec- Theeffectsofnewphysics,whichdoesnotnecessarilycou-
tionsearches.IfthemasssplittingisoftheorderofseveralkeV,
plestoSMfermions,manifestintheWandZbosonself-energies
theDMN actuallyhasenoughenergytoscatteroffnucleiand
1 andaremeasuredbythecorrectionstoobliqueparametersS,T
togointoitsexcitedstateN ,whichisthedefinitionofinelastic
2 andU. Thoseparametersarewellconstrainedbyelectroweak
scattering[49].
precision data and the allowed deviations from the SM model
The state of art for a 4th generation inelastic neutrino is
are[48]:
givenbyfigure3inthe{δ,m }-plane,wherethecross-section
N4
is fixed by the model, while the Majorana mass is allowed to ∆S =0.04±0.09 and ∆T =0.07±0.08 (15)
5
with∆U = 0,whichisagoodassumptionbecausetheoblique
contributionfroma4thgenerationto∆U isnegligible.
For a fourth generation of vector-like leptonic doublet the
100 obliquecorrectionsaregivenby:
0.02 0.02
0.001 1(cid:34)22y +14y 1 y 11y +1
∆S = 1 2 ln 1 + 1 f(y )
0.01 π 9 9 y 18 1
2
80 (cid:32) (cid:33)(cid:35)
7y −1 √ f(y )f(y )
+ 2 f(y )− y y 4+ 1 2 ,
2 1 2
8 2
(cid:76)V (cid:34)
(cid:45)(cid:72)mGeEN44 60 ∆T = 8π√s2θ1Wc2θW(cid:32)yy1++yy2−yy21y−1yy2(cid:33)2(cid:35)lnyy12
m + 2 y y 1 2 ln 1 −2 , (16)
(cid:61)m 40 0.005 1 2 y1−y2 y2
(cid:68)
having defined y = m2/m2 while s2 is the sine square of the
i i Z θW
Weinbergangle. Themasstermm referstothemassofthe4th
20 i
generationofleptons. Thefunction f(y)isdefinedas:
i
0 100 200 mN4(cid:72)Ge3V00(cid:76) 400 0.001500 f(yi)≡ −0(cid:112)2−(cid:112)∆∆(y(iy)i)ln(cid:32)a−r1c+ta√√n−∆√(y∆1i)(yi) −arctan √−∆1(yi)(cid:33) ∆∆∆(((yyyiii)))>=<000,,,
FTihgeurbela4c:kCsoonltiodulrinpelostifnodricthaeteosbolimqueerceoferrreecntcieonvsatloue∆sSfoinrt∆hSepalsanaef{umnNc4ti,o∆nmo}f. with∆(y) = −1+4y.−T1−hes−e∆r(eyis)ultsarederivedfrom[74]and
i i
the4thgenerationneutrinomassandoftheleptondoubletmasssplitting,as
agreewellwiththezeroYukawalimitin[42].
labelled.
Infigure4weshowtheobliquecorrectionstoS asafunc-
tionofm and∆m: theyarenegligiblysmallinalltheconsid-
N4
eredmassrangeandforabroadspectrumofmasssplittings.On
thecontrary,notefromfigure5that∆T issensitivetothemass
splitting between E and N only, and tends to zero for a de-
4 4
generatedoublet. Weconcludethatelectroweakprecisiondata
donotconstrainthemassrangeform ,whiletheyseverelyre-
E4
100 strict the mass splitting between the neutral and charged com-
ponent,whichcanbeatmost65GeVat3σ.
4.1. FourthGenerationLeptonsandColliderSearches
80
The nature of the vector-like doublet L makes it loosely
4
0.31 constrained by colliders; the drawback, however, is that it is
(cid:76)V
e elusiveasfarasitconcernsitsdetectionaswell. Theimposed
G 60 0.23
(cid:72) Z symmetry implies that in a collider the 4th generation lep-
N4 2
m
(cid:45) 0.15 tonsareproducedalwaysinaevennumber. Themostprobable
mE4 processes are (i) pair of charged fermions (E−E+) through the
(cid:61) 40 4 4
m exchangeofγ,Z bosons,(ii)combinationofchargedfermions
(cid:68) 0.07 plus its neutral partner E±N via the exchange of a W boson.
4 4
At LHC the W production is larger than the production of Z
20 bosonsandthepaircreationviatheprocessqq¯ → Z → N N¯
4 4
is reduced by almost two orders of magnitude with respect to
the production of a charged lepton plus its companion neu-
0 trino [75]. Therefore the dominant production rate of L par-
100 200 300 400 500 4
ticlesisthroughW boson,namelyviatheprocessqq(cid:48) →W →
mN4(cid:72)GeV(cid:76) E N . BecausethereisnomixingwiththeSMfermionicfami-
4 4
lies,E willdecaythroughtheprocessE → N W;ontheother
Figure5: Sameasfigure4fortheobliquecorrectionsto∆T. Aslabelled,the 4 4 4
blacksolidlinesindicatethecentralvalueaswellasthe1,2,3σcontours. handwerecallthatthe4thgenerationneutrinoisstable.
Incaseofpairproductionthewholeprocessispp→ E+E− →
4 4
N N¯ W+W−;subsequentlythepossiblefinalstatesare
4 4
1. onelepton+di-jetandmissingenergy,
6
2. twooppositelychargedleptonsandmissingenergy, [5] D.B.Kaplan,ASingleexplanationforboththebaryonanddarkmatter
3. 4di-jet+missingenergy, densities,Phys.Rev.Lett.68(1992)741–743.
[6] V.A.Kuzmin,ASimultaneoussolutiontobaryogenesisanddarkmat-
dependingonwhethertheWsdecayhadronically(mostproba- ter problems, Phys.Part.Nucl. 29 (1998) 257–265. arXiv:hep-ph/
9701269.
ble)ornot.
[7] M.Fujii,T.Yanagida,ASolutiontothecoincidencepuzzleofOmega(B)
In case the charged particles are produced along with its
and Omega (DM), Phys.Lett. B542 (2002) 80–88. arXiv:hep-ph/
neutralpartnerthecompleteprocessatLHCis pp → E4N4 → 0206066.
N N W. Thisresultsin [8] D.H.Oaknin,A.Zhitnitsky,Baryonasymmetry,darkmatterandquan-
4 4
tumchromodynamics,Phys.Rev.D71(2005)023519. arXiv:hep-ph/
1. di-jets+missingenergy, 0309086.
2. singlelepton+missingenergy. [9] D. Hooper, J. March-Russell, S. M. West, Asymmetric sneutrino dark
matterandtheOmega(b)/Omega(DM)puzzle,Phys.Lett.B605(2005)
228–236.arXiv:hep-ph/0410114.
Thesefinalstatesdonotrelyonaparticularsignatureratherit
[10] R.Kitano,I.Low,Darkmatterfrombaryonasymmetry,Phys.Rev.D71
willbelostinthehugeWbackgroundatLHC.Usually4thgen-
(2005)023510.arXiv:hep-ph/0411133.
eration of leptons are supposed to produce like sign di-lepton [11] N.Cosme,L.LopezHonorez,M.H.Tytgat,Leptogenesisanddarkmatter
signals,whichcanbewellseparatedfromthebackgroundwith related?,Phys.Rev.D72(2005)043505.arXiv:hep-ph/0506320.
[12] G. R. Farrar, G. Zaharijas, Dark matter and the baryon asymmetry,
the opportune cuts, however this holds only if the neutrino is
Phys.Rev.Lett.96(2006)041302.arXiv:hep-ph/0510079.
unstable and decays into the detector [76, 77]. Although N4 [13] L. Roszkowski, O. Seto, Axino dark matter from Q-balls in Affleck-
escapesundetectedatcolliders,itcanbeprobedbyDMdirect DinebaryogenesisandtheOmega(b)-Omega(DM)coincidenceprob-
searches. Constraintsona4thgenerationofleptonfromLHC lem,Phys.Rev.Lett.98(2007)161304.arXiv:hep-ph/0608013.
[14] J.McDonald, Right-handedsneutrinocondensatecolddarkmatterand
dataarebeyondthescopeofthispaper,howeverweremarkthat
thebaryon-to-darkmatterratio,JCAP0701(2007)001.arXiv:hep-ph/
thesemightbecarriedoutinasimilarwayasconstraintsonex- 0609126.
tra dimension have been sets by means of searches of exotic [15] D. E. Kaplan, M. A. Luty, K. M. Zurek, Asymmetric Dark Matter,
decaysofW bosons,seee.g.[78,79]. Phys.Rev.D79(2009)115016.arXiv:0901.4117.
[16] K.Kohri,A.Mazumdar,N.Sahu,P.Stephens,ProbingUnifiedOriginof
DarkMatterandBaryonAsymmetryatPAMELA/Fermi,Phys.Rev.D80
(2009)061302.arXiv:0907.0622.
5. Conclusions
[17] H. An, S.-L. Chen, R. N. Mohapatra, Y. Zhang, Leptogenesis as a
Common Origin for Matter and Dark Matter, JHEP 1003 (2010) 124.
In summary, we presented a simple extension of the stan-
arXiv:0911.4463.
dardmodelbytheadditionofavector-likemassiveleptondou- [18] M. T. Frandsen, S. Sarkar, Asymmetric dark matter and the Sun,
blet, wheretheneutralmemberofthedoublet N canplaythe Phys.Rev.Lett.105(2010)011301.arXiv:1003.4505.
4
[19] B.Feldstein,A.Fitzpatrick,DiscoveringAsymmetricDarkMatterwith
roleofadarkmatter,ifithasasmallMajoranamass. Boththe
Anti-Neutrinos,JCAP1009(2010)005.arXiv:1003.5662.
asymmetry in the lepton and dark matter sector are generated
[20] H.An,S.-L.Chen,R.N.Mohapatra,S.Nussinov,Y.Zhang,EnergyDe-
simultaneously via out-of-equilibrium decay of triplet scalars pendenceofDirectDetectionCrossSectionforAsymmetricMirrorDark
viatype-IIleptogenesis. Themodelseemstosatisfyallcosmo- Matter,Phys.Rev.D82(2010)023533.arXiv:1004.3296.
[21] T.Cohen,D.J.Phalen,A.Pierce,K.M.Zurek,AsymmetricDarkMat-
logical as well as laboratory constraints and has the potential
terfromaGeVHiddenSector,Phys.Rev.D82(2010)056001. arXiv:
toexplainthecurrentdarkmattersearchresults. Suchmodels 1005.1655.
couldalsobetheoreticallymotivatedbygrandunifiedtheories [22] J.Shelton,K.M.Zurek,Darkogenesis: Abaryonasymmetryfromthe
suchasE . darkmattersector,Phys.Rev.D82(2010)123512.arXiv:1008.1997.
6
[23] H.Davoudiasl,D.E.Morrissey,K.Sigurdson,S.Tulin,Hylogenesis: A
UnifiedOriginforBaryonicVisibleMatterandAntibaryonicDarkMat-
ter,Phys.Rev.Lett.105(2010)211304.arXiv:1008.2399.
Acknowledgements
[24] N.Haba, S.Matsumoto, BaryogenesisfromDarkSectorarXiv:1008.
2487.
One of the authors (RNM) would like to thank Z. Chacko
[25] P.-H. Gu, M. Lindner, U. Sarkar, X. Zhang, WIMP Dark Matter and
forsomediscussions.TheworkofRNMhasbeensupportedby BaryogenesisarXiv:1009.2690.
theNationalScienceFoundationgrantNo. PHY-0968854. CA [26] M.Blennow,B.Dasgupta,E.Fernandez-Martinez,N.Rius,Aidnogenesis
viaLeptogenesisandDarkSphalerons,JHEP1103(2011)014. arXiv:
issupportedbyaEuropeanCouncilStartingGrant,undergrant
1009.3159.
agreementNo. 277591,PIG.Bertone.
[27] J.McDonald,Baryomorphosis: RelatingtheBaryonAsymmetrytothe
’WIMPMiracle’,Phys.Rev.D83(2011)083509.arXiv:1009.3227.
[28] B.Dutta,J.Kumar,AsymmetricDarkMatterfromHiddenSectorBaryo-
References genesis,Phys.Lett.B699(2011)364–367.arXiv:1012.1341.
[29] N.Haba, S.Matsumoto, R.Sato, SneutrinoInflationwithAsymmetric
References DarkMatter,Phys.Rev.D84(2011)055016.arXiv:1101.5679.
[30] A. Falkowski, J. T. Ruderman, T. Volansky, Asymmetric Dark Matter
[1] e.Bertone,Gianfranco,Particledarkmatter: Observations,modelsand fromLeptogenesis,JHEP1105(2011)106.arXiv:1101.4936.
searches,Cambridge,UK,UniversityPress,2010. [31] E.J.Chun,MinimalDarkMatterandLeptogenesis,JHEP1103(2011)
[2] E.Komatsu,etal.,Seven-YearWilkinsonMicrowaveAnisotropyProbe 098.arXiv:1102.3455.
(WMAP)Observations:CosmologicalInterpretation,Astrophys.J.Suppl. [32] M. R. Buckley, Asymmetric Dark Matter and Effective Operators,
192(2011)18.arXiv:1001.4538. Phys.Rev.D84(2011)043510.arXiv:1104.1429.
[3] E.W.Kolb,M.S.Turner,TheEarlyuniverse,Front.Phys.69. [33] M.L.Graesser, I.M.Shoemaker, L.Vecchi, AsymmetricWIMPdark
[4] S.Dodelson,B.R.Greene,L.M.Widrow,Baryogenesis,darkmatterand matter,JHEP1110(2011)110.arXiv:1103.2771.
thewidthoftheZ,Nucl.Phys.B372(1992)467–493. [34] H.Iminniyaz,M.Drees,X.Chen,RelicAbundanceofAsymmetricDark
7
Matter,JCAP1107(2011)003.arXiv:1104.5548. [63] Y.Cui,D.E.Morrissey,D.Poland,L.Randall,CandidatesforInelastic
[35] J.J.Heckman,S.-J.Rey,BaryonandDarkMatterGenesisfromStrongly DarkMatter,JHEP0905(2009)076.arXiv:0901.0557.
CoupledStrings,JHEP06.arXiv:1102.5346. [64] E.K.Akhmedov,A.Wilhelm,Quantumfieldtheoreticapproachtoneu-
[36] J.March-Russell,M.McCullough,AsymmetricDarkMatterviaSponta- trinooscillationsinmatter.arXiv:1205.6231.
neousCo-Genesis,JCAP1203(2012)019.arXiv:1106.4319. [65] C. Arina, Chasing a consistent picture for dark matter direct searches,
[37] H. Davoudiasl, R. N. Mohapatra, On Relating the Genesis of Cosmic Phys.Rev.D86(2012)123527.arXiv:1210.4011.
Baryons and Dark Matter, New J.Phys. 14 (2012) 095011. arXiv: [66] R. Bernabei, P. Belli, F. Cappella, R. Cerulli, C. Dai, et al., New re-
1203.1247. sults from DAMA/LIBRA, Eur.Phys.J. C67 (2010) 39–49. arXiv:
[38] J.March-Russell,J.Unwin,S.M.West,ClosinginonAsymmetricDark 1002.1028.
MatterI:Modelindependentlimitsforinteractionswithquarks, JHEP [67] M.Buchkremer,J.-M.Gerard,F.Maltoni,Closinginonaperturbative
1208(2012)029.arXiv:1203.4854. fourthgeneration,JHEP1206(2012)135.arXiv:1204.5403.
[39] P.-H.Gu,FromDiracneutrinomassestobaryonicanddarkmatterasym- [68] O.Eberhardt,G.Herbert,H.Lacker,A.Lenz,A.Menzel,etal.,Impact
metriesarXiv:1209.4579. ofaHiggsbosonatamassof126GeVonthestandardmodelwiththree
[40] R. Mohapatra, X. Zhang, Restrictions on B-L symmetry breaking im- andfourfermiongenerations.arXiv:1209.1101.
pliedbyafourthgenerationneutrino,Phys.Lett.B305(1993)106–108. [69] S.Bar-Shalom,M.Geller,S.Nandi,A.Soni,TwoHiggsdoublets,a4th
arXiv:hep-ph/9301286. generationanda125GeVHiggs.arXiv:1208.3195.
[41] B. Holdom, W. Hou, T. Hurth, M. Mangano, S. Sultansoy, et al., [70] L. Bellantoni, J. Erler, J. J. Heckman, E. Ramirez-Homs, Masses of
FourStatementsabouttheFourthGeneration,PMCPhys.A3(2009)4. a Fourth Generation with Two Higgs Doublets, Phys.Rev. D86 (2012)
arXiv:0904.4698. 034022.arXiv:1205.5580.
[42] A.Joglekar,P.Schwaller,C.E.Wagner,DarkMatterandEnhancedHiggs [71] A.Djouadi,A.Lenz,Sealingthefateofafourthgenerationoffermions,
toDi-photonRatefromVector-likeLeptons.arXiv:1207.4235. Phys.Lett.B715(2012)310–314.arXiv:1204.1252.
[43] H.-S.Lee,A.Soni,FourthGenerationParity.arXiv:1206.6110. [72] M.E.Peskin,T.Takeuchi,Estimationofobliqueelectroweakcorrections,
[44] P.H.Frampton,P.Hung,M.Sher,Quarksandleptonsbeyondthethird Phys.Rev.D46(1992)381–409.
generation,Phys.Rept.330(2000)263.arXiv:hep-ph/9903387. [73] L.M.Carpenter,A.Rajaraman,RevisitingConstraintsonFourthGen-
[45] M.Geller,S.Bar-Shalom,G.Eilam,A.Soni,The125GeVHiggsinthe eration Neutrino Masses. , Phys.Rev. D82 (2010) 114019. arXiv:
contextoffourgenerationswith2Higgsdoublets,Phys.Rev.D86(2012) 1005.0628.
115008.arXiv:1209.4081. [74] L.Lavoura,J.P.Silva,TheObliquecorrectionsfromvector-likesinglet
[46] H.An,T.Liu,L.-T.Wang,125GeVHiggsBoson,EnhancedDi-photon anddoubletquarks,Phys.Rev.D47(1993)2046–2057.
Rate, and Gauged U(1)PQ-Extended MSSM, Phys.Rev. D86 (2012) [75] L.M.Carpenter,A.Rajaraman,D.Whiteson,SearchesforFourthGener-
075030.arXiv:1207.2473. ationChargedLeptons.arXiv:1010.1011.
[47] J.Erler,P.Langacker,PrecisionConstraintsonExtraFermionGenera- [76] L.M.Carpenter,FourthGenerationLeptonSectorswithStableMajorana
tions,Phys.Rev.Lett.105(2010)031801.arXiv:1003.3211. Neutrinos:FromLEPtoLHC.arXiv:1010.5502.
[48] J. Beringer, et al., Review of Particle Physics (RPP), Phys.Rev. D86 [77] A. Rajaraman, D. Whiteson, Tevatron Discovery Potential for Fourth
(2012)010001. Generation Neutrinos: Dirac, Majorana and Everything in Between. ,
[49] D.Tucker-Smith,N.Weiner,Inelasticdarkmatter,Phys.Rev.D64(2001) Phys.Rev.D82(2010)051702.arXiv:1005.4407.
043502.arXiv:hep-ph/0101138. [78] G.Aad,etal.,SearchfornewphenomenaintheWWtolnul’nu’final
[50] C.Arina,N.Sahu,AsymmetricInelasticInertDoubletDarkMatterfrom stateinppcollisionsatsqrt(s)=7TeVwiththeATLASdetector.arXiv:
TripletScalarLeptogenesis,Nucl.Phys.B854(2012)666–699. arXiv: 1208.2880.
1108.3967. [79] CMS,Searchforrandall-sundrumgravitonsdecayingintoajetplusmiss-
[51] C.Arina,J.-O.Gong,N.Sahu,Unifyingdarko-lepto-genesiswithscalar ingetatcms,CMSexoticapublicphysicsresults,2011run,CMS-PAS-
tripletinflation,Nucl.Phys.B865(2012)430–460.arXiv:1206.0009. EXO-11-061.
[52] J.A.Harvey,M.S.Turner,Cosmologicalbaryonandleptonnumberin
the presence of electroweak fermion number violation, Phys.Rev. D42
(1990)3344–3349.
[53] E.Aprile,etal.,DarkMatterResultsfrom225LiveDaysofXENON100
Data,Phys.Rev.Lett.109(2012)181301.arXiv:1207.5988.
[54] G.Angloher,M.Bauer,I.Bavykina,A.Bento,C.Bucci,etal.,Results
from730kgdaysoftheCRESST-IIDarkMatterSearch,Eur.Phys.J.C72
(2012)1971.arXiv:1109.0702.
[55] S.Kim,H.Bhang,J.Choi,W.Kang,B.Kim,etal.,NewLimitsonInter-
actionsbetweenWeaklyInteractingMassiveParticlesandNucleonsOb-
tainedwithCsI(Tl)CrystalDetectors,Phys.Rev.Lett.108(2012)181301.
arXiv:1204.2646.
[56] H.-S.Lee,Z.Liu,A.Soni,Neutrinodarkmattercandidateinfourthgen-
erationscenarios,Phys.Lett.B704(2011)30–35.arXiv:1105.3490.
[57] Y.-F.Zhou,ProbingthefourthgenerationMajorananeutrinodarkmatter,
Phys.Rev.D85(2012)053005.arXiv:1110.2930.
[58] S.Fukuda,etal.,Constraintsonneutrinooscillationsusing1258daysof
Super-Kamiokandesolarneutrinodata,Phys.Rev.Lett.86(2001)5656–
5660.arXiv:hep-ex/0103033.
[59] Q.Ahmad,etal.,Measurementofdayandnightneutrinoenergyspectra
atSNOandconstraintsonneutrinomixingparameters,Phys.Rev.Lett.89
(2002)011302.arXiv:nucl-ex/0204009.
[60] K. Eguchi, et al., A High sensitivity search for anti-nu(e)’s from the
sunandothersourcesatKamLAND,Phys.Rev.Lett.92(2004)071301.
arXiv:hep-ex/0310047.
[61] M.R.Buckley, S.Profumo, RegeneratingaSymmetryinAsymmetric
DarkMatter,Phys.Rev.Lett.108(2012)011301.arXiv:1109.2164.
[62] M. Cirelli, P. Panci, G. Servant, G. Zaharijas, Consequences of
DM/antiDM Oscillations for Asymmetric WIMP Dark Matter, JCAP
1203(2012)015.arXiv:1110.3809.
8