Neutrino masses, leptogenesis and dark matter in hybrid seesaw

Abstract

We suggest a hybrid seesaw model where relatively ``light''right-handed neutrinos give no contribution to the neutrino mass matrix due to a special symmetry. This allows their Yukawa couplings to the standard model particles to be relatively strong, so that the standard model Higgs boson can decay dominantly to a left and a right-handed neutrino, leaving another stable right-handed neutrino as cold dark matter. In our model neutrino masses arise via the type-II seesaw mechanism, the Higgs triplet scalars being also responsible for the generation of the matter-antimatter asymmetry via the leptogenesis mechanism.

Full text

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arXiv:0811.0953v1 [hep-ph] 6 Nov 2008
Neutrino masses, leptogenesis and dark matter in hybrid seesaw
Pei-Hong Gu1,∗M. Hirsch2,†Utpal Sarkar3,‡and J.W.F. Valle2§
1The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy
2AHEP Group, Institut de F´ ısica Corpuscular – C.S.I.C./Universitat de Val` encia
Edificio Institutos de Paterna, Apt 22085, E–46071 Valencia, Spain
3Physical Research Laboratory, Ahmedabad 380009, India
We suggest a hybrid seesaw model where relatively “light” right-handed neutrinos give no contri-
bution to the neutrino mass matrix due to a special symmetry. This allows their Yukawa couplings
to the standard model particles to be relatively strong, so that the standard model Higgs boson can
decay dominantly to a left and a right-handed neutrino, leaving another stable right-handed neu-
trino as cold dark matter. In our model neutrino masses arise via the type-II seesaw mechanism, the
Higgs triplet scalars being also responsible for the generation of the matter-antimatter asymmetry
via the leptogenesis mechanism.
PACS numbers: 14.60.Pq, 95.35.+d, 98.80.Cq
I. INTRODUCTION
Laboratory experiments with reactors and accelerator
neutrinos have confirmed the observations of solar and
atmospheric neutrinos [1], establishing the phenomenon
of neutrino oscillations and hence the need for small but
nonzero neutrino masses [2]. Since neutrinos are massless
in the SU(3)c× SU(2)L× U(1)YStandard Model (SM)
this implies the need for new physics, whose detailed na-
ture constitutes one of our deepest current challenges in
particle physics [3]. The simplest extension of the SM
to explain the neutrino masses is to include singlet right-
handed neutrinos and/or triplet scalars [4]. The inclusion
of the former is justified by the fact that there are right-
handed partners for all other fermions of the SM. The
singlet right-handed neutrinos will in general have Ma-
jorana masses as well as a Dirac mass term, of the order
of the charged fermion masses. The latter arise from the
usual Yukawa interaction between left- and right-handed
leptons, once the SM Higgs doublet acquires a vacuum
expectation value (vev). The terms involving the right-
handed neutrinos are,
L ⊃ −1
2(MN)ijNc
RiNRj− hijℓLiφNRj+ H.c..
(1)
Here NR, ℓL and φ denote the right-handed neutrinos,
the left-handed leptons and Higgs doublet, respectively.
∗Electronic address: pgu@ictp.it
†Electronic address: mahirsch@ific.uv.es
‡Electronic
URL: http://www.prl.res.in/∼utpal
§Electronic address: valle@ific.uv.es; URL: http://ahep.uv.es
address: utpal@prl.res.in;
In the basis (νL, Nc
R), the neutrino mass matrix reads,
Mν=
?
0
mD
mT
DMN
?
,
(2)
where (mD)ij= hij?φ? with ?φ? ≃ 174GeV. After block-
diagonalization, one gets
mν≃ −mD
1
MN
mT
D.
(3)
If the Majorana masses of the right-handed neutrinos are
much larger than the Dirac masses, the left-handed neu-
trinos will naturally acquire a tiny Majorana through the
type-I seesaw mechanism [4] [5, 6]. In order to account
for neutrino masses in the eV range one needs,
hijhkj(MN)−1
jk∼ 10−23GeV−1.
(4)
so that the Majorana masses MNare required to be or-
ders of magnitude larger than the electroweak symmetry
breaking scale ∼ ?φ?, unless the coefficients hijare very
small,
hij<∼10−11.
(5)
There is an attractive way to avoid this conclusion in
the framework of the inverse seesaw model [7, 8, 9]. In
this case the right-handed neutrinos pair-off with extra
singlet leptons to form Dirac-type neutral heavy leptons
in such a way that their mixing with the doublet neutri-
nos does not lead to light neutrino masses in the limit of
conserved lepton number. As a result of this “symmetry-
protection” right-neutrinos can lie at the TeV scale and
produce signals at accelerators [10, 11], without conflict
with the observed smallness of neutrino masses.
Here we focus on a seesaw mechanism without ad-
ditional fermion degrees of freedom. If one assumes

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“generic” violation of lepton number through right-
handed neutrino Majorana masses, acceptable neutrino
masses require very tiny effective Yukawa couplings con-
necting the right-handed neutrinos with the left-handed
neutrinos, Eqs. (4) and (5), hence the right-handed neu-
trinos can not be produced at the LHC, nor can the
Higgs boson decay into neutrinos. We explore the possi-
bility that the neutrino mass mνcan be exactly zero even
if the Majorana mass MNand the Dirac mass mDare
both non-vanishing [12, 13], as a result of a cancellation.
We present a model where the type-I seesaw contribu-
tion to the neutrino masses vanishes identically due to a
suitable symmetry, avoiding the main constraints on MN
and mD. Neutrino masses arise from the type-II triplet
seesaw mechanism [4]. As a result, relatively light right-
handed neutrinos could have sizeable Yukawa couplings.
If the Majorana masses of the right-handed neutrinos are
of the order of TeV or less, they may be produced at
the LHC. We also note that, if it is heavier than the
right-handed neutrino, the Higgs boson in this scenario
will also have a distinct decay channel into a left plus a
right-handed neutrino. Our explicit symmetry will also
protect one of the right-handed neutrinos from decaying,
as it has no SM Yukawa interactions. This naturally ac-
counts for a stable cold dark matter candidate [14, 15].
Finally, our scenario for the origin of neutrino masses also
provides successful leptogenesis [16, 17] induced by the
out-of-equilibrum decays of the heavy scalar triplets [18].
II. NEUTRINO MASS MATRICES
We shall first discuss the structure of the Dirac and
Majorana masses of the neutrinos and then present the
model in detail. To demonstrate the basic idea, consider
a two-generation scenario in which the type-I seesaw ma-
trix takes a particular form,
Mν=




0 0 a
0 0
a b M
a b
a
b
0
b
0 −M



,
(6)
with M ≫ a,b. Indeed, in this example, the two left-
handed neutrinos remain massless despite the coexistence
of Dirac and Majorana mass terms, as a result of the can-
celation between the contributions from the two right-
handed neutrinos. The latter may be due to some un-
derlying symmetry. In this case the Yukawa couplings
thus can be large even if the right-handed neutrinos have
“low” Majorana masses.
Consider the mass matrix
Mν=




0 0 0
0 0 0
0 0 0 M
a b M
a
b
0




(7)
It is easy to see that (i) this matrix reduces to the pre-
vious after diagonalizing out the right handed states and
(ii) it emerges from a Z3symmetry
NR1→ ω2NR1,
where ω is the cube-root of 1, ω3= 1 and 1 + ω + ω2=
0. All other charged fermions also transform under this
Z3 symmetry as f → ωf and the Higgs doublet φ is
invariant, so that all the usual couplings allowed in the
SM remain the same. The Lagrangian contributing to
the neutrino masses is then given by
NR2→ ωNR2,νLi→ ωνLi,
(8)
L ⊃ −MNc
R1NR2− hi2ℓLiφNR2+ H.c..
(9)
which clearly leads to the form in Eq. (7) once the vev
?φ? is generated. This symmetry makes the light neu-
trinos remain exactly massless. In order to generate the
required neutrino masses one may either break this Z3
softly or, alternatively, introduce triplet scalars for im-
plementing the type-II seesaw [4], without affecting the
symmetry in the right-handed neutrino sector.
This mass matrix can be generalized to three genera-
tions. Consider the 3 × 3 mass matrix





0 0 0 0
Mν =




0 0 0 a
0 0 0
0 0 0
a b c M
a b c
a
b
c
0
0
0
0
0
0
˜
M
b
c
0 −M
0









,
(10)
with M,˜
trinos remain exactly massless, while the masses of the
right-handed neutrinos are +M,−M,˜ M can be “low”
enough to be accessible to the LHC. Note, however, that
the third-generation right-handed neutrino decouples. In
another basis of the right-handed neutrinos one has,
M ≫ a,b,c. Clearly, the three left-handed neu-
Mν =









0 0 0 a
0 0 0
0 0 0
a b c
0 0 0 M
0 0 0 0
0
0
0
0
0
0
0
0
˜
M
b
c
0 M
0
0









.
(11)
This mass matrix could emerge from a Z3symmetry
NR1→ ωNR1, NR2→ ω2NR2, NR3→ NR3,
νLi→ ωνLi.
(12)

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or, alternatively, from an U(1) global symmetry. The
Lagrangian containing the right-handed neutrinos,
L ⊃ −MNc
implies, in the limit M ≫ hi1?φ?, two degenerate right-
handed neutrinos
1
√2(NR1± NR2) → NR1,2
with masses ±M (opposite CP signs). For M<
these two states NR1,2would be accessible to LHC
searches. On the other hand, a more interesting possibil-
ity may open up when the Higgs boson is heavier than
NR1and NR2. Given the mild constraint on the Dirac
mass term, the Yukawa couplings could be large enough
that the Higgs boson would dominantly decay into a left-
handed neutrino and a right-handed one, posing a new
challenge to the Higgs search program at the LHC. The
third right-handed neutrino NR3has mass˜
cay modes. Hence it could serve as the dark matter if its
relic density is consistent with the cosmological observa-
tions.
R1NR2−1
2
˜
MNc
R3NR3− hi1ℓLiφNR1+ H.c.. (13)
(14)
∼1TeV
M and no de-
III.LEPTOGENESIS, NEUTRINO MASS AND
DARK MATTER
We now propose a realistic model, which contains the
previous phenomenology of the right-handed neutrinos
and explains the matter-antimatter asymmetry, the neu-
trino masses and the dark matter. We extend the SM
by including three right-handed neutrinos, two triplet
Higgs scalars ξ1,2≡ (1,3,2) and two singlet scalar fields
σ,χ ≡ (1,1,0). In addition to the SM gauge symme-
try, we also impose a global U(1)lepsymmetry of lepton
number, under which the different fields transform as:
NR1NR2NR3ℓLiξ1 ξ2 σ χ φ
132 1 –2 –1 –4 1 0
TABLE I: Lepton number assignments. For simplicity, we do
not show the right-handed charged leptons, which carry the
same lepton number as their left-handed partners.
The relevant part of the Lagrangian is given as,
L ⊃ −α1σNc
−1
+H.c..
R1NR2−1
2α2σNc
R3NR3− hi1ℓLiφNR1
2fijℓc
Liiτ2ξ1ℓLj− α3χφTiτ2ξ2φ − µχξ†
2ξ1
(15)
After the singlet scalar σ develops its vev the first line
will induce the Lagrangian (13), so that the right-handed
neutrinos obtain their Majorana masses. The second line
will generate the type-II seesaw in the presence of ?χ?.
In our model, the global U(1)lepis assumed to break
at a very large scale by ?χ? ∼ 1013GeV. The triplet
scalars ξ1and ξ2, whose masses ∼ Mξare of the order of
?χ?, mix with each other and pick up tiny vevs after the
electroweak symmetry breaking,
?ξ2? ∼ −α3
?χ??φ?2
M2
ξ
,
?ξ1? ∼ −µ?χ??ξ2?
M2
ξ
.
(16)
These triplet vevs will give rise to the left-handed neu-
trinos Majorana mass matrix,
mνij= fij?ξ1? .
(17)
The CP-violating and out-of-equilibrium decays of the
triplet scalars ξ1 and ξ2 into the SM lepton and Higgs
doublets can generate a lepton asymmetry [18].
sphaleron [17] processes active in the range 100GeV<
T<
∼1012GeV, will partially convert this lepton asym-
metry to a baryon asymmetry for explaining the matter-
antimatter asymmetry of the universe. In order to suc-
cessfully induce leptogenesis and suppress washout pro-
cesses, we require that the singlet scalar σ develops its
vev after the sphaleron epoch is over, for example, we
take ?σ? ∼ 100GeV. Through their Yukawa couplings
to σ the right-handed neutrinos acquire their Majorana
masses M = α1?σ? and ˜
below 100GeV or so.
The spontaneous breakdown of the global lepton num-
ber global symmetry through ?χ?, leads to a Goldstone
boson, whose profile can be determined by the symme-
try [6], leading to,
The
∼
M = α2?σ?, expected to lie
G =
1
N
??χ?Im(χ) + ?ξ1?Im(ξ0
where N is a suitable normalization, which is of the order
of the lepton number breaking scale ∼ ?χ?. Clearly, the
triplet component of the Goldstone boson is highly sup-
pressed by the ratio of the triplet vevs over the singlet
vev, suppressing its coupling to the Z-bosons [6].
Note that since lepton number conservation forbids the
couplings of χ to the right-handed neutrinos, ?χ? will not
have any effect on them. The states NR1and NR2mix
maximally and in the basis where their Majorana mass
matrix is diagonal, the degenerate states NR1and NR2in
Eq. (14) with mass ±M both couple to the left-handed
neutrinos through equal Yukawa couplings. In addition,
the state NR3has no couplings to the left-handed neutri-
nos. Therefore, the resulting neutrino mass matrix is a
1) + ?ξ2?Im(ξ0
2)?.
(18)

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null matrix. This implies that the strongest constraints
on the couplings, for example those set by the smallness
of neutrino masses, are absent, very much like the case
of the inverse seesaw model [7, 9].
Another most severe constraint on the couplings of the
right-handed neutrinos with the charged leptons comes
from their contribution to µ → eγ, which is trivially re-
moved now. Since here only the NR1and NR2would me-
diate the process and they are degenerate, the µ → eγ
amplitude would depend on the effective light neutrino
masses, which now vanishes, hence avoiding the con-
straint on the couplings.
Note also that the physical Higgs boson can signifi-
cantly decay into h → νL+ NR1h → νL+ NR2, lead-
ing to a mono-jet-like signal.
h → νL+ NR3does not take place.
The third right-handed neutrino NR3can not decay at
all because its only Yukawa coupling is with the singlet
scalar σ. This means that NR3will contribute a sizeable
relic density to the Universe. One can indeed check that
NR3with the mass of a few GeV can have a desired cross
section to serve as the dark matter for ?σ? ∼ 100GeV.
As a last comment we note that there may be a sizeable
quartic interaction between the singlet scalar σ and the
SM Higgs doublet φ, i.e. λ(σ†σ)(φ†φ). This term can not
be forbidden by imposing extra symmetries, and there is
no a priori reason for λ to be small. In the presence
of such coupling this dark matter NR3can be searched
in the decays of the Higgs boson produced at the LHC,
h → NR3+NR3, resulting in a missing momentum signal.
In contrast, the decay
IV.SUMMARY
Due to some special symmetry it may happen that
the type-I seesaw mechanism does not generate the ob-
served neutrino masses, despite the co-existence of size-
able Dirac mass terms and relatively low right-handed
neutrino Majorana masses. Such null seesaw mechanism
can be understood as a cancelation between the contribu-
tions from the right-handed neutrinos. In this case there
is only a very mild constraint on the right-handed neu-
trinos, which can have sizeable Yukawa couplings to the
SM particles even if they are light. The leading Higgs bo-
son decay mode into a left-handed neutrino and a right-
handed neutrino could be probed at the LHC. In the
model we have presented, one of the right-handed neutri-
nos has no Yukawa couplings to the SM states, a fact that
follows from our assumed symmetry. Hence it can pro-
vide the relic density required to solve the puzzle of the
dark matter. Finally, in our model the source of neutrino
masses is the type-II seesaw contribution arising from the
induced vevs of scalar Higgs triplets. The CP-violating
and out-of-equilibrium decays of these scalar triplets may
also account for the matter-antimatter asymmetry of the
Universe through the leptogenesis mechanism.
This work was supported by Spanish grants FPA2008-
00319/FPA and FPA2008-01935-E/FPA and ILIAS/N6
Contract RII3-CT-2004-506222.
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