Journal of Modern Physics, 2010, 1, 393-398
doi:10.4236/jmp.2010.16056 Published Online December 2010 (http://www.SciRP.org/journal/jmp)
393
On Gaugino Dominated Dark Matter
Salah Eddine Ennadifi1, El Hassan Saidi1,2
1Laboratory of High Energy Physics, Modeling and Simul a t i on, Faculty of Sciences, Rabat, Morocco
2Centre of Physics and Ma thematics, CPM-CNESTEN, Rabat, Morocco
Received July 20, 2010; revised October 10, 2010; accepted October 25, 2010
Abstract
Using the neutral gauginos of



2
LY
SU U1 and hybridization ideas below the GUT scale, we approach
the Dark Matter particle within the Minimal Supersymmetric Standard Model. In the energy range
GUT Z
M
M where supergravity effects can be ignored, it is proposed that such DM particle could be inter-
preted in terms of a mixture of Bino and Wino states with a lower bound mass 65
DM
M
GeV not far
above the electroweak scale to account for the observed Dark Matter density. We establish the theoretical
origin of this particle and study as well its compositeness and its mass bound.
Keywords: Minimal Supersymmetric Standard Model, Gauginos, Dark Matter
1. Introduction
Precision cosmology data identify Dark Matter (DM) as
the main building block for all structures in the Universe
[1-3]; however they do not discriminate among the sev-
eral candidates discussed in the literature namely MA-
CHO’s [4], Axions [5], gluinos [6,7], the lightest sneu-
trino [8,9], which some of them have been excluded ex-
perimentally [10,11], and weakly interacting massive
particles (WIMP’s) [12]. Although alternative explana-
tions in terms of modified gravity (MOND) [13,14] can-
not be ignored, they can hardly be reconciled with the
most recent astrophysical observations [15,16] without
requiring additional matter beyond the observed baryons
[17].
Solving this puzzle is one of the greatest challenges in
modern physics. This problem, long regarded in astro-
physics and cosmology, is now deeply rooted in high
energy physics since it is in the context of theories be-
yond the Standard Model (SM) of elementary particles
[18] where the brightest candidates for DM arise. New
weakly interacting massive particles [19] are well moti-
vated by particle physics theory opening the door for
particle physics beyond the SM. The Minimal Super-
symmetric Standard Model (MSSM), the best motivated
extension of the SM, provides a good candidate for the
DM component of the Universe in terms of Lightest Su-
persymmetric Particle (LSP) if R-parity
P
R is con-
served [20]. In simple realistic supersymmetric models,
where supersymmetry is broken at the weak scale all SM
particles must have superpartners with masses 1TeV

.
These sparticles, existed in the early universe in thermal
equilibrium with the ordinary SM particles. As the uni-
verse cooled and expanded, the heavier sparticles could
no longer be produced, and they eventually annihilated
or decayed into LSP’s. Some of the LSP’s pair-annihi-
lated into final states not containing sparticles.
Given the outstanding advances in DM detection ex-
periments, as well as the forthcoming onset of the LHC
experiments, an exciting near future can be anticipated in
which this enigma might start being unveiled. In this
paper, we develop an approach to the DM weakly inter-
acting massive particle by using the pure gaugino sector
of MSSM and a hypothesis on hybridization of the wave
functions of the abelian gauginos of the MSSM gauge
group. Guided by LHC experiments, we will mainly fo-
cus on the




31
CIY
SUU U

1 Yang-Mills sector
of MSSM although a full picture should include super-
gravity since, along with gauginos, it is a potential can-
didate for DM through the gravitino sector. To proceed,
we first recall briefly the main evidence for DM. Then,
restricting to the gaugino sector of MSSM and using
wave function language, we present our proposal for DM
particle in terms of hybridization of the Bino B


and
the Wino W



fields, the supersymmetric partners of the
B

and W

gauge particles mediating the


1
I
U



1
Y
U gauge interaction sector of the SM. Next, we
focus on the identification of the DM particle and its
basic properties by varying the scale energy ε from the
grand unification scale to the electroweak
GUT
M
Z
M

S. E. ENNADIFI ET AL. 394
one, then we deduce the lower bound of DM particle
mass
D
M by translation into the electroweak scale.
We end this study by some comments and concluding
remarks.
M
Uni
2. The Problematic
Historically the observational evidence for the existence
of DM came only from galactic dynamics. Presence of
DM can be inferred from gravitational effects on visible
matter. According to present observations of universe
structures larger than galaxies as well as Big Bang cos-
mology inspired models, DM accounts for the vast ma-
jority of mass in the observable universe [21],

70%25% 5%
verse DEDMSM 



(1)
where DM stands for non baryonic dark matter and DE
for dark energy. Although the microscopic composition
of DM remains a mystery, it is clear that it cannot consist
of any elementary particles which have been discovered
so far. Since this exotic matter strongly exists in the form
of non-baryonic matter, the MSSM is therefore expected
to provide a good candidate for the DM component of
the Universe, thanks to the
P
R conservation. The cur-
rent largely adopted view on DM implies that it is mostly
made of WIMP’s [12]. Although these are hypothetical
massive particles that scarcely interact with regular mat-
ter, making them very hard to detect, a huge effort has
been made to discover them on a global scale. DM com-
ponent must be then an undiscovered, massive, stable or
long lived particle. So we envisage that is, as it is almost
widely accepted, supersymmetric, light, electrically neu-
tral and non-colored

em
Q

0


0C. This limits
our work to the following abelian dark sector

0
1em
nCQ
Dark
GU

 (2)
If weak-scale supersymmetry is realized in nature, the
LSP plays a special role in the search for supersymmetry
at colliders. All heavier particles rapidly cascade decay
to the LSP, since this occurs in all supersymmetric
events, the nature of the LSP and its behavior are deci-
sive for all supersymmetric signatures at the LHC. In the
MSSM, the most widely studied candidate the lightest
neutralino

, which is a very promising DM candidate
[22] in large region of the parameter space, and, if one of
its mass parameter contents is much lighter than the oth-
ers, the LSP will be predominately of this form.
N
For the remainder of this paper, we will restrict our-
selves to the case of gaugino dominated LSP, especially
a typical Bino-like content
B


as it often emerges from
minimal supergravity boundary conditions on the soft
parameters which tend to require it in order to get correct
electroweak symmetry breaking. Although Bino DM
generally gives higher DM density, it could be decreased
by considering just enough Wino o
W content allow-
ing for natural cold DM in accordance with astrophysical
datas.

Below, in the MSSM framework, we develop an ap-
proach to DM through the idea of the evolution of the
abelian gaugino hybrids state with the scale energy down
to the electroweak scale where the Higgsino sector con-
tributes
H



to DM state. Using specific properties
where gauge quantum numbers captured by matter in
adjoint representations take trivial values makes the de-
tection of their interactions a complicated task and where
LHC experiments are expected to bring more insight.
3. Dark Matter Building
Restriction to the neutral gauginos sector of MSSM as
the first source of DM makes the derivation of DM parti-
cle more tractable,

1
Dark I
GU

Y
U1. (3)
In fact, besides their masses generated by supersym-
metry breaking, the abelian gauginos


aa
,


 

(4D Majorana fermions) have the same quantum num-
bers under




31SUU U

1


0
0
:1,1
:1,

CIY
; they belong to un-
charged (real) representations of the gauge symmetry.
Restricting to the abelian subgroup (3,1), we have:
1
Bino B
Wino W





(4)
In absence of supergravity, the Bino B


and the
Wino of the W





1UU1

21U
IY
subsymmetry and
eventually the two gluinos in the Cartan sector
of the



3
C
SU color symmetry, are good candidates to
dominate the DM brick. Focusing on these two massive
particles in the
D
ark gauge sector of MSSM, we have
to deal with the two particle states,
G
00
, .
em
CQ 

B

em
CQ
BW




(5)
In this description, the field particles and W are
Majorana spinors standing respectively for the wave
functions associated with the gauginos

aa
and




,BB


aa
,WW



. In addition to the fact that experimentally are
hardly distinguishable, the trivial quantum numbers of
the B
 and W  states let understand that gauge in-
variance and supersymmetry do not prevent the existence
of mixed states of these “twin sparticles” in the linear
combination form,
fg,
fg
NB
NBW



 



W


(6)

S. E. ENNADIFI ET AL.395
1
even before the electroweak symmetry breaking
where the two Higgsinos
compete after getting the appropriate gauge quantum
numbers
 
21
LY em
SU UU
0
em
CQ
H



 (7)
Since are still eigenstates of the N

D
ark gauge
invariance and that Majorana condition still holds pro-
vided that the coefficients f and g are real which more-
over obey the normalization condition
G
22
fg1
0.
NN
NN







,
(8)
On the other hand seen that the hybridization property
(6) as well as the normalization condition (8) should hold
for the energy band where MSSM is supposed to govern
the dynamics of the universe evolution, we will assume
moreover that the real coefficients and g depend
somehow on the scale energy
f

, that is:
 
ff, g

  (9)
with

belonging more a less to the range GUT Z
M
M

and where it plays a similar role as in the renormalization
group equation for gauge coupling constants. In this pic-
ture, the DM component we are looking for depends on
the scale energy and other extra moduli fixed by dimen-
sional arguments; one of them, denoted τ, will be in-
ferred in a moment; see Equation (12). Within this view,
let us now focus on the explicit building of the states (6)
in terms of the scale energy. A priori, there are infinitely
many solutions for the normalization condition (8) since
the 2 × 2 rotation matrix is orthogonal, having a family
of one parameter solution. But here we need to solve the
constraint relation (8) in an explicitly energy dependent
manner that could somehow describe a quasi-realistic
model. Therefore seen that the involved coefficients
solve the orthogonality condition of the rota-
tion symmetry in the space generated by their associated
wave functions,
 2, RSO

fg 2, ,
gf
RSO




 R
0,
(10)
and taking into account the recurring feature that DM
particle is actually a Bino in the major portion of the
constrained MSSM parameter space
f1, g
ZZ
MM  
 (11)
we assume for reasons of simplicity, although more
complicated versions of the energy dependent solutions
are possible, that the gaugino state has the following ex-
plicit form
 
2
1
ZZ
MM
NeB eW
   



The scenario driven through this exponential behave-
iour1 permits to monitor continuously the system at dif-
ferent energy stages and thus a possible physical picture
of the DM state evolution. To make contact with the
property (8), it is enough to parameterize fcos

 and
gsin


and solve to get the relation



  be-
tween the involved angle and the scale energy

; later
on this angle will be interpreted as the Weinberg mixing
angle w

. The parameter 0

 is homogenous to time
(inverse of energy) which in general could be used to
characterize the different state configurations. When
varying the scale energy and keeping it fixed, we delimit
the dominating areas of each component:
In this view, the DM particle lies near the electroweak
scale or at least above a neighboring superparticle mass
scale S
M
with SZ MM



 refers to the fine gap
between the two scales.
4. Low Energy Constraints
To make this approach more predictive at weak mass
scale, we use the fixed GUT relationship between the
gauginos masses 2
BW as expected from renor-
malization group Equations [23] implying
MM
50
B
M
GeV
.
The phenomenological importance of this translation will
be enhanced in what follows: the mixed state, defined as
a hybridization of Bino and Wino, evolves at low energy
towards the Bino, interpreted as the effective DM brick
at low mass scales, with a remaining Wino content and
eventually a Higgsino contribution to acount for the cor-
rect observed DM density,

2
2
f,
g,
1.
Z
Z
M
B
M
W
B
HW








 



 (13)
Near this scale, the resulting DM state takes the form

12 .
H
NBW    





(14)
Accepting at this stage the compositeness could be
treated in terms of the Weinberg mixing angle
Z
M
w 



, using the parametrization: 2
fcos
Z
M
w 


,
Table 1. The DM compositeness evolution with the scale
energy.

2
2
Z
Ln
M 

 2
2
Z
L
n
M 

 2
2
Z
Ln
M 


Z
M
 
f,g fg

fg fg f1

N
 BW


 BW



 BW 


B


.

(12)
1The density could be thought of as the Boltzmann weight
2
fe

 
with

propotional to the inverse of temperature.

S. E. ENNADIFI ET AL. 396
and 2 gsin
Z
M
w 


, we deduce the DM copositeness
di the neglig
m
incluible Higgsino additional amount

2
H
ng

 

 (15)
in such approximation when addressing DM as a pure
gaugino mixture to make the analysis more economical.
Straightforward calculations lead to the hybridization:
In this vision, ignoring the Higgsino content and using
the 2 Casimir energy momentum operator P as well as
the relationship between gaugino masses expected from
renormalization group equations, we can express the
mass of the DM particle (14) in terms of mass eigen-
states as follows
2
13sin w
N
MB M



 (16)
where it depends mainly on the Bi

no mass. Generally,
the right DM abundance (by equilibrium freeze-out) is
approached by a WIMP particle lying near the elec-
troweak scale. Indeed, such suggestion is clearly shown
in this proposal where the lower bound of DM particle
mass could go down till
65
N
M
GeV
 (17)
This remarkable prediction strong
pa
ly suggests that such
rticle is tied to the electroweak scale and then should
produced at the LHC. This is an interesting result for a
relatively heavy elementary particle so that the previous
accelerator experiments did not have enough energy to
create them, whereas the Big Bang did once have energy
to make them.
If Bino-like particles really make up the cold DM,
with a local mass density of the order of that suspected in
our neighborhood to explain the dynamics of our own
galaxy, they should be distributed in a halo surrounding
our galaxy with a typical speed of 3
10vc

 [24] and
would coherently scatter off nuclei in terrestrial detectors
[25]. The detection of this kind of particles may be indi-
rectly via their self-annihilation products search
NN qq 
  or directly by studying their interac-
tion within the detector, the tiny shocks with its atomic
nuclei, with a mean energy of ׽ tens of
K
eV as re-
cently shown by the Cryogenic Dark Matter Search ex-
periment (CDMS II) data [26]. According to our ap-
proach, such energy is expected to be in the range
32.5 N
K
eV EMeV
 (18)
It’s a tiny energy deposit (recoiling
ve
energy) that is
ry hard to pick up against background from naturel
radioactivity which is typically of
M
eV. Direct search
experiments seek recoil signatures of these interactions
and have achieved the sensitivity to begin testing the
most interesting classes of WIMP’s models [27-30]. This
would let place for another unspecified DM candi-
B


H


W




Figure 1. The hybridization invloves greatly around 3/4 of
Binos and 1/4 of Winos.
cle might be some particle that
uch Bino-like particle decays into. One possibility be-
economical models for
persymmetry at the TeV scale can be used as conven-
the idea of compositeness in terms of
ga
date. Or, the DM parti
s
yond the MSSM remains the gravitino [31-33]. Of course
there is much to do in this path and thereby it would be
important to go deeper to derive more refined results.
5. Concluding Comments
We have seen that sensitive and
su
ient templates for experimental searches. The simplest
possibility is the MSSM, the popular extension of the
SM fulfilling aesthetically their gaps, is recently recog-
nized deserving to be tested experimentally. The meas-
urements of Sparticle masses, production cross-sections,
and decay modes will rule out some models for Susy
breaking and lend credence to others. These measure-
ments will be able to test the principle of R-parity con-
servation, the idea that Susy has something to do with the
DM, and possibly make connections to other aspects of
cosmology including baryogenesis and inflation. Perhaps
it is not a coincidence that such particles which may
solve crucial problems in particle physics also solve the
DM problem. An important remark is that, from the par-
ticle physics point of view, DM may naturally be com-
posite offering then an extra issue for interesting phe-
nomenology.
The approach developed in this paper realizes in a
simple manner
uginos wave functions hybridization. Although com-
positeness at high energies is somehow unlikely, nature
might be kind enough to carry out small ideas such as the
hybridization described in this study. Within the MSSM
in the rage GUT Z
M
M

and the analysis of Section 3
and 4, the DM particle resulting from sparticles decays

S. E. ENNADIFI ET AL.397
ays exist
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