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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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