Dark Matter and the elusive Z′ in a dynamical Inverse Seesaw scenario
JHE
Dark Matter and the elusive Z0 in a dynamical Inverse Seesaw scenario
Valentina De Romeri 0 1 3 6 7
Enrique FernandezMartinez 0 1 3 5 7
Julia Gehrlein 0 1 3 5 7
Pedro A.N. Machado 0 1 2 3 7
Viviana Niro 0 1 3 4 7
Cantoblanco E 0 1 3 7
Madrid 0 1 3 7
Spain 0 1 3 7
Instituto de F sica Teorica UAM/CSIC 0 1 3 7
0 Batavia, IL , 60510 , U.S.A
1 Calle Nicolas Cabrera 1315 , Cantoblanco E28049 Madrid , Spain
2 Theoretical Physics Department, Fermi National Accelerator Laboratory
3 Calle Catedratico Jose Beltran , 2 E46980 Paterna , Spain
4 Institut fur Theoretische Physik, RuprechtKarlsUniversitat Heidelberg
5 Departamento de F sica Teorica, Universidad Autonoma de Madrid
6 AHEP Group, Instituto de F sica Corpuscular, C.S.I.C./Universitat de Valencia
7 Philosophenweg 16 , 69120 Heidelberg , Germany
The Inverse Seesaw naturally explains the smallness of neutrino masses via
Beyond Standard Model; Neutrino Physics

an approximate B
L symmetry broken only by a correspondingly small parameter. In
this work the possible dynamical generation of the Inverse Seesaw neutrino mass
mechanism from the spontaneous breaking of a gauged U(
1
) B
L symmetry is investigated.
Interestingly, the Inverse Seesaw pattern requires a chiral content such that anomaly
cancellation predicts the existence of extra fermions belonging to a dark sector with large,
nontrivial, charges under the U(
1
) B
L. We investigate the phenomenology associated
to these new states and
nd that one of them is a viable dark matter candidate with mass
around the TeV scale, whose interaction with the Standard Model is mediated by the Z0
boson associated to the gauged U(
1
) B
L symmetry. Given the large charges required for
anomaly cancellation in the dark sector, the B
L Z0 interacts preferentially with this dark
sector rather than with the Standard Model. This suppresses the rate at direct detection
searches and thus alleviates the constraints on Z0mediated dark matter relic abundance.
The collider phenomenology of this elusive Z0 is also discussed.
1 Introduction The model 2 3
4
5
6
1
2.1
2.2
3.1
3.2
3.3
3.4
The fermion sector
The scalar sector
Relic density Direct detection Indirect detection
Collider phenomenology
Results
Conclusions
Introduction
Dark matter phenomenology
E ective number of neutrino species, Ne
The simplest and most popular mechanism to accommodate the evidence for neutrino
masses and mixings [1{6] and to naturally explain their extreme smallness, calls upon the
introduction of righthanded neutrinos through the celebrated Seesaw mechanism [7{12].
Its appeal stems from the simplicity of its particle content, consisting only of the
righthanded neutrinos otherwise conspicuously missing from the Standard Model (SM)
ingredients. In the Seesaw mechanism, the smallness of neutrino masses is explained through
the ratio of their Dirac masses and the Majorana mass term of the extra fermion singlets.
Unfortunately, this very same ratio suppresses any phenomenological probe of the
existence of this mechanism. Indeed, either the righthanded neutrino masses would be too
large to be reached by our highest energy colliders, or the Dirac masses, and hence the
Yukawa interactions that mediate the righthanded neutrino phenomenology, would be too
small for even our more accurate precision probes through avour and precision electroweak
observables.
However, a large hierarchy of scales is not the only possibility to naturally explain
the smallness of neutrino masses. Indeed, neutrino masses are protected by the B
L
(Baryon minus Lepton number) global symmetry, otherwise exact in the SM. Thus, if
this symmetry is only mildly broken, neutrino masses will be necessarily suppressed by
the small B
Lbreaking parameters. Conversely, the production and detection of the
extra righthanded neutrinos at colliders as well as their indirect e ects in
avour and
{ 1 {
precision electroweak observables are not protected by the B
L symmetry and therefore
not necessarily suppressed, leading to a much richer and interesting phenomenology. This
is the rationale behind the popular Inverse Seesaw Mechanism [13] (ISS) as well as the
Linear [14, 15] and Double Seesaw [13, 16{18] variants.
In the presence of righthanded neutrinos, B
L is the only
avouruniversal SM
quantum number that is not anomalous, besides hypercharge. Therefore, just like the
addition of righthanded neutrinos, a very natural plausible SM extension is the gauging
of this symmetry. In this work these two elements are combined to explore a possible
dynamical origin of the ISS pattern from the spontaneous breaking of the gauged B
L
symmetry.
Previous models in the literature have been constructed using the ISS idea or gauging
B
L to explain the smallness of the neutrino masses, see e.g. [19{24]. A minimal model
in which the ISS is realised dynamically and where the smallness of the Lepton Number
Violating (LNV) term is generated at the twoloop level was studied in [25]. Concerning
U(
1
)B L extensions of the SM with an ISS generation of neutrino masses, several models
have been investigated [26{29]. A common origin of both sterile neutrinos and Dark Matter
(DM) has been proposed in [30, 31]. An ISS model which incorporates a keV sterile neutrino
as a DM candidate was constructed in e.g. [32]. Neutrino masses break B
L, if this
symmetry is not gauged and dynamically broken, a massless Goldstone boson, the Majoron,
appears in the spectrum. Such models have been investigated for example in [30, 33].
Interestingly, since the ISS mechanism requires a chiral pattern in the neutrino sector,
the gauging of B
L predicts the existence of extra fermion singlets with nontrivial charges
so as to cancel the anomalies. We nd that these extra states may play the role of DM
candidates as thermally produced Weakly Interacting Massive Particles (WIMPs) (see for
instance [34, 35] for a review).
Indeed, the extra states would form a dark sector, only connected to the SM via the Z0
gauge boson associated to the B
L symmetry and, more indirectly, through the mixing
of the scalar responsible for the spontaneous symmetry breaking of B
L with the Higgs
boson. For the simplest charge assignment, this dark sector would be constituted by one
heavy Dirac and one massless Weyl fermion with large B
L charges. These large charges
make the Z0 couple preferentially to the dark sector rather than to the SM, making it
particularly elusive. In this work the phenomenology associated with this dark sector and
the elusive Z0 is investigated. We nd that the heavy Dirac fermion of the dark sector can
be a viable DM candidate with its relic abundance mediated by the elusive Z0. Conversely,
the massless Weyl fermion can be probed through measurements of the relativistic degrees
of freedom in the early Universe. The collider phenomenology of the elusive Z0 is also
investigated and the LHC bounds are derived.
The paper is structured as follows. In section 2 we describe the features of the
model, namely its Lagrangian and particle content. In section 3 we analyse the
phenomenology of the DM candidate and its viability. The collider phenomenology of the
Z0 boson is discussed in section 4. Finally, in sections 5 and 6 we summarise our results
and conclude.
{ 2 {
HJEP10(27)69
The usual ISS model consists of the addition of a pair of righthanded SM singlet fermions
(righthanded neutrinos) for each massive active neutrino [13, 36{38]. These extra fermion
copies, say NR and N R0, carry a global Lepton Number (LN) of +1 and
1, respectively, and this leads to the following mass Lagrangian
LISS = LY He NR + N RcMN N R0 + N R0c N R0 + h:c:;
where Y is the neutrino Yukawa coupling matrix, He = i 2H
(H being the SM Higgs
tor [39] which generates masses for the light, active neutrinos of the form:
m
v2Y MN 1 (MNT ) 1Y T :
Having TeVscale righthanded neutrinos (e.g. motivated by naturalness [40, 41]) and O(
1
)
Yukawa couplings would require
O(keV). In the original ISS formulation [13], the
smallness of this LNV parameter arises from a superstring inspired E6 scenario. Alternative
explanations call upon other extensions of the SM such as Supersymmetry and Grand
Uni ed Theories (see for instance [15, 42]). Here a dynamical origin for
will be instead
explored. The
parameter is technically natural: since it is the only parameter that breaks
LN, its running is multiplicative and thus once chosen to be small, it will remain small at
all energy scales.
To promote the LN breaking parameter
in the ISS scenario to a dynamical quantity,
we choose to gauge the B
L number [43]. The spontaneous breaking of this symmetry
will convey LN breaking, generate neutrino masses via a scalar vev, and give rise to a
massive vector boson, dubbed here Z0. B
L is an accidental symmetry of the SM, and
it is well motivated in theories in which quarks and leptons are uni ed [44{47]. In uni ed
theories, the chiral anomalies cancel within each family, provided that SM fermion singlets
with charge +1 are included. In the usual ISS framework, this is not the case due to the
presence of righthanded neutrinos with charges +1 and
1. The triangle anomalies that
do not cancel are those involving three U(
1
)B L vertices, as well as one U(
1
)B L vertex and
gravity. Therefore, to achieve anomaly cancellation for gauged B
L we have to include additional chiral content to the model with charges that satisfy
X Qi = 0 )
X Qi3 = 0 )
X QiL
X QiL
3
X QiR = 0;
X Qi3R = 0;
where the rst and second equation refer to the mixed gravityU(
1
)B L and U(
1
)3B L
anomalies, respectively. The index i runs through all fermions of the model.
In the following subsections we will discuss the fermion and the scalar sectors of the
model in more detail.
{ 3 {
(2.1)
(2.2)
(2.3)
(2.4)
Particle
U(
1
)B L charge
Multiplicity
+1
1
+2
1
+1
3
+5
1
+4
1
!
+4
1
1;2 are SM singlet scalars while NR, N R0 and R are righthanded and L and ! are lefthanded
SM singlet fermions respectively.
2.1
The fermion sector
Besides the anomaly constraint, the ISS mechanism can only work with a certain number of
NR and N R0
elds (see, e.g., ref. [48]). We nd a phenomenologically interesting and viable
scenario which consists of the following copies of SM fermion singlets and their respective
1; 3 N R0 with charge +1; 1 R with charge +5; 1 L with
charge +4 and 1 ! with charge +4.1 Some of these righthanded neutrinos allow for a mass
term, namely, MN N RcN R0, but to lift the mass of the other sterile fermions and to generate
SM neutrino masses, two extra scalars are introduced. Thus, besides the Higgs doublet H,
the scalar elds 1 with B
L charge +1 and 2 with charge +2 are considered. The SM
leptons have B
L charge
1, while the quarks have charge 1=3. The scalar and fermion
content of the model, related to neutrino mass generation, is summarised in table 1. The
most general Lagrangian in the neutrino sector is then given by2
L = LY He NR + N RcMN N R0 + 2N RcYN NR + 2(N R0)c YN0 N R0 + 1 L Y
R+h:c:;
(2.5)
where the capitalised variables are to be understood as matrices (the indices were omitted).
The singlet fermion spectrum splits into two parts, an ISS sector composed by L, NR,
and N R0, and a dark sector with
written in the basis ( Lc; NR; N R0; cL; R):
L and
R, as can be seen in the following mass matrix
0
B
M = BBB
B Y T Hy YN 2 MN
e
MNT YN0 2
Y He
0
0
0
0
0
0
0
0
0
Y T 1
Y
0
0
0
0
1
C
C
C :
C
C
develops a vacuum expectation value (vev) a Dirac fermion
= ( L; R) and a massless
1Introducing 2 NR and 3 N R0 as for example in [32] leads to a keV sterile neutrino as a potentially
interesting warm DM candidate [49] in the spectrum due to the mismatch between the number of NR and
N R0. However, the relic abundance of this sterile neutrino, if thermally produced via freeze out, is an order
of magnitude too large. Thus, in order to avoid its thermalisation, very small Yukawa couplings and mixings
must be adopted instead.
rotation between ! and L.
oneloop level and is therefore typically subleading.
2Notice that a coupling 1!Y! R, while allowed, can always be reabsorbed into 1 LY R through a
3The analogous term YN 2  also dynamically generated  contributes to neutrino masses only at the
{ 4 {
HJEP10(27)69
v1
fermion ! are formed in the dark sector. Although the cosmological impact of this extra
relativistic degree of freedom may seem worrisome at
rst, we will show later that the
contribution to Ne is suppressed as this sector is well secluded from the SM.
To recover a TeVscale ISS scenario with the correct neutrino masses and O(
1
) Yukawa
couplings, v2
MR
h 2i
keV
v (where v = hHi = 246 GeV is the electroweak vev) and
TeV are needed. Moreover, the mass of the B
L gauge boson will be linked to
the vevs of 1 and
2, and hence to lift its mass above the electroweak scale will require
h 1i & TeV. In particular, we will show that a triple scalar coupling
2
1 2 can induce
a small v2 even when v1 is large, similar to what occurs in the typeII seesaw [12, 52{55].
After the spontaneous symmetry breaking, the particle spectrum would then consist of a
The scalar potential of the model can be written as
+
2
V =
m2H HyH +
H
2
(HyH)2 +
m21
2
m22
2
Both m2H and m21 are negative, but m22 is positive and large. Then, for suitable values of
the quartic couplings, the vev of 2, v2, is only induced by the vev of 1, v1, through
thus it can be made small. With the convention j = (vj + 'j + i aj )=p2 and the neutral
component of the complex Higgs eld given by H0 = (v + h + iGZ )=p2 (where GZ is the
and
Goldstone associated with the Z boson mass), the minimisation of the potential yields
1H v12 + 2H v22 + 2 H v2
'
1H v12 + 2 H v2 ;
2 1v12 + 1H v2
p
2
4 2 v2 + 12v2
2 1v12 + 1H v2 ;
1
2
p
'
2 v
v2
1
2
2
1
;
! 0 or m22 ! 1, the vev of 2 goes to zero. For example, to obtain
v2
O(keV), one could have m2
10 TeV, v1
10 TeV, and
10 5 GeV. The neutral
scalar mass matrix is then given by
0
H v2
0
1H v1v=2
p
1v12
Higgs data constrain the mixing angle between Re(H0) and Re( 01) to be below
Moreover, since
m2; v1, the mixing between the new scalars is also small. Thus, the
masses of the physical scalars h, '1 and '2 are approximately
m2h =
H v2;
and
while the mixing angles 1 and 2 between h
TeV and the quartics 1 and 1H are O(
1
), the mixing 1 is expected to be small
but nonnegligible. A mixing between the Higgs doublet and a scalar singlet can only
diminish the Higgs couplings to SM particles. Concretely, the couplings of the Higgs to
gauge bosons and fermions, relative to the SM couplings, are
F = V = cos 1
;
which is constrained to be cos 1 > 0:92 (or equivalently sin 1 < 0:39) [57]. Since the
massless fermion does not couple to any scalar, and all other extra particles in the model
are heavy, the modi cations to the SM Higgs couplings are the only phenomenological
impact of the model on Higgs physics. The other mixing angle, 2, is very small since it is
proportional to the LN breaking vev and thus is related to neutrino masses. Its presence
will induce a mixing between the Higgs and '2, but for the parameters of interest here it
is unobservable.
Besides Higgs physics, the direct production of '1 at LHC via its mixing with the
Higgs would be possible if it is light enough. Otherwise, loop e ects that would change the
W mass bound can also test this scenario imposing sin 1 . 0:2 for m'1 = 800 GeV [56].
Apart from that, the only physical pseudoscalar degree of freedom is
1
A =
pv12 + 4v22 [2v2a1
v1a2]
(2.16)
and its mass is degenerate with the heavy scalar mass, mA ' m'2 .
We have built this model in SARAH 4.9 [58{61]. This Mathematica package produces the
model les for SPheno 3.3.8 [62, 63] and CalcHep [64] which are then used to study the DM
phenomenology with Micromegas 4.3 [65]. We have used these packages to compute the
results presented in the following sections. Moreover, we will present analytical estimations
to further interpret the numerical results.
{ 6 {
(2.12)
(2.13)
(2.14)
(2.15)
χ
χ
χ
if
3.1
where
Relic density
Z′
χ
f
Z
′
Z
′
χ
χ
χ
χ
channel opens up when MZ20 < m2 . Since the process
diagram is typically subleading.
! f f via the Z0 boson and
! Z0Z0. The
! Z0Z0
! '1 ! Z0Z0 is velocity suppressed this
3
Dark matter phenomenology
As discussed in the previous section, in this dynamical realisation of the ISS mechanism
we have two stable fermions. One of them is a Dirac fermion,
= ( L; R), which acquires
a mass from
1, and therefore is manifest at the TeV scale. The other, !, is massless and
will contribute to the number of relativistic species in the early Universe. First we analyse
can yield the observed DM abundance of the Universe.
In the early Universe, is in thermal equilibrium with the plasma due to its gauge interaction with Z0. The relevant part of the Lagrangian is
LDM =
gBL
(5PR + 4PL) Z0 +
MZ20 Z0 Z0
m
;
MZ0 = gBL
qv12 + 4v22 ' gBLv1; and m
= Y v1=p2;
1
2
and PR;L are the chirality projectors.
The main annihilation channels of are
! Z0Z0  if kinematically allowed (see gure 1).
The annihilation cross section to a fermion species f , at leading order in v, reads:
h viff ' nc(q L + q R )
2 qf2L + qf2R
8
(4m2
gB4Lm2
MZ20 )2 + 2Z0 MZ20 + O v2 ;
see e.g. [66, 67], where nc is the color factor of the nal state fermion (=1 for leptons),
q L = 4 and q R = 5 and qfL;R are the B
L charges of the left and righthanded
components of the DM candidate
and of the fermion f , respectively. Moreover, the
partial decay width of the Z0 into a pair of fermions (including the DM, for which f = )
is given by
fZf0 = nc gBL
2
6qfL qfR mf2 + q
f2L + qf2R
MZ20
m2
f
qMZ20
4mf2
′
Z
′
section for this process (lower diagrams in
gure 1) is given by (to leading order in the
relative velocity) [66]
h viZ0Z0 ' 256 m2 MZ20
1
1
pressed and hence typically subleading. Further decay channels like
! Z0'1 open when 2m
> m'1 +m'1 (m'1 +mZ0 ). With m
mZ0 = gBLv1 and the additional constraint from perturbativity Y
= Y =p2v1; m'1 = p
1v1;
! '1'1 and
1 we get only small
kinematically allowed regions which play a subleading role for the relic abundance. The
cross section for the annihilation channel
angle
1 between '1
h
0 which is small although nonnegligible (cf. eq. (2.14)).
! Z0h0 is also subleading due to the mixing
The relic density of
has been computed numerically with Micromegas obtaining
also, for several points of the parameter space, the DM freezeout temperature at which
the annihilation rate becomes smaller than the Hubble rate h vin
. H. Given the
freezeout temperature and the annihilation cross sections of eqs. (3.3) and (3.5), the DM relic
density can thus be estimated by [68]:
(3.6)
(3.7)
where g? is the number of degrees of freedom in radiation at the temperature of freezeout
1:2 1019 GeV is the Planck mass. In section 5 we will use this estimation of
of the DM (T f:o:), h vi is its thermally averaged annihilation cross section and MPl =
h2 together
with its constraint
h
2
' 0:1186
space for which the correct DM relic abundance is obtained.
0:0020 [69, 70] to explore the regions of the parameter
3.2
Direct detection
The same Z0 couplings that contribute to the relic abundance can give rise to signals in DM
direct detection experiments. The DMSM interactions in the model via the Z0 are either
vectorvector or axialvector interactions. Indeed, the Z0SM interactions are vectorial
(with the exception of the couplings to neutrinos) while
has di erent left and
righthanded charges. The axialvector interaction does not lead to a signal in direct detection
and the vectorvector interaction leads to a spinindependent cross section [71].
The cross section for coherent elastic scattering on a nucleon is
where
N is the reduced mass of the DMnucleon system. The strongest bounds on the
spinindependent scattering cross section come from LUX [72] and XENON1T [73]. The
DD =
2
N
9 gB2L
and
DD < 10 8 pb for m
= 10 TeV. The experimental bound on the spinindependent
cross section (eq. (3.7)) allows to derive a lower bound on the vev of 1
:
this bound translates into a lower limit on the vev of 1: v1 & 40 TeV (with Y
Next generation experiments such as XENON1T [74] and LZ [75] are expected to improve
the current bounds by an order of magnitude and could test the parameter space of this
model, as it will be discussed in section 5.
3.3
Indirect detection
In full generality, the annihilation of today could lead also to indirect detection signatures,
in the form of charged cosmic rays, neutrinos and gamma rays. However, since the main
annihilation channel of
is via the Z0 which couples dominantly to the dark sector, the
bounds from indirect detection searches turn out to be subdominant.
The strongest experimental bounds come from gamma rays produced through direct
+
emission from the annihilation of
into
. Both the constraints from the FermiLAT
Space Telescope (6year observation of gamma rays from dwarf spheroidal galaxies) [76] and
H.E.S.S. (10year observation of gamma rays from the Galactic Center) [77] are not very
stringent for the range of DM masses considered here. Indeed, the current experimental
bounds on the velocityweighted annihilation cross section <
v > (
from 10 25 cm3s 1 to 10 22 cm3s 1 for DM masses between 1 and 10 TeV. These values
are more than two orders of magnitude above the values obtained for the regions of the
parameter space in which we obtain the correct relic abundance (notice that the branching
ratio of the DM annihilation to
into
+
is only about 5%). Future experiments like
CTA [78] could be suited to sensitively address DM masses in the range of interest of this
!
+
) range
model (m
& 1 TeV).
3.4
E ective number of neutrino species, Ne
The presence of the massless fermion ! implies a contribution to the number of relativistic
degrees of freedom in the early Universe. In the following, we discuss its contribution
to the e ective number of neutrino species, Ne , which has been measured to be N exp =
e
3:04 0:33 [69]. Since the massless ! only interacts with the SM via the Z0, its contribution
to Ne
will be washed out through entropy injection to the thermal bath by the number
of relativistic degrees of freedom g?(T ) at the time of its decoupling:
Ne =
T f:o: 4
!
T
=
11
2g?(T!f:o:)
4=3
;
(3.9)
where T f:o: is the freezeout temperature of ! and T is the temperature of the neutrino
!
background. The freezeout temperature can be estimated when the Hubble expansion
{ 9 {
rate of the Universe H = 1:66pg?T 2=MPl overcomes the ! interaction rate
=< v > n!
leading to:
(T!f:o:)3
2:16pg?MZ40
MPlgB4L
Pf (qf2L
+ qf2R )
:
With the typical values that satisfy the correct DM relic abundance: mZ0
and gBL
O(0.1) ! would therefore freeze out at T f:o:
!
4 GeV, before the QCD phase transition. Thus, the SM bath will heat signi cantly after ! decouples and the contribution of the latter to the number of degrees of freedom in radiation will be suppressed:
which is one order of magnitude smaller than the current uncertainty on Ne . For gauge
boson masses between 150 TeV and gauge couplings between 0.01 and 0.5,
Ne 2 [0:02; 0:04].
Nevertheless, this deviation from Ne
matches the sensitivity expected from a EUCLIDlike
survey [79, 80] and would be an interesting probe of the model in the future.
4
Collider phenomenology
The new gauge boson can lead to resonant signals at the LHC. Dissimilarly from the widely
studied case of a sequential Z0 boson, where the new boson decays dominantly to dijets,
the elusive Z0 couples more strongly to leptons than to quarks (due to the B
L number). Furthermore, it has large couplings to the SM singlets, specially and ! which carry large
L charges. Thus, typical branching ratios are
70% invisible (i.e. into SM neutrinos
and !),
12% to quarks and
18% to charged leptons.4 LHC Z0 ! e+e ; +
resonant
searches [81, 82] can be easily recast into constraints on the elusive Z0. The production
cross section times branching ratio to dileptons is given by
(3.10)
O(10 TeV)
(3.11)
X
q
Cqq
sMZ0
(pp ! Z0 ! ``) =
(Z0 ! qq)BR(Z0 ! ``);
(4.1)
where s is the center of mass energy, (Z0 ! qq) is the partial width to qq pair given by
eq. (3.4), and Cqq is the qq luminosity function obtained here using the parton distribution
function MSTW2008NLO [83]. To have some insight on what to expect, we compare our
Z0 with the usual sequential standard model (SSM) Z0, in which all couplings to fermions
are equal to the Z couplings. The dominant production mode is again qq ! Z0 though the
coupling in our case is mostly vectorial. The main dissimilarity arrives from the branching
ratio to dileptons, as there are many additional fermions charged under the new gauge
group. In summary, only O(
1
) di erences in the gauge coupling bounds are expected,
between the SSM Z0 and our elusive Z0.
4If the decay channels to the other SM singlets are kinematically accessible, specially into
and into
the NR; N R0 pseudoDirac pairs, the invisible branching ratio can go up to
87%, making the Z0 even more
elusive and rendering these collider constraints irrelevant with respect to direct DM searches.
HJEP10(27)69
0.7
nonperturbative region
Ωm>0.12
LUX
XENON1T (2yr)
LZ (1000d)
6
4
mZ' [TeV]
mχ= 10 TeV
8
10
X
U
L
E
X
O
N
L
Z
T
1
N
1
(
0
0
r
y
)
2
(
0
d
)
Ωm>0.12
mZ' [TeV]
mχ= 5 TeV
nonperturbative region
X
L
U
X
E
N
O
N
1
T (
2
yr)
LZ (1000d)
Ωm>0.12
5
10
mZ' [TeV]
mχ= 20 TeV
15
20
s
t
n
i
a
r
t
s
n
o
c
C
H
L
straints on the Z0 (see text for details), the region above gBL > 0:5 is nonperturbative due to
gBL qmax
2 . In the blue shaded region DM is overabundant. The orange coloured region is
already excluded by direct detection constraints from LUX [72], the shortdashed line indicates the
future constraints from XENON1T [74] (projected sensitivity assuming 2t y), the longdashed line
the future constraints from LZ [75] (projected sensitivity for 1000d of data taking).
5
Results
We now combine in gure 2 the constraints coming from DM relic abundance, DM direct
detection experiments and collider searches. We can clearly see the synergy between these
di erent observables. Since the DM candidate in our model is a thermal WIMP, the relic
abundance constraint puts a lower bound on the gauge coupling, excluding the blue shaded
region in the panels of gure 2. On the other hand, LHC resonant searches essentially put
a lower bound on the mass of the Z0 (red shaded region), while the LUX direct detection
p
2
experiment constrains the product gBL
MZ0 from above (orange shaded region). For
reference, we also show the prospects for future direct detection experiments, namely,
XENON1T (orange shortdashed line, projected sensitivity assuming 2t y) and LZ (orange
longdashed line, projected sensitivity for 1000d of data taking). Finally, if the gauge
coupling is too large, perturbativity will be lost. To estimate this region we adopt the
constraint gBL
qmax
and being the largest B
L charge qmax = 5, we obtain
gBL > 0:5 for the nonperturbative region. The white region in these panels represents the
allowed region. We present four di erent DM masses so as to exemplify the dependence
on m . First, we see that for DM masses at 1 TeV (upper left panel), there is only a tiny
allowed region in which the relic abundance is set via resonant
For larger masses, the allowed region grows but some amount of enhancement is in any case
needed so that the Z0 mass needs to be around twice the DM mass in order to obtain the
correct relic abundance. For m
above 20 TeV (lower right panel), the allowed parameter
space cannot be fully probed even with generation2 DM direct detection experiments.
On top of the DM and collider phenomenology discussed here, this model allows for
a rich phenomenology in other sectors. In full analogy to the standard ISS model, the
dynamical ISS mechanism here considered is also capable of generating a large CP
asymmetry in the lepton sector at the TeV scale, thus allowing for a possible explanation of the
baryon asymmetry of the Universe via leptogenesis [84{87].
Moreover, the heavy sterile states typically introduced in ISS scenarios, namely the
three pseudoDirac pairs from the states NR and N R0 can lead to new contributions to a
wide array of observables [12, 88{111] such as weak universality, lepton avour violating or
precision electroweak observables, which allow to constrain the mixing of the SM neutrinos
with the extra heavy pseudoDirac pairs to the level of 10 2 or even better for some
! Z0 ! f f annihilation.
elements [112, 113].
6
Conclusions
The simplest extension to the SM particle content so as to accommodate the experimental
evidence for neutrino masses and mixings is the addition of righthanded neutrinos, making
the neutrino sector more symmetric to its charged lepton and quark counterparts. In this
context, the popular Seesaw mechanism also gives a rationale for the extreme smallness
of these neutrino masses as compared to the rest of the SM fermions through a hierarchy
between two di erent energy scales: the electroweak scale  at which Dirac neutrino masses
are induced  and a much larger energy scale tantalizingly close to the Grand Uni cation
scale at which Lepton Number is explicitly broken by the Majorana mass of the
righthanded neutrinos. On the other hand, this very natural option to explain the smallness of
neutrino masses automatically makes the mass of the Higgs extremely unnatural, given the
hierarchy problem that is hence introduced between the electroweak scale and the heavy
Seesaw scale.
The ISS mechanism provides an elegant solution to this tension by lowering the Seesaw
scale close to the electroweak scale, thus avoiding the Higgs hierarchy problem altogether.
In the ISS the smallness of neutrino masses is thus not explained by a strong hierarchy
between these scales but rather by a symmetry argument. Since neutrino masses are
protected by the Lepton Number symmetry, or rather B
L in its nonanomalous version,
if this symmetry is only mildly broken, neutrino masses will be naturally suppressed by
the small parameters breaking this symmetry. In this work, the possibility of breaking this
gauged symmetry dynamically has been explored.
Since the ISS mechanism requires a chiral structure of the extra righthanded neutrinos
under the B
L symmetry, some extra states are predicted for this symmetry to be gauged
due to anomaly cancellation. The minimal such extension requires the addition of three
new
B
elds with large nontrivial B
L charges. Upon the spontaneous breaking of the
L symmetry, two of these extra elds become a massive heavy fermion around the
TeV scale while the third remains massless. Given their large charges, the Z0 gauge boson
mediating the B
L symmetry couples preferentially to this new dark sector and much
more weakly to the SM leptons and particularly to quarks, making it rather elusive.
The phenomenology of this new dark sector and the elusive Z0 has been investigated.
We nd that the heavy Dirac fermion is a viable DM candidate in some regions of the
parameter space. While the elusive nature of the heavy Z0 makes its search rather challenging
at the LHC, it would also mediate spinindependent direct detection cross sections for the
DM candidate, which place very stringent constraints in the scenario. Given its preference
to couple to the dark sector and its suppressed couplings to quarks, the strong tension
between direct detection searches and the correct relic abundance for Z0 mediated DM
is mildly alleviated and some parts of the parameter space, not far from the resonance,
survive present constraints. Future DM searches by XENON1T and LZ will be able to
constrain this possibility even further. Finally, the massless dark fermion will contribute to
the amount of relativistic degrees of freedom in the early Universe. While its contribution
to the e ective number of neutrinos is too small to be constrained with present data, future
EUCLIDlike surveys could reach a sensitivity close to their expected contribution, making
this alternative probe a promising complementary way to test this scenario.
Acknowledgments
VDR would like to thank A. Vicente for valuable assistance on SARAH and SPheno. JG
would like to thank Fermilab for kind hospitality during the
nal stages of this project.
This work is supported in part by the EU grants H2020MSCAITN2015/674896Elusives
and H2020MSCA2015690575InvisiblesPlus. VDR acknowledges support by the Spanish
grant SEV20140398 (MINECO) and partial support by the Spanish grants
FPA201458183P, Multidark CSD200900064 and PROMETEOII/2014/084 (Generalitat
Valenciana). EFM acknowledges support from the EU FP7 Marie Curie Actions CIG NeuProbes
(PCIG11GA2012321582), \Spanish Agencia Estatal de Investigacion" (AEI) and the EU
\Fondo Europeo de Desarrollo Regional" (FEDER) through the project FPA201678645P
and the Spanish MINECO through the \Ramon y Cajal" programme (RYC201107710)
and through the Centro de Excelencia Severo Ochoa Program under grant SEV20120249
and the HPCHydra cluster at IFT. The work of VN was supported by the SFBTransregio
TR33 \The Dark Universe". This manuscript has been authored by Fermi Research
Alliance, LLC under Contract No. DEAC0207CH11359 with the U.S. Department of
Energy, O ce of Science, O ce of High Energy Physics. The United States Government
retains and the publisher, by accepting the article for publication, acknowledges that the
United States Government retains a nonexclusive, paidup, irrevocable, worldwide license
to publish or reproduce the published form of this manuscript, or allow others to do so, for
United States Government purposes.
Open Access.
This article is distributed under the terms of the Creative Commons
Attribution License (CCBY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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