Vector Higgs-portal dark matter and the invisible Higgs

0.25 MB·English

by  Oleg Lebedev

CERN-PH-TH-2011-271, DESY 11-202, LPT–Orsay 11/90
Vector Higgs–portal dark matter and the invisible Higgs
Oleg Lebedeva,∗ Hyun Min Leeb,† and Yann Mambrinic‡
a DESY Theory Group, Notkestrasse 85, D-22607 Hamburg, Germany
b CERN, Theory Division, CH-1211 Geneva 23, Switzerland and
c Laboratoire de Physique Th´eorique Universit´e Paris-Sud, F-91405 Orsay, France
The Higgs sector of the Standard Model offers a unique probe of the hidden sector. In this
work,weexplorethepossibility ofrenormalizable Higgscouplingstothehiddensectorvectorfields
whichcanconstitutedarkmatter(DM).Abeliangaugesectorswithminimalfieldcontent,necessary
to render the gauge fields massive, have a natural Z2 parity. This symmetry ensures stability of
the vector fields making them viable dark matter candidates, while evading the usual electroweak
constraints. We illustrate this idea with the Stu¨ckelberg and Higgs mechanisms. Vector DM is
consistent with the WMAP,XENON100, and LHC constraints, while it can affect significantly the
2
invisibleHiggsdecay. DuetotheenhancedbranchingratiofortheHiggsdecayintothelongitudinal
1
components of the vector field, the vector Higgs portal provides an efficient way to hide the Higgs
0
at the LHC. This could be the reason why the latest combined ATLAS/CMS data did not bring
2
evidencefor theexistence of theHiggs boson.

n
a
J
I. INTRODUCTION II. VECTOR HIGGS PORTAL

0
1
Two of the most important issues in particle physics The Higgs sector offers a unique opportunity to probe

] phenomenologyarethenatureofdarkmatterandunder- the hidden sector. The operator H¯H is the only dim-
h
standing electroweaksymmetry breaking. While 85%of 2 gauge and Lorentz invariant operator in the Standard
p
- matter is dark [1], it remains elusive to direct detection model. Thereforerenormalizableinteractionsoftheform
p and the Weakly Interacting Massive Particle (WIMP)
e paradigm becomes more and more constrained [2]. On ∆ = λhs H¯H (S2+m S) (1)
h scalar hs
L 4
the other front, the accelerator collaborations ATLAS
[
[3, 4], CMS [5] and D0/CDF [6, 7] have obtained impor- are possible, where S is a hidden sector (real) scalar.
3 tant results concerning the Higgs searches. If the Higgs These are known as the scalar “Higgs portal” (the name
v
2 bosonisthemaincommunicatorbetweenthedarkworld was coined in [10]). More generally, one can also have a
8 and ours, Higgs hunting is intimately related to direct dim-4 vector Higgs portal, which couples the Higgs dou-
4 DM detection. To reconcile all the constraints is then blet to a massive vector field X from the hidden sector,
µ
4 a non–trivial task [8] (see also [9] for more general sce-
11. ncoanritoesx)t.oWf shcearleaars(tohrisfeirdmeaioins)ndoarrmkamllyatctoern,siidnetrhedisiwnotrhke, ∆Lvector = λ4hv H¯H XµXµ+(ξ1 H¯iDµH Xµ
1 westudythepossibilityofvectorialdarkmatterinteract- +ξ H¯H i∂ Xµ+h.c.), (2)
1 ing with the visible sector through the Higgs portal. We 2 µ
: show that this framework is well motivated theoretically
v where the covariant derivative D is taken with respect
and,whilebeingconsistentwiththeexistingconstraints, µ
i to the Standard Model (SM) gauge group.1 X can be
X can affect significantly the ongoing Higgs search at the µ
associatedwithahiddenU(1). Itbecomesmassivedueto
r LHC.
a theHiggsorStu¨ckelbergmechanisminthehiddensector.
The paper is organizedas follows: in section II we intro-
Ahiddenvectorfieldcanbeagooddarkmattercandi-
duce the vector Higgs portal and provide its theoretical
date. Supposeitsdecayintothehiddensectoriskinemat-
basis; in section III we study relevant dark matter and
icallyforbiddenandtheonlycommunicationwiththeSM
accelerator constraints, and discuss implications for the
isgivenbyEq.2. Itisthenstableifξ arezero,inwhich
LHC Higgs search; our conclusions are presented in sec- 1,2
casetheHiggsportalhasaZ symmetryX X . In
tion IV. 2 µ →− µ
principle, X can also be made long–lived by adjusting
µ
ξ and ξ to be very small. In particular, if there are
1 2
fields charged under the U(1) apart from those provid-
ing longitudinal components of the gauge bosons, these
terms are usually generated and it requires non–trivial
engineeringtomakeX stableonthecosmologicalscale.
µ
∗ [email protected]
† [email protected] 1 For generality, wehave includedthe ∂µXµ term, whichmay be
‡ [email protected] relevantinmodelswithfield–dependent massterms.
2
Inthe absenceofsuchchargedfields, the Lagrangianen- (ii) Consider another example, where H¯HX Xµ is
µ
joys a natural Z parity which makes X stable. This generated through the singlet Higgs portal. Take
2 µ
applies both to the Higgs and the Stu¨ckelberg mecha-
nisms. Let us consider examples, starting with the less m2 =µ2 S2 , (8)
common Stu¨ckelberg dark matter. M2
where S is a hidden sector scalar with a potential V(S)
and a Higgs portal coupling (λ /4)H¯HS2. We have
hs
A. Examples: Stu¨ckelberg and “Higgsed” dark factoredoutµ2 inorderto haveasmoothmasslesslimit.
matter Obviously,integratingoutheavyS attreelevelproduces
the required coupling with
Consider a U(1) vector field which becomes massive µ2 S 2
through the Stu¨ckelberg mechanism (for a review, see λ =2λ h i , (9)
hv hs M2m2
[11]), S
where m is the mass of S. Note that λ can also be
1 1 S hv
LSt =−4FµνFµν + 2m2XµXµ , (3) wourtittisenjuassti2fiλehdsmas2Xl/omng2S.asThme2p,mro2ceduremo2f.inItnegpraraticntgiseS,
h X ≪ S
where X is composed of a vector potential X′ and a these quantities candiffer by,say,anorderofmagnitude
µ µ so that λ can be as large as (10−1 1). In the same
Stu¨ckelberg axion–like field φ with the following gauge hv O −
fashion, self–interaction
transformation rule
1 µ4 S 2
Xν ≡Xν′ + µ1 ∂νφ, 2 Mh4mi2S (XµXµ)2 (10)
δXν′ =∂νǫ, is also induced. Note also that the physical Higgs boson
δφ= µǫ. (4) mixeswithSinthisexample,withthemixinganglebeing
−
of order v/ S .
h i
Here µ is a mass scale and ǫ is a gauge transfromation Furthermore, at one loop, both H¯H X Xµ and
µ
parameter. NotethattheLagrangianpossessesasymme- (X Xµ)2 aregeneratedwith(formally)log–divergentco-
µ
try Xµ Xµ, which in terms of the original variables efficients. Keeping in mind that we are dealing with an
reads X→µ′ →−−Xµ′, φ→−φ.2 Taking µ=m corresponds effectivetheory,theseareregularizedbythecutoffwhich
to choosing a canonical kinetic term for the axion. In is expected to be of order M. This implies that λ can
hv
general, however, m2 can be field–dependent, in which be taken as a free parameter at low energies.
case the axion kinetic term involves a function of other
As the Higgs doublet develops a VEV, an additional
fields of the system. Expressing
mass termλ v2/2 for the vectoris generated. It canbe
hv
m2 =µ2f(S), (5) of either sign, as seen from the above examples. There-
fore some cancellation between the original Stu¨ckelberg
mass and the Higgs–induced one is allowed.
with S being a scalar, we recover the axion kinetic term
1/2f(S)(∂ φ)2 in the massless limit µ 0. Consider 2 It is important that the linear in X terms vanish in
µ µ
→
simple possibilities. these examples,
(i) One may allow for a Higgs–dependent mass term
ξ =ξ =0. (11)
1 2
H¯H
m2 =µ2 1+ζ , (6) This is because, in the absence of fields charged under
M2 U(1) (apart from the axion absorbed in X ), the La-
(cid:18) (cid:19) µ
grangianpossesses a natural parity
where M is another scale. In this case, the Higgs portal
coupling H¯HX Xµ is generated with X X . (12)
µ µ µ
→−
µ2 Note that here we consider a U(1) “orthogonal” to the
λhv =2ζ M2 . (7) SM gaugegroup,so there is no mixing with hypercharge
attree level, nor is it induced radiatively. Thus,the new
ApriorineitherofthesescalesisrelatedtotheEWscale, vector boson evades the usual electroweak constraints.
nor to each other so that λ can be significant.
hv Some of the ingredients of this construction are well
known in string theory. In particular, most of realistic
models(seee.g. [12])involvean“anomalous”U(1)whose
anomaly is cancelled by the Green–Schwarz mechanism.
2 Thissymmetryisalsopreservedbythegaugefixingterm. In this process, the U(1) gauge boson becomes massive
3
through the Stu¨ckelberg mechanism. The corresponding (a2 b)E2 for E m . Note that in the Standard
A∼ − v2 ≫ X
axion has a dilaton–dependent kinetic term, so that the Model an analogous amplitude vanishes, whereas here it
vector mass term in Planck units is (see e.g. [13]) is proportional to the “non–Higgs” mass term m2. Re-
quiringthepartialwaveamplitudea tobelessthan1/2
0
2
1 1 (see e.g. [14]) and ignoring order 1 factors, we find that
δ X ∂ a , (13)
4s2 2 µ− µ the unitarity cutoff is of order
(cid:18) (cid:19)
whereaandsaretheaxionandthedilaton,respectively, 16πm2
E X . (17)
andδisaGreen–Schwarzparameter. Itisthereforequite
∼ λ m
natural to expect a field–dependent vector boson mass, r hv
althoughintypicalstringconstructionsthismassisclose Abovethisenergy,additionalstatesshouldbetakeninto
to the Planck scale. account. Further, the amplitude for XX XX pro-
→
ceeding through the Higgs exchange approaches a con-
(iii)Finally,onecanequallywellusetheHiggsmecha-
stant at E m ,m , which imposes m >λ v/√8π.
nisminthehiddensector. SupposewehaveaU(1)gauge ≫ h X X hv
Finally,inthepresenceofX self–interaction,unitarityin
field and a chargedcomplex scalar S, which has a scalar
XX XX requires roughly E < (8π/λ)1/4m , where
Higgs portal coupling, → X
λ is the X quartic coupling.
1 λ
= F Fµν+D S∗DµS V(S)+ hsH¯HS∗S . We see that there is a fundamental difference between
Higgs µν µ
L −4 − 4 the vector and scalar Higgs portals: the former is UV–
(14)
incomplete, whereas the latter is UV–complete. In the
This system enjoys a symmetry (charge conjugation)
vector case, some amplitudes grow indefinitely with en-
ergy meaning that the Higgs portal description breaks
X′ X′ ,
µ →− µ down. This can be traced back to the derivative cou-
S S∗ , (15) plings of the Goldstone bosons (or longitudinal polariza-
→
tion vectors growing with energy) and the fact that m2
where X′ is the massless gauge field.3 This symmetry is
µ appears as a “hard” mass term. Only in the full the-
retained in the broken phase, that is, the massive gauge
ory, which contains extra states, is the “soft” origin of
field can be reversed: Xµ Xµ. The physical Higgs– m2 manifest. In contrast, the scalar mass term is not
→ −
like excitation has no interactions which are odd under
problematicandthescalarHiggsportalisUV–complete.
X X , so integrating it out in the unitary gauge
µ µ
→ −
will only produce even interactions and ξ = 0. On
1,2
the otherhand, H¯HX Xµ is generatedatboth tree and
µ III. PHENOMENOLOGY
loop level, the latter being log–divergent. Note that the
vector field remains light as long as g2 λ , where g is
S
≪
the gaugecoupling and λS is the singlet self–interaction. The relevant Z2–symmetric Lagrangianis given by
Otherwise, the analysis is very similar to that of the
Stu¨ckelberg case. = λhv H¯H X Xµ+ 1m2X Xµ+ λ(X Xµ)2 . (18)
µ µ µ
L 4 2 4
It is important to remember that these examples are
validwithin effective field theory. Indeed, we either inte- Note that upon EW symmetry breaking the mass of the
grate out a heavy “hidden Higgs” or use higher dimen- vector field is m = m2+λ v2/2. In what follows,
X hv
sional operators for the field–dependent kinetic terms. we will take an agnostic attitude to the origin of the
The range of validity of the effective description can be various terms and willpsimply scan over λ and m to
hv X
estimatedfromunitarityconsiderations. Thevectorpor- see their phenomenological implications (see also [15]).
tal coupling together with the m2 mass term from the We setλ=0forsimplicity andallowforλ upto order
hv
hidden sector results in one,whichisconsistentwithperturbativityupto10TeV
1 2h h2 orso. Sincetherelevantratesdependonλ2hv,intheplots
∆ = m2 1+a +b X Xµ , (16) we will only display the absolute value of λ , whereas
LX 2 X v v2 µ hv
it is understood that its contribution to m can be of
(cid:16) (cid:17) X
where the Higgs field is decomposed as H0 =v+h/√2; both signs. Finally, reliable computations can be made
m2 = m2 + 1λ v2 and a/√2 = b = λhvv2. This form as long as the unitarity constraint (17) is satisfied. For
X 2 hv 4m2X light X, we require the theory to be valid up to the EW
isusefulforcomparisonwiththeStandardModelHiggs–
scale v, whereas for heavy X we take the cutoff to be
vector scattering. The tree level amplitude for the pro- ∼
of order 2m .
X
cess hh XX (and hX hX) grows with energy as
→ → In our numerical analysis, we have adapted the code
Micromegas [16] to our model in order to compute the
thermal WIMP relic abundance. We have also modified
3 Notethatthisparitydoesnotgeneralizetothenon–abeliancase thedirectdetectioncrosssectiontotakeintoaccountre-
duetothetriplegaugebosonvertex. centlatticeresultsonthequarkstructureofthenucleon,
4
Xµ Xµ λ
hv
Xµ
Xµ
SM
MIN
h h Lattice
h
MAX
Xµ SM Xµ 1
q q
<σv> σXS−IP ΓHinv
FIG. 1. Feynman diagrams for DM annihilation (left), direct de-
tection(center) andinvisibleHiggsdecay(right). WMAP
−1
10
which appear more reliable than those extracted from XENON1T
the pion–nucleon cross section. Concerning the Higgs
physics, we use the code Hdecay [17] to compute the
Higgs decay widths.
−2
10
50 100 150 200
m (GeV)
A. Direct detection and relic abundance X
constraints
FIG. 2. Parameter space allowedbyWMAP (between the “gull–
shaped”curves)andXENON100formh=150GeV,andprospects
TheHiggsportalcouplingallowsthe vectorialdarkmat-
forXENON1T.
ter to annihilate into the light Standard Model species
as well as to scatter off nuclei through the Higgs ex-
change. Fig.1 displays the relevant types of Feynman
m 2m , which implies lower values of the coupling
diagrams. (Numerically, we also take into account anni- h X
≃
hilation through the quartic vertex X Xµhh which can λhv. In Fig. 2, we also display the XENON100 con-
µ
be efficientatm &m , althoughwealwaysfinditsub- straint on the DM–nucleon interaction [2]. The spin–
X h
dominant.) independent cross section is given by
Someaspectsoftheanalysisaresimilartothoseofthe λ2 m4 f2
scalar singlet extension of the SM. The latter was stud- σVSI−N = 16πhmv 4 (m +N mN )2 , (20)
ied in [15, 18–33]. Using this framework, some authors h X N
haveattempted toexplainthe DAMA and/orCOGENT where m is the nucleon mass and f parametrizes the
N N
excess [34–36]. Others have studied its implications for Higgs–nucleon coupling. The latter subsumes contribu-
indirectsearches[37–39] andconstraintsfromthe earlier tions of the light quarks (f ) and heavy quarks (f ),
L H
XENON data [40–42]. In what follows, we analyze the f = f +3 2 f . There exist different estima-
N L × 27 H
sameconstraintsintheframeworkofvectorialdarkmat- tions of this factor and in what follows we will use the
ter. We note that some phenomenologicalaspects of the latticePresultf =0.326[45]aswellasthe MILC results
N
vectorHiggsportalwerestudiedin[15],whilevectordark [46] which provide the minimal value f = 0.260 and
N
matter in somewhat different contexts was considered in the maximal value f = 0.629. Since the cross section
N
[43],[44]. is rather sensitive to f , we dispay 3 curves correspond-
N
The relic abundance of DM is dictated by the s– ing to these benchmark values. The region above these
channel annihilation through the Higgs exchange. For curves is excluded by XENON100, so the maximal al-
example, the cross section for annihilation into fermions lowed value for λhv at mh = 150 GeV is a few times
is given by 10−1. This is still consistent with WMAP, especially
aroundtheresonantannihilationregion. Wealsoseethat
λ2 m2 (1 m2/m2 )3/2 essentially the entire parameter space will be probed by
hσff¯vi= h4v8πf (4−m2f mX2)2 . (19) XENON1T.Ourresults agreewellwith those of[15] (up
X − h to the XENON100bound whichwasnot availableatthe
time of publication of [15]).
The calculational procedure is well known (see e.g. [15])
and here we will only quote the result. The 5σ WMAP– Finally, we have checked that the unitarity constraint
allowed [1] parameter space λ ,m for m = 150 (17)issatisfiedintheentireWMAP–allowedband,apart
hv X h
{ }
GeV is shown in Fig. 2 between the two “gull–shaped” from the region λ > 1 where DM is light. For λ
hv hv
curves. As in any Higgs portal model, DM annihila- 10−2, the cutoff is almost 2 orders of magnitude abov∼e
tionbecomes muchmoreefficientaroundthe Higgspole, m .
X
5
Inwhatfollows,wewillusetheXENON100constraint
based on the lattice evaluation of f .
N
B. Implications for the Higgs search
Ifthemassofthedarkmatterparticleislessthanahalf
of the Higgs boson mass, dark matter can efficiently be
produced in the “invisible” Higgs decay h XX. This
→
wouldaffecttheHiggsdecaybranchingratios,whileleav-
ing the production cross section unchanged. The partial
widthfortheHiggsdecayintovectordarkmattercanbe
read off from (16),
λ2 v2m3 m2 m4
Γinv = hv h 1 4 X +12 X
h→XµXµ 256πm4 − m2 m4
X (cid:18) h h(cid:19)
m2
1 4 X , (21)
×s − m2h
where v = 174 GeV. We observe that this width grows
fast with the Higgs mass, m3. This is because the
∝ h
decay rate into the longitudinal components of the vec-
torfieldor,equivalently,thewould–beGoldstonebosons,
grows with energy due to the derivative couplings of the
latter. This is to be contrasted with the decay rate into
the usual scalars which decreases with the Higgs mass.
Thus evena smallcouplingλ canleadto a largeinvis-
hv
ible branching fraction for a light X. In Fig. 3, we show
theresultofourscanover(m , m , λ )takingintoac-
h X hv
count the WMAP and XENON100 constraints. We find
that points with a large, up to 85%, invisible branching
ratio survive for low Higgs masses. There is a sharp fall
in BRinv around 160 GeV, when the h WW mode is
→ FIG. 3. Branching ratio for the Higgs invisible decay as a func-
in full force. The lightest m consistent with WMAP
X tion of the Higgs mass (top) and the dark matter mass (bottom).
and XENON100 is close to mh/2, in which case λhv is The scan is over (mh, mX, λhv) and subject to the WMAP and
smaller than the gauge coupling and the invisible decay
XENON100constraints.
is subdominant. Nevertheless,BRinv canstillbe aslarge
as 20-30%.
h αα is reduced by a factor of . Consequently, the
C. LHC constraints ev→entratesusedintheATLAS/CMRSanalysis[3,4]would
be overestimatedby 1/ and the actual exclusion limits
R
would be weaker. For example, m & 141 GeV is no
The invisible Higgs decay into dark matter can have a h
longer ruled out by ATLAS/CMS.
significantimpactonthe Higgssearchatthe LHC.Since
the standard Higgs decay modes such as γγ, bb, etc. are Fig. 4 displays the result of our scan over mX and λhv
not affected, the effective branching ratiofor a givenSM subject to the WMAP, XENON100 and ATLAS/CMS
decay h αα decreases by a factor of , constraints. For each mh, we find appropriate mX and
→ R
λ such that the WMAP and XENON100 constraints
hv
BR(h→αα)SM+Xµ =R Br(h→αα)SM , (22) aresatisfiedandrecalculatethecrosssectionforqq/gg →
h αα. We find that the invisible decay branching
where →
ratio can be as large as 85% for m up to 150 GeV.
h
= ΓtSoMt . (23) For mh > 160 GeV it drops to 20-30%, in which case
R Γtot +Γ(h X X ) thedecayisalmostSM–likeandthecorrespondingHiggs
SM → µ µ mass range is largely excluded by ATLAS/CMS. Note,
Sincetheproductionmodesqq/gg hremainthesame, however, that the window 230 250 GeV is still open
→ −
the “measured” cross section for the process qq/gg and consistent with all the constraints.
→
6
similar, there is an important difference in the invisible
decay of the Higgs. While the DM scattering cross sec-
tion on nucleons is the same in both cases (for the same
couplings and masses),
λ2 m4 f2
σSI = hs N N , (24)
S−N 16πm4 (m +m )2
h S N
the invisible Higgs width for scalars is
λ2 v2 m2
Γinv = hs 1 4 S , (25)
h→SS 64πmhs − m2h
where λ is the analog of λ (see Eq. 1). Unlike in the
hs hv
vectorcase(21), the decayrate decreaseswith the Higgs
mass. As we mentioned before, this difference has to do
withthenatureofmassivevectorfields,whichabsorbthe
would–be Goldstone bosons. This results in a higher de-
cay rate at higher energies, i.e. for a heavier Higgs. The
decay rate into vectors is enhanced by m4/m4 , which
h X
is a large factor for a light X. In the region of interest
to us, m 2m and the enhancement is an order of
h X
∼
magnitude. There are also other numerical differences
in the scalar versus vector dark matter. For example,
WMAP requires roughly twice as large λ as λ . This
hv hs
is because the annihilation cross section for scalars is
λ2 m2 (1 m2/m2)3/2
hσff¯vi= h1s6πf (4−m2f mS2)2 , (26)
S − h
which is triple that for vectors (due to averaging over
polarizations)4 with the same couplings and masses. Fi-
nally,the phasespacecoefficientsinΓinv aredifferentfor
vectors and scalars. We find that these factors compen-
sateeachother andthe originalesimate m4/m4 gives
∼ h X
FIG.4. BranchingratiofortheinvisibleHiggsdecayasafunction approximately the right answer. To give an example, at
ofthe Higgsmass (top) andthe darkmatter mass(bottom). The mh = 170 GeV the WMAP/XENON100 constraints are
scanisover(mh,mX,λhv)andsubjecttotheWMAP,XENON100 satisfied for λhs = 0.13 and mS = 71 GeV. The corre-
andATLAS/CMSconstraints. sponding BRinv is 2%. The vector counterpart of this
example is λ = 0.21 and m = 72 GeV, which gives
hv X
BRinv = 25%. As expected, the invisible decay is an
order of magnitude more efficient for the vectors.
The lower bound on m is determined roughly by
X Although Γinv for vectors is much larger than that for
m m /2fortheminimalpossiblem ,whichisabout
X ∼ h h scalars, the effect on BRinv = Γinv/(Γinv +Γvis) is less
50 GeV. Higher masses m > m /2, up to TeV, are al-
X h significant if the Higgs decays predominantly into dark
lowedbyalltheconstraints. However,theinvisibledecay
matter. At m < 150 GeV, the maximal BRinv for vec-
is inefficient in this case. h
tors is 85% while that for scalars is 65% (excluding the
Finally, let us remarkthat if one gives upthe assump- specialcaseofverylight 5GeVDM).Weillustratethis
tionofthermallyproducedvectordarkmatter,BRinvcan in Fig. 5 which displays∼BRinv consistent with WMAP,
be even larger.
XENON100 and ATLAS/CMS constraints for the scalar
case.5 Notethat,uptotheabovereservations,theHiggs
D. Comparison with scalar dark matter
4 At low energies, the vector field can also be viewed as a set of
3 types of scalars which can only annihilate with scalars of the
Analogous analyses have recently appeared in the
sametype. Thisreducestheannihilationcrosssectionbyafactor
framework of scalar dark matter interacting with the of3.
StandardModelthroughthe Higgsportal[8,47–50]. Al- 5 ThestripatthetopcorrespondstoverylightscalarDMstudied
though in many respects the scalar and vector cases are in[35].
7
invisible decay is inefficient for a heavy Higgs.
Animportantdifferencebetweenthe vectorandscalar
cases is that in the former case very light dark matter is
not allowedby unitarity. For m 5 GeV and λ 1,
X hv
∼ ∼
theunitaritycutoffisless10GeVmeaningthattheHiggs
portalisnotasensibledescriptionofthecompletemodel.
Additional states must be invoked to restore unitarity,
which in turn would modify our DM analysis. This also
applies to the case of m 50 GeV, λ 2 WMAP–
X hv
∼ ∼
allowedregion(Fig.2),wherethecutoffisbelowtheEW
scale.
IV. CONCLUSION
We have studied the possibility that dark matter is of
vectorialnature and it communicates with the Standard
Modelthroughthe Higgs portal. We find this possibility
well motivated because abelian gauge theories with the
minimal field content, which is necessary to render the
vectorfieldsmassive,possessanaturalZ parity(charge
2
conjugation) making dark matter stable. Vector dark
matter is consistent with cosmological and direct detec-
tion constraints, and can lead to invisible Higgs decay.
The latteris enhancedcomparedto the scalardarkmat-
ter case and provides an efficient way to hide the Higgs
at the LHC. A combination of sensitive direct detection
experiments (XENON1T) and further collider searches
will probe most of parameter space of this scenario.
Acknowledgements. Theauthorswouldliketothank
particularlyM. Kado andJ.B. Devivie for their valuable
help with the combined ATLAS/CMS analysis. Y.M.
thanks E. Bragina and the Magic Monday Journal Club
for very useful discussions and comments. We are also
grateful to S. Pukhov for his help in solving technical
FIG. 5. Branchingratioforthe invisibleHiggsdecay into scalars problems related to micrOMEGAs. This work was sup-
as a function of the Higgs mass (top) and the dark matter mass ported by the French ANR TAPDMS ANR-09-JCJC-
(bottom). The scan is over (mh, mS, λhs) and subject to the 0146andtheSpanishMICINNsConsolider-Ingenio2010
WMAP,XENON100andATLAS/CMSconstraints. Programmeunder grantMulti- Dark CSD2009-00064.
HMLispartiallysupportedbytheCERN-Koreanfellow-
ship.
mass window 230 250 GeV is not available since the
−
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