The Flavour Portal to Dark Matter

0.59 MB·English

by  Lorenzo Calibbi

ULB-TH/15-01, CERN-PH-TH-2015-010
The Flavour Portal to Dark Matter
Lorenzo Calibbi,1 Andreas Crivellin,2 and Bryan Zald´ıvar1
1Service de Physique Th´eorique, Universit´e Libre de Bruxelles, C.P. 225, B-1050 Brussels, Belgium
2CERN Theory Division, CH-1211 Geneva 23, Switzerland
Wepresentaclassofmodelsinwhichdarkmatter(DM)isafermionicsingletundertheStandard
Model (SM) gauge group but is charged under a symmetry of flavour that acts as well on the
SM fermions. Interactions between DM and SM particles are mediated by the scalar fields that
spontaneously break the flavour symmetry, the so-called flavons. In the case of gauged flavour
symmetries, the interactions are also mediated by the flavour gauge bosons. We first discuss the
construction and the generic features of this class of models. Then a concrete example with an
abelian flavour symmetry is considered. We compute the complementary constraints from the relic
abundance, direct detection experiments and flavour observables, showing that wide portions of
the parameter space are still viable. Other possibilities like non-abelian flavour symmetries can be
analysed within the same framework.
5
1
0 I. INTRODUCTION thesamedynamicsgeneratingfermionmassesintheSM.
2
Furthermore, relating Dark Matter and flavour models

l provides a handle on the otherwise unspecified flavour-
u Establishing the nature of dark matter (DM) is one
breaking scale, motivating the possibility of low-energy
J of the fundamental open problems in particle physics
realisations with interesting phenomenology that would
1 and cosmology. A weakly interacting massive particle
allow insights into the flavour sector [34].
(WIMP)isanexcellentcandidatesince(forGeVtoTeV

]
scalemasses)itnaturallyprovidesarelicabundancecon-
h
p sistent with observations [1]. Since WIMPs must be
- weakly interacting, a likely possibility is that DM is a II. GENERAL SETUP
p
singlet under the Standard Model (SM) gauge group. In
e
h thiscasetheinteractionswiththeSMparticlesaretrans- In this section, we examine the generic features of
[ mitted by mediators, i.e. by the “dark sector”. Many “flavour portal” models that do not depend on the spe-
possibilitiesformediatorshavenbeendiscussedinthelit- cific implementation, e.g. the transformation properties
2
v erature, amongthemZ(cid:48) models[2–5], Higgsportalmod- of SM and DM fields under the flavour symmetry.
els [6–12], Z portal [13], pseudoscalar mediation [14, 15],
8 Inmodels`alaFroggatt-Nielsen[29,35–38],anewsym-
6 darkcolor[16–18]andmodelswithflavouredDM[19–28]. metry of flavour ( ), under which the SM fermions are
F
2 Flavour models aim at explaining the Yukawa struc- charged, is introdGuced, such that the Yukawa couplings
7 ture by introducing a flavour symmetry under which the oftheSMareforbiddenattherenormalisablelevel(with
0
SM fermions transform non-trivially. After this symme- the possible exception of the top Yukawa) and fermion
.
1 tryisspontaneouslybrokenbyscalarfields(i.e. flavons), masses arise once the symmetry is broken as higher di-
0 theobservedfermionsmassesandmixinganglesaregen- mensional operators:
5
erated as non-renormalisable operators. Froggatt and
1
: Nielsen proposed the first flavour model by introducing (cid:18) φ (cid:19)nfij v
v an abelian U(1) flavour symmetry and heavy vector-like (m ) =af (cid:104) (cid:105) . (1)
i quarks[29]. Lateron,manyotherpossibilitieshavebeen f ij ij M √2
X
studied, among them SU(2) [30, 31], SU(3) [32] as well
r Here v = 246 GeV is the vev of the SM Higgs h and φ
a as discrete flavour symmetries like A4 [33]. ∼
represents one or more scalar fields, the flavons, whose
In this article we propose a new mechanism generat-
vev breaks the flavour symmetry. M is a cutoff that can
ing the interactions of DM with the visible sector: DM
be interpreted as the mass of vector-like fermions, that
and the SM particles are charged under a flavour sym-
constitute the UV completion of the model.2 The expo-
metry and interact with each other only via flavour in-
nents nf are dictated by the transformation properties
teractions.1 This is an appealing possibility since it is ij
minimal in the sense that no ad hoc quantum numbers ofthefieldsunderGF,whileafij areunknowncoefficients
mustbeintroducedandDMinteractionsaredescribedby originating from the fundamental couplings of SM fields,
flavonsandmessengersintheUV-completetheory. They
1 Note that our framework shares this starting assumption with
some flavoured DM models, e.g. [21, 23, 25, 28]. Nevertheless, 2 In Ref. [39] it has been discussed that heavy scalars with the
the crucial difference is that we propose either flavour-breaking quantum numbers of the SM Higgs field can also be used for a
scalars or flavour gauge bosons as the only mediators between similar mechanism. Model building details and phenomenology
thedarkandtheSMsectors. ofthemessengersectorhavebeendiscussedinRef.[34,39].
2
are commonly assumed to be O(1), so that the the ob- χ f χ ∼m⟨φχ⟩ φ
served hierarchies of the Yukawas are solely accounted
φ
for by the flavour symmetry breaking. This can be done
by a suitable choice of the flavour charges or representa- mχ mf
tionsoftheSMfermions(onecanassumethattheHiggs χ ∼⟨φ⟩ ∼⟨φ⟩ f
χ mχ φ
field is neutral under F), provided that (cid:15) φ /M is a ∼⟨φ⟩
G ≡(cid:104) (cid:105)
small expansion parameter, typically of the order of the (a) (b)
Cabibbo angle or smaller.
χ f
A. GF as a global symmetry Z′
If the flavour symmetry is global, there are no extra χ ∼gF ∼gF f
gauge bosons associated to it, so that for a DM particle
which carries flavour charge, the only interactions with (c)
the visible sector are through flavon fields φ. In particu-
FIG. 1: Feynman diagrams contributing to DM annihilation
lar, we are going to consider two chiral fermions χ and
L inpresenceoflightflavons(a)and(b)andlightflavourgauge
χ ,whichareSMsingletsbuttransformnon-triviallyun-
R bosons (c).
der . InperfectanalogywiththeSMfermions,theDM
F
G
particle acquires a Dirac mass term though the flavour
symmetry breaking:
that:
(cid:18) (cid:19)nχ
φ m =k φ . (4)
mχ =bχ (cid:104) (cid:105) φ , (2) φ (cid:104) (cid:105)
M (cid:104) (cid:105)
Sincewearenotgoingtospecifythedetailsofthescalar
where again b is an (1) coefficient and nχ depends on potentialandthesymmetrybreaking,wetakek asafree
χ
the flavour representaOtions/charges of χ and χ . Note parameter.
L R
that in this setup the stability of the DM particles is From the above Lagrangian, we can see that our
automatically guarantied (at least for what concerns the setup shares some similarities to the Higgs-portal sce-
quarksector)byanaccidentalsymmetryrelatedtotheir nario [6, 7, 10–12], in particular the fact that the medi-
singlet nature. In fact, due to Lorentz and SU(3) invari- ator prefers to couple to heavier fermions, but also the
ance, DM could only decay by violating baryon number. possible correlations between the DM annihilation and
However, like in the SM, baryon number is an accidental scattering with nuclei.
symmetryofourmodel,sincethedarksector,i.e.theDM In Fig. 1 we show the Feynman diagrams (a) and
fields and the DM messengers which constitute the UV (b) contributing to DM annihilation in presence of light
completion of Eq. (2), is composed only by SM singlets. flavons. Notice that the contribution (b) requires mχ >
This guarantees the stability of DM at least at the per- mφ. From the figure, we can immediately infer the para-
turbative level, since the dark sector fields can not mix metric dependence of the annihilation processes we are
with quarks and Froggatt-Nielsen messengers (i.e. heavy interestedin. Concerningthes-channelprocesses(a),we
vector-like quarks) because of colour and charge conser- seethatthethermally-averagedannihilationcrosssection
vation. mediated by flavons scales as:
From Eqs. (1, 2) we can obtain the couplings of both
λ2λ2m
DM and SM fermions to a dynamical flavon, without σSv χ f χ T , (5)
further specifying the details of the model: (cid:104) φ (cid:105)∼ (4m2 m2)2+Γ2m2
χ− φ φ φ
nfmffLfRφ+(nχ+1)mχχLχRφ where the flavon decay width Γφ depends on λ2f and λ2χ.
L⊃ φ φ From Eq. (3), we see that the flavon-mediated process
(cid:104) (cid:105) (cid:104) (cid:105)
λ f f φ+λ χ χ φ. (3) preferably involves the heaviest fermions that are kine-
f L R χ L R
≡
matically accessible and it can be doubly suppressed in
Here,wesuppressedflavourindicesbutonehastokeepin the case of heavy flavons: both by the propagator and
mindthatthecouplingstofermionsareingeneralflavour by the couplings (that scale as 1/m ). This is the rea-
φ
changing. In fact, λ is not diagonal in the same basis son why, as we will see in the explicit example of the
f
as the fermion mass matrix m , as a consequence of the next sections, the correct relic abundance might require
f
flavour dependence of the exponents nf. The above ex- aresonantenhancementoftheannihilationcrosssection,
pressionscanbeeasilygeneralisedtothecaseofmultiple i.e. m m /2. Note also that the annihilation cross
χ φ
(cid:39)
flavons. section in Eq. (5) depends linearly of the temperature,
For what concerns the flavon mass, we assume that which is a consequence of the velocity-suppression of the
it also arises from the flavour symmetry breaking, such process. The contribution of the diagram (b) of Fig. 1
3
scales like III. CONSTRUCTION OF AN EXPLICIT
MODEL
λ4
σtv χ T (6)
(cid:104) φ (cid:105)∼ m3
χ Letusnowconsideranexplicitexampleofourgeneral
inthelimitm m ,andfeaturesap-wavesuppression idea that DM is communicating with the SM fields via
χ φ
as well. (cid:29) flavourinteractions. ForsimplicitywechooseaFroggatt-
Elastic DM-nuclei scattering can only be mediated by Nielsen U(1)F model.3 We assign flavour charges to the
φ,hencebeingcontrolledbythesamecouplingsdepicted SM quarks, Qqi, Qui and Qdi. The SM scalar doublet
in the diagram (a) of Fig. 1. Therefore, the parametric is neutral under U(1)F and the flavour symmetry is bro-
dependence of the spin-independent cross section is: ken by a single flavon with φ = 1. In addition we
Q −
introduce new fermion which are singlets under the SM
σSI λ2χλ2φNµ2 , (7) gauge group but carry U(1)F charges: the dark matter
φ ∼ m4 χN particles.
φ
The SM Yukawas read:
Here µ is the DM-nucleon reduced mass, and λ
χN φN
∝
λf is the scalar couplings to nucleons [40]. yiuj =auij(cid:15)Qqi+Quj, yidj =adij(cid:15)Qqi+Qdj, (11)
where a(u,d) are assumed to be (1) numbers and (cid:15)
B. GF as a local symmetry ij O ≡
φ /M. We take (cid:15) = 0.2 to reproduce the observed
(cid:104) (cid:105)
quarkshierarchiesanddefinetherotationstothefermion
We also consider the possibility that the flavour sym-
mass basis as
metry is gauged, leading to extra gauge boson(s) with
coupling gF. The phenomenology of the model dras- (Vu)†yuVu yˆu, (Vd)†ydVd yˆd, (12)
tically changes. The reason is that the couplings of L R ≡ L R ≡
fermions and dark matter to Z(cid:48) are completely deter- where yˆ(u,d) are diagonal matrices.
mined by the flavour charges ( X in our abelian exam- Given the hierarchical structure of the Yukawas, the
Q
ple) of the particles: rotations are approximated by ratios of the Yukawa en-
tries:
g χγµ( P + P )χ Z(cid:48)+
L⊃ F QχL L QχR R µ
g fγµ( P + P )f Z(cid:48) . (8) y(u,d) a(u,d)
As we can see,Fthe couQpflLingLs arQefnRotRsupprµessed by the (VL(u,d))ij ≈ yi(ju,d) = ai(ju,d)(cid:15)Qqi−Qqj, (13)
jj jj
flavour-breakingscale,asinthecaseofflavonmediation.
y(u,d) a(u,d)
Fpruerftehrearbmlyorceo,uupnlelitkoehfleaavvoynsfl,aflvaovuorusragnadutgheebDoMsonasndnoihniloat- (VR(u,d))ij ≈ yj(ui,d) = aj(ui,d)(cid:15)Q(ui,di)−Q(uj,dj), (14)
jj jj
tion,depictedinFig.1(c),ispotentiallyefficientevenfor
flavour-breaking scales well above the TeV. In fact, the where i j. From Eq. (11), it follows that the couplings
≥
flavour gauge bosons can be substantially lighter than to a dynamical flavon defined in Eq. (3) are given by
flavons if the coupling is weak. In fact, in the abelian
v
esmxaamllpvlaeluabesovoef wge hwaovueldmsZu(cid:48)p=pre√ss2gtFh(cid:104)eφa(cid:105)n.nOihfilcaotuiorsne,evtoeno λi(ju,d) =a(iju,d)(Qqi +Q(uj,dj))(cid:15)Qqi+Q(uj,dj) φ , (15)
F (cid:104) (cid:105)
ifZ(cid:48) islight. Fromthediagram(c)ofFig.1,weseethat:
Using the above expressions for the rotations, we can
g4 then easily estimate the couplings λ(u,d) in terms of
(cid:104)σZ(cid:48)v(cid:105)∼ (m2 4m2F)2+Γ2 m2 m2χ, (9) fermionmassesandmixingangles. Forinstance,wehave:
Z(cid:48) − χ Z(cid:48) Z(cid:48)
where the Z(cid:48) width ΓZ(cid:48) is proportional to gF2. Also, as λu12 ≈(Qq1 +Qu2)mc(VLu)12/(cid:104)φ(cid:105), (16)
we can see the s-channel annihilation is not p-wave sup- λu ( + )m (Vu) / φ . (17)
pressed (unlike the flavon-mediation case). 21 ≈ Qq2 Qu1 c R 12 (cid:104) (cid:105)
As in the flavon case the Z(cid:48) interactions are in gen- Aswecansee,thesecouplingsarethusexpressedinterms
eral flavour-violating, since quarks of different families ofphysicalobservableswiththeresidualuncertaintyfrom
couple in general differently to the Z(cid:48). This feature is theunknown (1)coefficientsencodedintheV andV
L R
going to induce severe constraints on the Z(cid:48) mass from O
flavour observables. The direct detection interaction is
also determined by the gauge boson exchange:
3 Inthecasethesymmetryisglobal,weshouldratherconsidera
g2λ2
σSI F Z(cid:48)Nµ2 . (10) discretesubgroupZN ⊂U(1),inordertoavoidmasslessNambu-
Z(cid:48) ∼ m4 χN Goldstone bosons. For large enough N, this does not substan-
Z(cid:48)
tiallymodifytheeffectivetheory,suchthatwecanstillworkin
The vector coupling to the nucleons is λZ(cid:48)N gF. termsofchargesofacontinuousU(1)[36].
∝
4
rotations.4 The DM mass arises as in Eq. (2) with the IV. PHENOMENOLOGICAL ANALYSIS
exponent given by:
A. Flavour Constraints
n = + 1. (18)
χ QχL QχR −
As we have seen, both in the global and in the local
versionofourU(1) exampleFCNCappearattree-level.
Therefore, the model with the global U(1) is com- F
F Using the bounds on FCNC operators reported in [34,
pletely defined – up to (1) coefficients – by the param-
O 45], we can estimate the limits on the flavon/Z(cid:48) mass.
eters:
The strongest limit to the flavon mass comes from the
(s d )(s d ) operator, contributing to K K mixing.
L R R L
−
m , m , k m / φ , (19) Integrating out the flavon the above operator is induced
φ χ φ
≡ (cid:104) (cid:105) with the coefficient λd λd /m2. The bounds result:
12 21 φ
where a given value of m can be obtained by suitable
χ
choices of QχL, QχR and bχ. ∆MK : mφ >∼√k(cid:113)×580 GeV, (21)
There are few possibilities how U(1)F can be chosen (cid:15) : m >√k arg(λd λd ) 2.3 TeV, (22)
such that the measured fermion masses and mixing can K φ ∼ × 12 21 ×
be reproduced. Out of the possibilities outlined in [41],
whereweneglectedanoverallcoefficient,productoffun-
here we adopt the following example:
damental (1) Yukawa-like couplings, which can still
O
conspire to relax the bound to some extent. Although
(Qq1, Qq2, Qq3)=(3, 2, 0), the limit from CP violation in K −K mixing is rather
( , , )=(3, 2, 0), strong, we see that a mild suppression of the overall
Qu1 Qu2 Qu3 phase, arg(λd λd ) 0.1, is enough to reduce it at the
(Qd1, Qd2, Qd3)=(4, 2, 2). (20) level of the b1o2un2d1 fr≈om ∆M .
K
In the Z(cid:48) case, the strongest bounds also come
Ni.eo.tneothuants,uspipnrceessfoerducosuQpqli3n=goQfuth3e=fl0av,ownethoatvheeλtu3o3p.=A0s, f(rsomγµdK)(−s γKd m),ixwinhgo.se WiTlshoen cloeeaffidicnigentorpeeardast:or is
L L R µ R
aconsequencethelargestcouplingoftheflavonisflavour
violating: φtL,RcR,L. g2
F ∆ (Vd) ∆ (Vd) , (23)
In the case U(1)F is local, we additionally have a m2Z(cid:48) Qq1q2 L 12 Qd1d2 R 12
Z(cid:48) whose couplings are shown in Eq. (8). Given the
charge assignment above, couplings to light generations where ∆ . The bounds on the Z(cid:48) mass
Qf1f2 ≡Qf1−Qf2
are larger. Furthermore, once the rotations in Eq. (12) then result:
are applied to go to the fermion mass basis, flavour-
(cid:16) g (cid:17)
v(agQtioqtlfjaroe−treinQ-algeqgvici)evo×le,un(spVelZtiL(nt(cid:48)uig,nmdsg)a)aissjrtsi.r.soeTnhgfrisolimimnditEuscqoe.ns(Z8th)(cid:48)-,emogefaduitaghteeecdfooFurCpmlNin∼Cg ∆M(cid:15)KK :: mmZZ(cid:48)(cid:48) >∼>∼(cid:16)11g00FF−−33(cid:17)××2(cid:113)1a0rGg(cid:0)e(VV,Ld)12(VRd)12(cid:1)(24)
F 3.3 TeV, (25)
The above adopted charge assignment is anomalous ×
[41], as it is a common feature of U(1)F models that where again we omitted an (1) uncertainty due to the
successfully reproduce the fermion masses and mixing O
coefficients entering the rotations in Eqs. (13, 14). The
[37, 38, 42, 43].5 As the usually invoked Green-Schwarz
stringent bound from (cid:15) can be relaxed at the level of
K
mechanismwouldrequireaflavour-breakingscalecloseto the CP conserving limit if arg(cid:0)(Vd) (Vd) (cid:1) 0.01.
the Planck scale, we have to assume that anomalies are L 12 R 12 ≈
The fields that constitute the UV completion of
canceled by the unspecified field content of the hidden
Froggatt-Nielsen models (vector-like quarks or heavy
and/orthemessengersector. Inparticular, iftheflavour
scalars) can give contributions to the FCNC that are
messengers are heavy quarks in vector-like representa-
largerthanthosemediatedbyflavonexchanges[34],even
tions ofthe SMgauge group, theydo notneed necessary
though they enter at the one-loop level. The reason is
tobevector-likeundertheflavoursymmetrytoo,leaving
thattheflavoncouplingsareproportionaltothefermion
large freedom to cope with the U(1) anomalies.
F masses,suppressingprocessesinvolvinglightgenerations.
Adopting the model-independent approach of [34], we
find that, in our model, the strongest bound in the
hypothesis of suppressed phases to the messenger scale
4 GiventhehierarchicalstructureoftheYukawa,theorderofmag- comes from D D mixing and it can be translated to a
nitudeoftheentriesofλ(u,d)donotchangeafterrotatingtothe −
limit on the flavon mass:
massbasis,onlytheunknownO(1)saremodified.
5 However, cf. an anomaly-free solution presented in [42] and the
recentstudy[44]inthecontextofSU(5)GUT. mφ >CD k 2.3 TeV, (26)
∼ × ×
5
where C parameterises a product of unknown (1) co- detection experiments is comparably much weaker. As a
D
O
efficients. In presence of (1) CP-violating phases, we result, onlyanarrowregion, depictedingreen, isstillvi-
O
obtain the following bound from (cid:15) : able. The best way to probe this surviving region seems
K
to rely on an increased sensitivity of FCNC constraints,
mφ >CK k 27 TeV. (27) especially in the D D and K K systems.
∼ × × − −
As it will be clear from the discussion in the following
subsection, the phenomenologically interesting region of
C. Collider signals
the parameter space would be excluded by this limit,
unlessweassumethattheoverallphaseinC canreduce
K
it by about one order of magnitude. Thereareinprincipleveryinterestingsignalsthatcan
besearchedforattheLHC.Infact,thelargestbranching
ratiooftheflavonisφ tc, tc,whichisaround60%,but
→
B. Relic abundance and Direct Detection alsothebborbschannelsaresizeable(whiletheBRtoχχ
isverysuppressedbecauseitisatthresholdorbelowdue
to relic density constraints), leading for example to final
We have implemented our model in the MicrOmegas
code [46] in order to obtain an accurate numerical cal- states like pp tctc or pp bbbb. However, the produc-
culation of the relic abundance and the direct detection tioncrosssect→ionofφissm→all,atthelevelof0.1(10−3)fb
cross section. In the case of a global U(1) , we work forLHC@14TeVforflavonswithmφ =500(1000)GeV,
F
values already at the edge of the flavour constraints. A
with the free parameters m , m , k m / φ and set
the (1) coefficients to uniφty. Iχn th≡e gauφge(cid:104)d(cid:105)case, we similar situation happens in the Z(cid:48) case, where flavour
O bounds make any LHC signal very challenging.
have in addition mZ(cid:48) and gF and the dependence on un-
Finally, let us mention that Higgs-flavon mixing can
known coefficients (in the fermion rotation matrices) is
be induced by quartic terms in the scalar potential such
muchmilder. Werequiretherelicabundancenottoover-
shoot the Planck measurement [1], taking as a conserva- as H†Hφ†φ as well as by loops of SM fermions. We
tive limit Ω h2 0.13. checked that in the former case the mixing scales like
DM
GlobalU(1) c≤ase. Theresultsfortheglobalcaseare (v/ φ )2, while it is suppressed by a further factor v/ φ
F (cid:104) (cid:105) (cid:104) (cid:105)
in the latter case, due to an additional flavon-fermion
showninthefirstplotofFig.2. Aswecansee,besidesthe
vertex. As a consequence, any effect on the properties of
flavon resonance, there is a wide region with m > m
χ φ
theobservedHiggswillbesuppressedbyatleastafactor
where efficient annihilation is provided by diagram (b)
ofFig.1andFCNCconstraintsaresatisfied. Wedisplay (v/ φ )4 sothatthemixingwillaffectthehdecaywidths
(cid:104) (cid:105)
hereonlytheboundofEq.(21)fromflavonexchange,as- at most at the level of few percent for φ satisfying the
flavourboundsdiscussedabove. Weleaveamoredetailed
suming a mild suppression of the CP-violating phases at
discussionofthisinterestingaspectoflow-energyflavour
theleveldiscussedintheprevioussubsection. Weneglect
models to future research.
the more stringent bounds of Eq. (26) as they rely on
theadditionalassumptionofaweakly-coupledmessenger
sector at the scale M. We just notice that they would
exclude the region where χχ φφ provides the correct V. CONCLUSIONS AND OUTLOOK
→
relic density, leaving the resonance at m m /2 as
χ φ
≈
theonlyviablesolution,unlessamildsuppressioncomes InthisarticlewediscussedthepossibilitythattheDM
from the coefficient C . This would be also the effect particle is a singlet under the SM gauge group but car-
D
of the bound from (cid:15) , cf. Eq. (22), in presence of (1) ries flavour charges, such that it can communicate with
K
O
phases. The points shaded in grey at low values of m the SM only through flavour gauge bosons or flavour-
φ
do not fulfil the LUX constraints [47], shown in the sec- breaking scalars. We discussed the general features of
ond plot. As we can see, most of the parameter space such flavour portal scenario. We studied an explicit ex-
has good prospects to be tested by next generation di- ample with an abelian U(1) flavour symmetry. For this
rectsearchesexperimentsandtheonlypointsthatmight modeltherelevantphenomenologicalconstraintsarerelic
be hidden under the neutrino background correspond to density, direct detection and flavour observables. These
resonant annihilating DM with m >1 TeV. measurements often constrain the model to be close to
χ
Local U(1)F case. In the local c∼ase, we find that the theresonantregimemχ mφ,Z(cid:48)/2,butstillfuturedirect
∼
only viable possibility to fulfil the relic density bounds detectionexperimentswillbeabletoprobeanimportant
relies on resonant Z(cid:48) exchange, mχ mZ(cid:48)/2, as a con- part of the parameter space of the model.
≈
sequence of the stringent FCNC constraint of Eq. (25). Extensions of these kinds of models to the leptonic
Hence,wevariedgF andmZ(cid:48) andscannedmχaroundthe sector are straightforward. Without entering the details,
resonant condition. The result is shown in the right plot here we just notice that, for the sake of dark matter sta-
of Fig. 2. We see that for a given mZ(cid:48), too small values bility, mixing of the χ singlets with neutrinos must be
of g cannot give the correct relic density, even on the avoided, e.g. by enforcing a conserved symmetry (a nat-
F
resonance, whilethereisanupperboundong fromthe ural choice would be the lepton number itself) or by a
F
FCNC bound of Eq. (25) and the limit given by direct suitableconstructionoftheUVcompletionofthemodel.
6
FIG. 2: Left: points with Ω h2 ≤ 0.13 in the (m , m ) plane for different values of k. The dashed lines represents the
DM χ φ
corresponding lower bounds on m from FCNC constraints. Centre: nucleon-DM scattering cross section scaled by the actual
φ
DM density ξ·σSI (with ξ ≡Ωχh2/0.11) for the same points as before. Right: (gF, MZ(cid:48)) plane in the local U(1)F case; only
the green band is allowed by all data.
While we illustrated our concept for a specific model, ityandpartialsupportduringtheworkshop“ProbingtheTeV
the basic features of flavour portals models as discussed scaleandbeyond”wherethisprojectwasinitiated. Wethank
in Sec. II are generic. On the other hand, the details of P. Tziveloglou for useful discussions. AC is supported by a
thephenomenologywilldependofthespecificrealisation. MarieCurieIntra-EuropeanFellowshipoftheEuropeanCom-
Therefore it will be interesting to extend the above dis- munity’s 7th Framework Programme under contract number
cussion to different charges assignments or other flavour (PIEF-GA-2012-326948). TheworkofBZissupportedbythe
groups, in particular non-abelian symmetries. IISN,anULB-ARCgrantandbytheBelgianFederalScience
Acknowledgments.— The authors are grateful to the Policy through the Interuniversity Attraction Pole P7/37.
Mainz Institute for Theoretical Physics (MITP) for hospital-
[1] P. Ade et al. (Planck Collaboration), Astron.Astrophys. [16] R. Kitano and I. Low, Phys.Rev. D71, 023510 (2005),
571, A1 (2014), 1303.5062. hep-ph/0411133.
[2] P. Langacker, Rev.Mod.Phys. 81, 1199 (2009), [17] R. Kitano, H. Murayama, and M. Ratz, Phys.Lett.
0801.1345. B669, 145 (2008), 0807.4313.
[3] X.Chu,T.Hambye,andM.H.Tytgat,JCAP1205,034 [18] Y.BaiandP.Schwaller,Phys.Rev.D89,063522(2014),
(2012), 1112.0493. 1306.4676.
[4] A. Alves, S. Profumo, and F. S. Queiroz, JHEP 1404, [19] M.Hirsch,S.Morisi,E.Peinado,andJ.Valle,Phys.Rev.
063 (2014), 1312.5281. D82, 116003 (2010), 1007.0871.
[5] G. Arcadi, Y. Mambrini, M. H. G. Tytgat, and B. Zal- [20] M. Boucenna, M. Hirsch, S. Morisi, E. Peinado,
divar, JHEP 1403, 134 (2014), 1401.0221. M. Taoso, et al., JHEP 1105, 037 (2011), 1101.2874.
[6] B. Patt and F. Wilczek (2006), hep-ph/0605188. [21] J. Kile and A. Soni, Phys.Rev. D84, 035016 (2011),
[7] A. Djouadi, Phys.Rept. 457, 1 (2008), hep-ph/0503172. 1104.5239.
[8] C. Arina, F.-X. Josse-Michaux, and N. Sahu, Phys.Lett. [22] B. Batell, J. Pradler, and M. Spannowsky, JHEP 1108,
B691, 219 (2010), 1004.0645. 038 (2011), 1105.1781.
[9] C. Arina, F.-X. Josse-Michaux, and N. Sahu, Phys.Rev. [23] J. F. Kamenik and J. Zupan, Phys.Rev. D84, 111502
D82, 015005 (2010), 1004.3953. (2011), 1107.0623.
[10] L.Lopez-Honorez,T.Schwetz,andJ.Zupan,Phys.Lett. [24] P. Agrawal, S. Blanchet, Z. Chacko, and C. Kilic,
B716, 179 (2012), 1203.2064. Phys.Rev. D86, 055002 (2012), 1109.3516.
[11] A. Djouadi, A. Falkowski, Y. Mambrini, and J. Quevil- [25] L. Lopez-Honorez and L. Merlo, Phys.Lett. B722, 135
lon, Eur.Phys.J. C73, 2455 (2013), 1205.3169. (2013), 1303.1087.
[12] A. Greljo, J. Julio, J. F. Kamenik, C. Smith, and J. Zu- [26] B. Batell, T. Lin, and L.-T. Wang, JHEP 1401, 075
pan, JHEP 1311, 190 (2013), 1309.3561. (2014), 1309.4462.
[13] G. Arcadi, Y. Mambrini, and F. Richard (2014), [27] P.Agrawal,B.Batell,D.Hooper,andT.Lin,Phys.Rev.
1411.2985. D90, 063512 (2014), 1404.1373.
[14] C. Boehm, M. J. Dolan, C. McCabe, M. Spannowsky, [28] P. Agrawal, M. Blanke, and K. Gemmler, JHEP 1410,
and C. J. Wallace, JCAP 1405, 009 (2014), 1401.6458. 72 (2014), 1405.6709.
[15] C. Arina, E. Del Nobile, and P. Panci, Phys.Rev.Lett. [29] C. Froggatt and H. B. Nielsen, Nucl.Phys. B147, 277
114, 011301 (2015), 1406.5542. (1979).
7
[30] A. Pomarol and D. Tommasini, Nucl.Phys. B466, 3 1206, 018 (2012), 1203.1489.
(1996), hep-ph/9507462. [40] A. Crivellin, M. Hoferichter, and M. Procura (2013),
[31] R. Barbieri, G. Dvali, and L. J. Hall, Phys.Lett. B377, 1312.4951.
76 (1996), hep-ph/9512388. [41] P. H. Chankowski, K. Kowalska, S. Lavignac, and
[32] S. King and G. G. Ross, Phys.Lett. B520, 243 (2001), S. Pokorski, Phys.Rev. D71, 055004 (2005), hep-
hep-ph/0108112. ph/0501071.
[33] G.AltarelliandF.Feruglio,Nucl.Phys.B720,64(2005), [42] E. Dudas, S. Pokorski, and C. A. Savoy, Phys.Lett.
hep-ph/0504165. B356, 45 (1995), hep-ph/9504292.
[34] L. Calibbi, Z. Lalak, S. Pokorski, and R. Ziegler, JHEP [43] P. Binetruy, S. Lavignac, and P. Ramond, Nucl.Phys.
1207, 004 (2012), 1204.1275. B477, 353 (1996), hep-ph/9601243.
[35] M.Leurer,Y.Nir,andN.Seiberg,Nucl.Phys.B398,319 [44] Z. Tavartkiladze, Phys.Lett. B706, 398 (2012),
(1993), hep-ph/9212278. 1109.2642.
[36] M.Leurer,Y.Nir,andN.Seiberg,Nucl.Phys.B420,468 [45] G.Isidori,Y.Nir,andG.Perez,Ann.Rev.Nucl.Part.Sci.
(1994), hep-ph/9310320. 60, 355 (2010), 1002.0900.
[37] L. E. Ibanez and G. G. Ross, Phys.Lett. B332, 100 [46] G. B´elanger, F. Boudjema, A. Pukhov, and A. Semenov
(1994), hep-ph/9403338. (2013), 1305.0237.
[38] P.BinetruyandP.Ramond,Phys.Lett.B350,49(1995), [47] D.Akeribetal.(LUXCollaboration)(2013), 1310.8214.
hep-ph/9412385.
[39] L. Calibbi, Z. Lalak, S. Pokorski, and R. Ziegler, JHEP