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arXiv:1205.1996v1 [hep-ph] 9 May 2012
SINP-APC-12/3
Gamma Ray and Neutrino Flux from Annihilation
of Neutralino Dark Matter at Galactic Halo
Region in mAMSB Model
Kamakshya Prasad Modak1and Debasish Majumdar2
Astroparticle Physics and Cosmology Division,
Saha Institute of Nuclear Physics,
1/AF Bidhannagar, Kolkata 700064, India.
Abstract
We consider the lightest supersymmetric particle (LSP), neutralino in min-
imal anomaly mediated supersymmetry breaking model (mAMSB) to be a
possible candidate for weakly interacting massive particles (WIMP) or cold
dark matter and investigate its direct and indirect detections. The supersym-
metric parametric space for such a model is constrained by the WMAP results
for relic densities. The spin independent and spin dependent scattering cross
sections for dark matter off nucleon are thus constrained from the WMAP
results. They are found to be within the allowed regions of different ongoing
direct detection experiments. The annihilation of such dark matter candi-
dates at the galactic centre produce different standard model particles such as
gamma rays, neutrinos etc. In this work, we investigate the possible fluxes of
such particles from galactic centre. The neutrino flux from the galactic centre
and at different locations away from the galactic centre produced by WIMP
annihilation in this model are also obtained for four types of dark matter halo
profile. The possibility of detection of such neutrinos from galactic centre at
the ANTARES under sea neutrino detector is also investigated. We have stud-
ied signals from dark matter annihilations from different angles of observations
for different spherically symmetric dark matter halo distribution models in the
galaxy. We have compared our gamma ray flux results for four different halo
models with the HESS experimental data.
1email: kamakshya.modak@saha.ac.in
2email: debasish.majumdar@saha.ac.in
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1 Introduction
Cosmological observations like flattening of rotation curves of spiral galaxies [1], the
gravitational microlensing [2], observations on Virgo and Coma clusters [3, 4], bullet
clusters [5], etc. provide indications of existence of huge amount of non-luminous
matter or dark matter (DM) in the universe. The Wilkinson Microwave Anisotropy
Probe (WMAP) experiment [6] suggests that about 85% of the total matter content of
the universe and almost 23% of the total content of the universe is dark matter. The
general wisdom is that in order to account for the relic abundance of DM, a candidate
for dark matter should be massive, very weakly interacting and non-relativistic (cold
dark matter or CDM) particles. This allows the structure formation on large scales.
In the present work, we consider such weakly interacting massive particles (WIMPs)
[7, 8, 9, 10] to consist of the total DM content of the universe.
The theory of Supersymmetry provides a solution to hierarchy problem and uni-
fication of gauge coupling constants via renornalization group evolution (RGE). R-
parity conserving SUSY also provides very naturally the lightest supersymmetric
particles (LSP) to be a possible candidate for DM. In the present work, we consider
neutralino to be the LSP and hence the candidate for dark matter.
In SUSY models, R-parity, or some similar parity property, allows only an even
number of supersymmetric partner particles to interact on a fundamental interaction
vertex. This stabilizes the lightest supersymmetric particle (LSP), which becomes
the cold dark matter candidate. Minimal Supersymmetric Standard model (MSSM)
with softly broken supersymmetry is the main candidate of physics beyond the Stan-
dard Model. Supersymmetry, if it exists, must be broken spontaneously. Dynamical
or spontaneous breaking of supersymmetry at high scale leads to the soft Supersym-
metry breaking terms appearing in MSSM as low energy remnants. This dynamical
or spontaneous breaking is supposed to take place in some ’hidden’ sector (HS) and
this breaking is mediated to the observable sector (OS). This mediation mechanism
leads to many interesting theories including gravity-mediation (SUGRA) with grav-
itino mass (m3
mediation with m3
metry Breaking (AMSB) mechanism is one of the most well-known and attractive
set-ups for supersymmetry breaking because,
1. the soft supersymmetry (SUSY) breaking terms are completely calculable in
terms of just one free parameter (the gravitino mass, m3/2),
2. the soft terms are real and flavor invariant, thus solving the SUSY flavor and
CP problems,
3. the soft terms are actually renormalization group invariant [11], and can be
calculated at any convenient scale choice,
2) (∼ 1TeV), Gauge mediation (GMSB) with m3
2∼ 100 TeV. The superconformal Anomaly Mediated Supersym-
2< 1 TeV, anomaly
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4. the scale of the gravitino mass is too high to affect the Big Bang neucleosyn-
thesis (BBN) bound and cosmological gravitino problem which was the main problem
in SUGRA model.
Supersymmetry breaking effects in the observable sector have in this framework
a gravitational origin. In ordinary gravity-mediated supersymmetry breaking model,
the supersymmetry breaking is transmitted from HS to OS via tree level exchanges
with gravitational coupling. But in AMSB, the HS and the OS superfields are as-
sumed to be located in two parallel but distinct 3-branes and the 3-branes are sep-
arated by bulk distance which is of the order of compactification radius, rc. Thus
any tree level exchange with mass higher than the inverse of rcis exponentially sup-
pressed. So, the supersymmetry breaking is propagated from the HS to the OS via
loop generated superconformal anomaly. The soft SUSY breaking terms related to
gauginos and sleptons are calculated to be,
Mi =
βg
gim3
2,(1)
m2
Q
= −1
= −βy
4
?∂γ
ym3
∂gβg+∂γ
∂yγy
?
m2
3
2,(2)
Ay
2,(3)
where Mi is the gaugino mass term, mQ is slepton mass and Ay is the trilinear
parameter. γ is the anomalous dimension and β is the beta function of this theory.
γ and β are defined as,
γ ≡dlnZ
dlnµ, βg≡
dg
dlnµ, βy≡
dy
dlnµ,
(4)
where Z is the renormalization constant for the gauge coupling, µ is the Higgsino
mass. where βgand βyare, respectively, the gauge coupling and Yukawa coupling
β-functions, and their correspond anomalous dimensions are denoted by γ. Another
feature of AMSB is that slepton mass-squared terms are negative giving to tachy-
onic states as seen from equation. The problem is tackled by adding an universal
mass-squared term m2
this theory, namely, minimal anomaly mediated supersymmetry breaking (mAMSB)
model ([12, 13]). A sparticle spectrum in this model is fixed by three parameters, m3
which is gravitino mass, tanβ which is the ratio of the vacuum expectation values of
the two Higgs fields (H0
an universal mass squared term (m2
ultimately, with m0, four parameters are needed to generate spectrum in mAMSB.
So, we can generate various LSP neutralino masses out of these four parameters in
this model. The neutralino is the lowest mass eigenstate of linear superposition of
0to all the squared scalar masses in the minimal extension to
2
1and H0
2) and sign(µ), where µ is the Higgsino mass. Also,
0) is needed to make all sparticle positive. So,
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the photino (˜ γ), zino (˜Z), and the two Higgsino states (˜H0
1and˜H0
2) [14], written as,
χ = a1˜ γ + a2˜Z + a3˜
H0
1+ a4˜
H0
2. (5)
This state is obtained by diagonalising the neutralino mass matrix, which is given
by,
M =
M1
0
0−mzcosβsinθw
mzcosβcosθw
0
−µ
mzsinβsinθw
−mzsinβcosθw
−µ
o
M2
−mzcosβsinθw
mzsinβsinθw
mzcosβcosθw
−mzsinβcosθw
?
in the basis
Here β is the ratio of vacuum expectation values between the two Higgs doublets,
mzis the mass of the Z0, θwis the weak mixing angle, and M1,M2,µ are the U(1)
and SU(2) gaugino and Higgsino mass parameters, respectively
But there are certain phenomenological bounds on the parameters space, i.e,
1. A lower limit on m3
charginos causing direct search at the CERN-LEP.
2. For a certain m3
sleptons are observables.
3. For some choices of SUSY parameters, unbounded from below (UFB) directions
of scalar potential are obtained and that parameter space region is not allowed.
In a recent work V´ asquez et al. [15] has given a detailed analysis of the allowed
parameter space for a neutralino dark matter in the framework of NMSSM model.
In their case the dark matter (neutralino) mass was within the range of ∼ 80 GeV
and hence the energies of the gamma rays from such dark matter annihilations can
be probed by FermiLAT [16] experiment. In the present calculation, we instead
consider the neutralino dark matter in mAMSB model mentioned above. Some of
the earlier works on dark matter phenomenology in AMSB model include Baer et
al. [17], Moroi et al. [18], Ullio et al. [19] etc. In Refs. [17] and [19] the γ flux
from the galactic centre are discussed and although neutrinos from the neutralino
annihilations are mentioned in Ref. [17] but they have not discussed elaborately.
Moreover only two halo models are considered for their analysis. In an another
earlier work ([20]), a neutralino dark matter in AMSB model is studied to obtain the
region in scalar cross section (σscalar- mχ) parameter space. But in this case WMAP
limit has not been taken into account. In Ref. [21], the γ signal from galactic centre
region due to dark matter annihilation is addressed mainly for the case of GLAST
[22] satellite-borne experiment. Ref. [23] discusses the the γ-flux from galactic centre
region, originated by dark matter annihilations. The authors made the analysis with
different particle dark matter candidates with reference to MSSM, Kaluza-Klein extra
?
˜ γ
˜Z
˜
H0
1
˜
H0
2
.
2coming from the lower bound of mmin
˜
χ±= 86 GeV on
2, there is a lower bound on m0 below which ˜ τ is LSP or
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dimensional model etc. for different halo profiles and taking into account the Fermi-
LAT experiment. But the neutrinos as dark matter annihilation products are not
addressed. In another work by Allahverdi et al [24] considered MSSM and U(1)B−L
extened MSSM model for dark matter candidate and calculated γ and neutrino fluxes
from galactic and extra-galactic origins by annihilating dark matter. But they have
considered only NFW halo profile and they have not shown the neutrinos flux for
different neutrino flavours. Moreover, no detailed comparison of their results with
high energy neutrino or gamma search experiments.
The phenomenology of the AMSB model (adopted in this work) was investigated
by Datta et al. [25], among others, in an earlier work where they have calculated the
allowed supersymmetric parameter space for different values of tanβ. In this work, we
adopt their results for supersymmetric parameters such as m0and m3
neutralino masses upto TeV scale using the allowed region of m0-m3
shown by Datta et al. [25]. The relic densities for such dark matter were then
computed using these SUSY parameters and they were compared with the WMAP
results. The parameter, thus constrained further was then used to calculate the spin
independent and spin dependent cross sections (σscatt) for different neutralino masses
(mχ) (obtained using the restricted parameter space) in the cases of neutralino-
nucleon scattering processes. These processes are essential for direct searches of dark
matter. We found that the allowed mχ− σscattregion, thus obtained, are found to
be within the allowed limits of most of the direct detection experiment results.
The indirect detection of dark matter involves the detecting the particles (and
their subsequent decays) or photons produced due to dark matter annihilations.
These annihilation products can be fermions or γ photons. The dark matter parti-
cles if trapped by the gravity of a massive body like sun or galactic centre they can
annihilate there to produce these particles. in this work we investigated gamma rays
from such annihilations of dark matter from the galactic centre and galactic halo re-
gions. Using the constrained mAMSB parameter space discussed above we found the
gamma ray flux from the galactic centre. We have also calculated the galactic neu-
trino flux from such annihilations of mAMSB neutralino dark matter. These studies
are performed for different galactic dark matter halo profiles. We found that the
gamma spectrum from galactic centre and halo produced by neutralino dark matter
within the framework of the present mAMSB model, is highly energetic. The exper-
iment like HESS [26, 27], that can probe high energy gamma rays and which being
in the southern hemisphere has better visibility of the galactic centre will be suitable
to test the viability of the present dark matter candidate in mAMSB model.
The possibility of detecting neutrinos from galactic halo from dark matter annihi-
lations are also addressed with reference to Astronomy with a Neutrino Telescope and
Abyss environmental RESearch (ANTARES) [28] under sea neutrino experiment.
2and obtained
2parameter space
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The paer is organised as follows. In section 2 we discuss the calculation of relic
densities of mAMSB neutralinos for the parameter space obtained from [25]. The
relic densities are then compared with the WMAP results. The parameter space
thus constrained further by WMAP is then used to calculate the spin dependent
and spin independent scattering cross sections. They are compared with the existing
direct detection experiment limits. These are discussed in section 3. In section 4 the
indirect detection of the mAMSB dark matter from their annihilations at galactic
centre and halo are discussed. To this end the gamma signals and neutrino signals
are addressed. Finally in section 5 we give discussions and conclusions.
2 Relic Abundance Calculation
In order to calculate the relic abundance of the LSP, χ, one needs to consider annihila-
tion of N supersymmetric particles with masses mi(i=1,2,..,N) and internal degrees
of freedom girespectively. If, R parity is conserved, then all the heavier supersym-
metric paricles will decay to LSP. The relic abundance is obtained by numerically
solving the Boltzmann’s equation,
dn
dt+ 3Hn = −?σv?(n2− n2
eq) ,(6)
where n is the total number density of all the supersymmetric particles ni
n = Σini ,
and neqis the value of n when the particles for dark matter candidate were in chemical
equilibrium. At this epoch the temperature T of the universe was greater than Tf
(T > Tf), the freeze out temperature of the particle considered. At a temperature
below the freeze-out temperature Tf, the particles falls out of chemical and thermal
equilibrium and their co-moving number density becomes fixed or “frozen”. In Eq.
6, H denotes the Hubble parameter and ?σv? is the thermal average of the product of
annihilation cross section and the relative velocity of the two annihilating particles.
?σv? =
?
i,j
?σijvij?n(i)
eqn(j)
n2
eq
eq
,(7)
with
vij=
?
(pi.pj)2− m2
EiEj
im2
j
.
In the above, (pi,pj) and (Ei,Ej) are the momenta and energies respectively for the
ith and jth particles. The entropy conservation principle enables one to work with a
useful quantity called abundance, Y = n/s [29] where s is the total entropy density
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we have chosen the ANTARES under sea detector and calculated the muon yield
for muon neutrinos from galactic centre in this model for all the four halo models
considered. The calculations of neutrinos in case of different halo profiles also exhibit
similar trend as those for the calculation of γ flux.
The value of thermal average of the squared halo density, ?ρ2(r)? is generally
greater than (?ρ(r)?)2due to the influence of a probable clumpy structure of dark
matter halo profile, Fc(r), which is related to dark matter halo profile by,
?ρ2(˜ r)? = ρ2
0F2
halo(r)Fc(r) (49)
The clump structure of dark matter halo gives enhancement factor. In the present
study of different models of galactic halo structures, we did not consider any clumpy
halo of dark matter. This study is for posterity.
The WMAP allowed zone(s) for the mAMSB model for dark matter, are around
(∼ 1 TeV and ∼ 2 TeV) which are high in mass regime like Kaluza-Klein dark matter.
The future collider experiment may verify their existence.
6Acknowledgements
The authors thank Pratik Majumdar for some useful discussions.
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