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arXiv:1004.0649v2 [hep-ph] 25 May 2010
Multicomponent Dark Matter in Supersymmetric
Hidden Sector Extensions
Daniel Feldman1,a, Zuowei Liu2,b, Pran Nath3,c, and Gregory Peim4,c
aMichigan Center for Theoretical Physics, Ann Arbor, Michigan 48104, USA
bC.N. Yang Institute for Theoretical Physics, Stony Brook, New York, 11794, USA
cDepartment of Physics, Northeastern University, Boston, Massachusetts 02115, USA
Abstract
Most analyses of dark matter within supersymmetry assume the entire cold dark matter
arising only from weakly interacting neutralinos. We study a new class of models consisting of
U(1)nhidden sector extensions of the minimal supersymmetric standard model that includes
several stable particles, both fermionic and bosonic, which can be interpreted as constituents
of dark matter. In one such class of models, dark matter is made up of both a Majorana dark
matter particle, i.e., a neutralino, and a Dirac fermion with the current relic density of dark
matter as given by WMAP being composed of the relic density of the two species. These
models can explain the PAMELA positron data and are consistent with the antiproton flux
data, as well as the photon data from FERMI-LAT. Further, it is shown that such models
can also simultaneously produce spin-independent cross sections which can be probed in
CDMS-II, XENON-100 and other ongoing dark matter experiments. The implications of the
models at the LHC and at the next linear collider (NLC) are also briefly discussed.
1e-mail: djfeld@umich.edu
2e-mail: liu@max2.physics.sunysb.edu
3e-mail: nath@neu.edu
4e-mail: peim.g@neu.edu
Preprint Numbers: MCTP-10-15, YITP-SB-10-08, NUB-3266
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1 Introduction
Recently several particle physics models have been constructed that connect the standard
model (SM) to hidden sectors and lead to massive narrow vector boson resonances as well
as other signatures which can be detected at colliders [1, 2, 3]. The connection to the
hidden sector arises via mass mixings and kinetic mixings[1, 2, 3, 4, 5, 6] and via higher
dimensional operators. Models with the above forms of communication between the sectors
also have important implications for dark matter [7, 3, 6] (for a review see [8, 9]).
this work we show that multicomponent dark matter can arise from U(1)nextensions of
the minimal supersymmetric standard model (MSSM) with Abelian hidden sectors which
In
include hidden sector matter. Our motivation stems in part from the results of several dark
matter experiments that have recently appeared. Thus the PAMELA Collaboration [10] has
observed a positron excess improving previous results from HEAT and AMS experiments
[11]. One possible explanation of such an excess is via the annihilation of dark matter in the
galaxy[12]. Additionally, recent data from CDMS-II hints at the possibility of dark matter
events above the background, and this will be explored further by the upgraded XENON
experiment [13, 14].
For a thermal relic, the PAMELA data and CDMS-II data taken together at face value
do raise a theoretical puzzle if indeed both signals arise from the annihilation of cold dark
matter. Thus most models which aim to explain the PAMELA positron excess do not give
a significant number of dark matter events in the direct detection experiments currently
operating. Conversely, models which can give a detectable signal in direct detection exper-
iments typically do not explain the PAMELA data without the use of enormous so-called
boost factors. As we will show here, this can be circumvented in models where the dark
matter has several components. Thus, motivated in part by the recent cosmic anomalies we
develop supersymmetric models which contain minimally a hidden Abelian sector broken at
the sub-TeV scale where the mass generation of the hidden states involves nontrivial mixings
with the field content of the electroweak sector of the minimal supersymmetric extension of
the standard model leading to dark matter which can have several components which can
be both bosonic and fermionic.
More specifically, in this work we go beyond the simple theoretical construction that ther-
mal dark matter compatible with WMAP observations is composed of a single fundamental
particle. There is no overriding principle that requires such a restriction, and nonbaryonic
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dark matter (DM) may indeed be constituted of several components, so in general one has
(Ωh2)DM =?
contribute to the total nonbaryonic (Ωh2)DM. In fact we already know that neutrinos do
contribute to dark matter although their contribution is relatively small. Thus we propose
i(Ωh2)DMi, where i refers to the various species of dark particles that can
here a new class of multicomponent cold dark matter models in Abelian U(1) extensions of
MSSM which can simultaneously provide an explanation of the PAMELA and WMAP data
through a Breit-Wigner enhancement [12], while producing detectable signals for the direct
searches for dark matter with CDMS/XENON and other dark matter experiments.
A simultaneous satisfaction of the PAMELA positron excess and the satisfaction of
WMAP relic density constraints can also occur if there is a nonthermal mechanism for
the annihilation of dark matter with a wino lightest (R parity odd) supersymmetric particle
(LSP) [15, 16, 17, 18, 8, 9]. However, a detectable spin-independent cross section in such a
nonthermal framework does require that a pure wino is supplemented by a suitable admix-
ture of Higgsino content as in the analysis of [19] and in [20], the later for a thermal relic.
We remark that multiple U(1) factors and its influence on dark matter have very recently
been studied [20, 21]. We also remark, some other works have recently looked at dark matter
with more than 1 component [22]. The models proposed and analyzed here are very different
from these.
The outline of the rest of the paper is as follows: In Sec.(2) we give a detailed description
of the two models one of which is based on a U(1)X extension of the MSSM where U(1)X
is a hidden sector gauge group with Dirac fermions in the hidden sector. This model allows
for dark matter consisting of Dirac, Majorana, and spin zero particles. The second model is
based on a U(1)X×U(1)Cextension of MSSM, where U(1)Cis a gauged leptophilic symmetry
and U(1)X, as before, is the hidden sector gauge group which also contains Dirac particles in
the hidden sector. This model too has Dirac, Majorana, and spin zero particles as possible
dark matter. In both cases we will primarily focus on the possibility that dark matter
consists of Dirac and Majorana particles, and we will not discuss in detail the possibility
of dark matter with bosonic degrees of freedom. In Sec.(3) we discuss the relic densities in
the two component models. In Sec.(4) we give an analysis of the positron, antiproton, and
photon fluxes in the two models. In Sec.(5) we give an analysis of event rates for the proposed
models for CDMS-II and for XENON-100. We give the analysis within the framework of
supergravity grand unified models [23, 24] defined by the parameters m0,m1/2,A0,tanβ, and
sign(µ) with nonuniversalities (NUSUGRA) defined by δ1,2,3in the gaugino sector so that
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U(1)Y×SU(2)L×SU(3)Cgaugino masses at the grand unified theory (GUT) scale are given
by ˜ mi= m1/2(1 + δi) (i = 1,2,3) (see, e.g., [25] and references therein). We also discuss the
possible new physics one might observe at the LHC (for a recent review see also [9]) and
elsewhere for these models. Conclusions are given in Sec.(7).
2Multicomponent Hidden Sector Models
2.1 Multicomponent U(1)Xmodel
A U(1)Xextension of the minimal supersymmetric standard model involves the coupling of
a Stueckelberg chiral multiplet S = (ρ + iσ,χS,FS) to vector supermultiplets X,B, where
ρ is a real scalar and σ is an axionic pseudoscalar. Here X is the U(1)X vector multiplet
which is neutral with respect to the SM gauge group with components X = (Xµ,λX,DX),
and B is the U(1)Y vector multiplet with components (Bµ,λB,DB), where the components
are written in the Wess-Zumino gauge. The chiral multiplet S transforms under both U(1)X
and U(1)Y and acts as the connector sector between the visible and the hidden sectors. The
total Lagrangian of the system is given by
L = LMSSM+ LU(1)X+ LSt
(1)
where LU(1)Xis the kinetic energy piece for the X vector multiplet and LStis the supersym-
metric Stueckelberg mixing between the X and the B vector multiplets so that [1, 7] (see
also [26, 27, 20])
LSt=
?
d2θd2¯θ (M1X + M2B + S +¯S)2, (2)
where M1and M2are mass parameters. The Lagrangian of Eq.(1) is invariant under the
U(1)Y and U(1)Xgauge transformations, i.e., under
δXX = ζX+¯ζX,δXS = −M1ζX, δYB = ζY+¯ζY ,δYS = −M2ζY, (3)
where ζ is an infinitesimal transformation chiral superfield. In component form we have for
the Stueckelberg sector with U(1)X× U(1)Y
LSt = −1
+ρ(M1DX+ M2DB) + ¯ χS(M1¯λX+ M2¯λB) + χS(M1λX+ M2λB) .
2(M1Xµ+ M2Bµ+ ∂µσ)2−1
2(∂µρ)2− iχSσµ∂µ¯ χS+ 2|FS|2
(4)
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In addition, one may include a supersymmetric kinetic mixing term between the U(1)Xand
U(1)Y gauge fields [7] leading to L = LMSSM+ LU(1)X+ LKM+ LSt, where
LU(1)X+ LKM = −1
−δ
4XµνXµν− iλXσµ∂µ¯λX+1
2XµνBµν− iδ(λXσµ∂µ¯λB+ λBσµ∂µ¯λX) + δDBDX.
2D2
X
(5)
One can also add additional D terms as in [7]. Both Stueckelberg and kinetic mixings of the
gauge fields U(1)Xand U(1)Y are constrained by the electroweak data[2]. As a consequence
of the mixings, the extra gauge boson of the hidden sector couples with the standard model
fermions and can become visible at colliders. The Lagrangian for matter interacting with
the U(1) gauge fields is given by
Lmatt =
?
d2θd2¯θ
?
i
?¯Φie2gYQYB+2gXQXXΦi+¯Φhid,ie2gYQYB+2gXQXXΦhid,i
?
.(6)
where the visible sector chiral superfields are denoted by Φi(quarks, squarks, leptons, slep-
tons, Higgs, and Higgsinos of the MSSM) and the hidden sector chiral superfields are denoted
by Φhid,i. In the above, QYis the hypercharge normalized so that Q = T3+QY. As mentioned
already, the SM matter fields do not carry any charge under the hidden gauge group and vice
versa, i.e. QXΦi= 0 and QSMΦhid= 0. The minimal matter content of the hidden sector
consists of a left chiral multiplet Φhid= (φ,f,F) and a charge conjugate Φc
so that Φhid and Φc
tion. A mass Mψfor the Dirac field ψ arises from an additional term in the superpotential
Wψ= MψΦΦc, where ψ is composed of f and f′. The scalar fields acquire soft masses of
size m0from spontaneous breaking of supersymmetry by gravity mediation, and in addition
acquire a mass from the term in the superpotential so that
hid= (φ′,f′,F′)
hidhave opposite U(1)X charges and form an anomaly-free combina-
m2
φ= m2
0+ M2
ψ= m2
φ′. (7)
After spontaneous breaking of the electroweak symmetry there would be mixing between
the vector fields Xµ,Bµ,A3µ, where A3µ is the third component of the SU(2)L field Aaµ,
(a = 1,2,3). After diagonalization VT= (X,B,A3) can be expressed in the terms of the
mass eigenstates ET= (Z′,Z,γ) as follows:
Vi= OijEi, i,j = 1 − 3,E = (Z′,Z,γ). (8)
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