As the electromagnetic gauge symmetry makes the electron stable, a new
abelian gauge symmetry may be responsible for the stability of superheavy dark
matter. The gauge boson associated with the new gauge symmetry naturally plays
the role of dark radiation and contributes to the effective number of `neutrino
species', which has been recently measured by Planck. We estimate the
contribution of dark radiation from the radiative decay of a scalar particle
induced by the WIMPZILLA in the loop. The scalar particle may affect the
invisible decay of the Higgs boson by the Higgs portal type coupling.Comment: 4 pages, 3 figure

Park, Jong-Chul

Park, Seong Chan

English

arXiv

AbstractAs the electromagnetic gauge symmetry makes the electron stable, a new abelian gauge symmetry may be responsible for the stability of superheavy dark matter. The gauge boson associated with the new gauge symmetry naturally plays the role of dark radiation and contributes to the effective number of ‘neutrino species’, which has been recently measured by Planck. We estimate the contribution of dark radiation from the radiative decay of a scalar particle induced by the WIMPZILLA in the loop. The scalar particle may affect the invisible decay of the Higgs boson by the Higgs portal type coupling

Elsevier - Publisher Connector 

Physics Letters B 728 (2014) 41–44Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
A testable scenario of WIMPZILLA with dark radiation
Jong-Chul Park, Seong Chan Park
Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
a r t i c l e i n f o a b s t r a c t
Article history:
Received 10 October 2013
Accepted 11 November 2013
Available online 22 November 2013
Editor: J. Hisano
As the electromagnetic gauge symmetry makes the electron stable, a new abelian gauge symmetry may
be responsible for the stability of superheavy dark matter. The gauge boson associated with the new
gauge symmetry naturally plays the role of dark radiation and contributes to the effective number of
‘neutrino species’, which has been recently measured by Planck. We estimate the contribution of dark
radiation from the radiative decay of a scalar particle induced by the WIMPZILLA in the loop. The scalar
particle may affect the invisible decay of the Higgs boson by the Higgs portal type coupling.
© 2013 The Authors. Published by Elsevier B.V. Open access under CC BY license.1. Introduction
Having no ﬁrmly established evidence for weakly interacting
massive particle (WIMP) at the LHC and direct detection exper-
iments below a TeV, we are motivated to consider dark matter
(DM) in a heavier energy regime. If the DM particle is heavier than
a TeV, however, some crucial diﬃculties arise as follows.
• Overclosure of the universe: The pair-annihilation cross section
of dark matter, 〈σ v〉 ∝ 1/m2DM, becomes small and leads to
the overclosure of the universe with a large density, ΩDM =
ρDM/ρC > 1, where ρC is the critical density.
• Instability of dark matter: A heavy particle, in general, tends to
be unstable if no symmetry principle forbids its decay.
• Lack of testability: In currently on-going or future running ex-
periments, heavier dark matter well above a TeV range is hard
to get tested [1,2].
Rather surprisingly, the overclosure of the universe can be re-
solved in the case of superheavy dark matter, dubbed WIMPZILLA,
in a mass window mDM ≈ 1012–14 GeV providing a nice ﬁt to the
observed DM abundance, ΩDM  0.2–0.3, independently of the
nongravitational interactions of the DM particles. The superheavy
dark matter can be produced in various stages of cosmological his-
tory: during preheating, reheating and at the end of the inﬂation-
ary era or in the bubble collision in a ﬁrst-order phase transition
as studied in detail in Refs. [3,4].
E-mail address: s.park@skku.edu (S.C. Park).0370-2693 © 2013 The Authors. Published by Elsevier B.V.
http://dx.doi.org/10.1016/j.physletb.2013.11.027
Open access under CC BY licensHowever, the stability problem is worse for WIMPZILLA with its
extremely high mass. A global symmetry, such as R-parity in su-
persymmetry models, does not work since in the presence of grav-
ity, especially in the vicinity of black hole, all the stable particles
(strings and branes) should be associated with gauge symmetries
[5,6]. An interesting observation is that the electron is stable due
to the exact electromagnetic U(1)em gauge symmetry in the stan-
dard model (SM). Here we consider the similar possibility that an
abelian group U(1)H is responsible for the stability of superheavy
dark matter. The gauge symmetry may originate from a compact
group such as E6 or even larger group [7]. Just like the photon
with U(1)em , a new massless gauge boson is associated with the
new gauge symmetry and the presence of new gauge boson opens
a new window of testability of WIMPZILLA!1
The new gauge boson does not directly interact with the SM
sector since it is associatively introduced for dark matter. We thus
regard the new gauge boson as hidden photon or dark radiation.
Dark radiation may have left the evidence of its presence in vari-
ous circumstances in cosmological history of the universe. Indeed,
recent observations show that there may exist non-standard model
relativistic particles at the time of Big Bang nucleosynthesis (BBN)
and also at the era of recombination shown in cosmic microwave
background radiation (CMBR).
In the rest of this Letter, we examine possible experimental
tests of this WIMPZILLA associated dark radiation in BBN and
CMBR [9–12] and also collider physics [13] based on a model,
which is shortly introduced.
1 The possibility that primordial superheavy particles with a new U(1) gauge
charge is the source of Ultra High Energy Cosmic Rays is considered in [8].e.
42 J.-C. Park, S.C. Park / Physics Letters B 728 (2014) 41–44Fig. 1. A scalar particle (φ) decaying into two hidden photons through the
WIMPZILLA (ψ ) loop.
2. The model
The minimal model, which we propose, includes two new hid-
den sector particles: A Dirac fermion ψ and a scalar φ. The fermion
is charged under the ‘hidden’ abelian gauge symmetry, U(1)H , and
identiﬁed with dark matter. The scalar particle is neutral under
the gauge symmetry as well as the standard model interactions
but is responsible for the late time decay to dark radiation. Obvi-
ously the model is free from anomaly. The generic gauge invariant
Lagrangian2 is given by
L⊃ LSM +Lφ + λφHφ2
(
H†H
)− 1
4
FHμν F
μν
H
− yψφψψ + iψγ μ
(
∂μ − igH AHμ
)
ψ −mψψψ, (1)
where the kinetic term for the scalar ﬁeld is denoted as Lφ =
1
2 [(∂φ)2 − m2φφ2] and the ‘Higgs portal’ interaction with the cou-
pling constant λφH [16] is allowed. We comment on the mass
scales in our model. Due to the vectorlike mass term the new
fermion is naturally heavy and nice ﬁt to the WIMPZILLA picture.
However, to account the late time decay, the new scalar is required
to be much lighter than the WIMPZILLA thus has a similar hierar-
chy problem for the SM Higgs boson, which is much lighter than
a high scale, e.g. Planck scale. In our case, since the scalar particle
is in the hidden sector, we are allowed to rely on a (super)sym-
metry in hidden sector due to which the scalar boson is protected
from the radiative correction. Also unnecessary term, e.g., φH†H
is forbidden automatically. The details will be presented in other
place [17].
Differently from the dark matter particle, which is protected
by U(1)H , the scalar particle is unstable and decays into two hid-
den photons at one-loop level through the triangle diagram with
the virtual ψ in the loop as can be seen in Fig. 1. The decay width
of φ is highly suppressed by the heavy mass of ψ :
1
τφ→2γH
≈ (αH yψ)
2
144π3
m3φ
m2ψ
, (2)
where the structure constant is αH = g2H/4π . With reasonable
choice of parameters, the lifetime can lie in particularly interest-
ing epochs:
• the BBN epoch, tBBN ≈O(0.1–1000) s,
• the CMB epoch, tCMB ≈ 3.8× 105 yr≈ 1.2× 1013 s,
thus, in principle, we can test the idea of WIMPZILLA by observing
dark radiation in these epochs.
2 The kinetic mixing term ∼ Fμν FμνH can be another source of communication
between the hidden sector and the SM sector [14,15] if there exists a bi-charged
particle of both sectors, which is absent in the current model. This is consistent
with the fact that there is no charged particle under the hidden as well as the SM
gauge symmetries.3. Observational bounds
Now we are ready to consider dark radiation components see-
ing in CMB and BBN data and the possible contribution to the
Higgs invisible decay at the LHC.
Dark radiation: The effective number of relativistic degrees
of freedom, Neff, is recently observed by Planck [18], WMAP
9 year [19] and also BBN [20]:
NCMBeff = 3.30± 0.27 (Planck 2013),
NCMBeff = 3.84± 0.40 (WMAP9),
NBBNeff = 3.71+0.47−0.45 (BBN). (3)
Compared to the SM expectation, NSMeff = 3.046 [21], there ex-
ists some deviation in particular in WMAP9 and BBN results,
which may be explained by dark radiation. It is worth noticing
that adding the H0 measurement to the Planck CMB data gives
Neff = 3.62 ± 0.25, which is 2.3σ level away from the SM expec-
tation [18]. Indeed new relativistic degree of freedom relieves the
tension between the CMB data and H0.
In our case, a sizable dark radiation component at CMB or BBN
epoch is obtained if dark radiation is produced by a late time de-
cay of a particle, the scalar particle φ in our case. The scalar φ
is in contact with the SM through the Higgs portal. Provided that
φ never has dominated the expansion of the universe, but pro-
duced extra relativistic degrees of freedom by its decay [9–12,22],
the extra contribution to the effective number of relativistic degree
of freedom, Neff, is calculated with Yφ = nφ/s, the number den-
sity over the entropy density of the universe describing the actual
number of particles per comoving volume and the mass and the
lifetime of φ by a simple formula [9,23]
NCMBφ decay = 8.3(Yφmφ/MeV)(τφ/s)1/2. (4)
In addition to the DR component originated from φ decay, the
primordial hidden photon γH can contribute to Neff. The primor-
dial γH is produced through the interactions with the SM thermal
bath and we can calculate the contribution conveniently as a rela-
tive ratio compared to the energy density of one neutrino species:
Nprimo γH = ργH /ρν . The energy densities are given by ργH =
gγH T
4
γH ,0
and ρν = (7/8)gν T 4ν,0 where Ti,0 = ( g∗S,0g∗S,i dec )1/3Tγ ,0 and
gi and Ti,0 are the degrees of freedom and the present tempera-
ture of the species i. g∗S,0 and g∗S,i dec are respectively the total
degrees of freedom associated with entropy at present and the
decoupling time of the species i. We then found the primordial
contribution is quite suppressed as
Nprimo γH =
2
(7/8) · 2
(
11
4
)4/3( g∗S,0
g∗S,γH dec
)4/3
≈ 0.053, (5)
where we took g∗S,0 = 3.91 and g∗S,γH dec = 107.75 for γH and
g∗S,0/g∗S,ν dec = 4/11 for neutrino. This small contribution is un-
derstandable since the interaction between the hidden photon γH
and the SM thermal bath is loop suppressed with the WIMPZILLA
in the loop thus the hidden photon is decoupled from the SM ther-
mal bath at a high temperature well beyond the electroweak scale.
Finally, we get the total contribution of the WIMPZILLA as
NWZeff = Neff − NSMeff
= NCMBφ decay + Nprimo γH , (6)
which we should compare with the observational results in Eq. (3),
in particular, the Planck 2013 result.
J.-C. Park, S.C. Park / Physics Letters B 728 (2014) 41–44 43Fig. 2. Contour plots for NWZeff in the mφ–λφH plane when the decay lifetime of φ , τφ , is ﬁxed as 0.1, 100 and 10
4 s from left to right panels. The shaded region is excluded
by the conservative invisible Higgs decay width limit [26], BRinv < 0.28 at 95% C.L. allowing non-standard values for h → γ γ and h → gg modes. The left-lower regions
below solid lines are constrained by the effective number of relativistic degrees of freedom limit from the Planck observation [18] at 1σ and 2σ level, respectively.In Fig. 2, we plotted NWZeff at CMB epoch with the Higgs
portal coupling λφH ∈ (10−5,10−1) with respect to mφ in (100,
102.5) GeV with the interesting lifetime of φ given as 10−1 s (left),
102 s (middle) and 104 s (right), respectively. These particular time
scales are chosen as they coincide with before, during or after
BBN time, respectively. We show the best ﬁt lines for the Planck
observation taking 1σ and 2σ deviations into account [18]. The
left-lower regions below solid lines provide too big contribution to
DR component so are excluded. In each plot, a dip structure around
mφ = mh/2 appears due to the resonant s-channel annihilation
of φ into SM particles mediated by the Higgs boson through the
dependence on Yφ which is controlled by the annihilation cross
section of φ into SM particles.
To see the contribution at BBN epoch, we follow the discussion
in Ref. [9]. When the scalar decays early, τφ→2γH  0.1 s, the con-
tribution to BBN is essentially same with the contribution to CMB
because all of the energy density of φ should be converted into
the dark photon γH before BBN. On the other hand, if the scalar
decays after the BBN time, τφ→2γH  1000 s, the effect is entirely
due to the energy density of φ, thus, NBBNφ /N
CMB
φ→2γH decreases.
Since the constraint from the BBN is weaker than that by CMB
(Planck 2013) as in Eq. (3), and the contribution from φ decay is
smaller with the longer lifetime, we do not ﬁnd any useful bound
beyond the bound from the CMB measurement in this regime.
Invisible decay of the Higgs: Our scenario includes a light scalar,
φ, and it interacts with the SM Higgs boson, we can ﬁnd another
important channel to test our idea in collider experiments. Hav-
ing non-vanishing ‘Higgs portal’ interaction, which induces com-
munication between the hidden and visible sectors, the decay of
the Higgs boson to the hidden sector scalar particles is available
when kinematically allowed. Actually, the invisible branching frac-
tion of the Higgs is recently measured by ATLAS and CMS [24,25].
A global ﬁt analysis to all the Higgs search data sets a stringent
limit on the branching fraction to the invisible Higgs decay width:
BRinv = ΓH→invisible/ΓH→all < 0.19 at 95% C.L. assuming the SM de-
cay rates for all the visible Higgs decay modes and BRinv < 0.28 at
95% C.L. allowing non-standard values for h → γ γ and h → gg
modes, [26]. From these constraints, we obtained a bound on the
Higgs portal coupling as is depicted in Fig. 2 where the shaded
regions are excluded.4. Conclusion
Superheavy dark matter with mDM ≈ 1012–14 GeV, dubbed
WIMPZILLA, can satisfy the observed dark matter abundance but
the stability of WIMPZILLA requires an explanation. In this Let-
ter, a new gauge symmetry U(1)H is introduced to stabilize
WIMPZILLA just like the electromagnetic gauge symmetry to the
electron. This simple cure provides interesting possibilities of prob-
ing WIMPZILLA by cosmological observations of dark radiation in
CMBR and BBN data also by collider experiments of measuring in-
visible decay of the Higgs boson.
Acknowledgements
This work is supported by Basic Science Research Program
through the National Research Foundation of Korea funded by the
Ministry of Education, Science and Technology (2011-0010294) and
(2011-0029758).
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A testable scenario of WIMPZILLA with dark radiation 

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A testable scenario of WIMPZILLA with Dark Radiation

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