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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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