Theoretical Physics

Simulation of Dark Matter Using micrOMEGAs

Nikolaos Kalkitsas and Thom Jäderlundkalk@kth.se, thomja@kth.se

SA104X Degree Project in Engineering Physics, First LevelDepartment of Theoretical Physics

Royal Institute of Technology (KTH)Supervisors: Tommy Ohlsson, Mattias Blennow

May 21, 2015

Abstract

Weakly interactive massive particles (WIMPs) are one of the most popular dark mat-ter candidates and in our study we have decided on a WIMP based model due to itsaccurate predictions of the dark matter (DM) relic density. To determine a possibleWIMP, we have used the minimal supersymmetric model (MSSM), an extension of su-perymmetry (SUSY). Using micrOMEGAs we have made predictions of the direct andindirect detection for two different sets of parameters for a MSSM model considering theneutralino as the lightest supersymmetric particle (LSP). The results showed a discretedifference for the two sets of parameters in order of magnitude and the energy range,experimental data can rule in favour of one of the sets accordingly. We also found thatit was preferable to have indirect detectors aimed at the Sun rather than the Earth.

Weakly Interactive Massive Particles (WIMPs) anses vara en av de mest populära kan-didaterna för mörk materia och i denna studie har en supersymmetrisk WIMP mod-ell använts, där supersymmetrin beskrivs av den minimala supersymmetriska modellen(MSSM) och WIMPs för dess noggranna förutsägelse av relikdensiteten hos mörk mate-ria. Simuleringar gjordes i programmet micrOMEGAs för direkt och indirekt detektionbaserat på två varianter av MSSM-modellen och antagandet att neutralinon är den lät-taste supersymmetriska partikeln (LSP). Resultaten visade en tydlig skillnad mellan detvå varianterna i storleksordning och energiomfång och således kan experimentellt datauppmätts, vilket kan gynna en av varienterna. Det har även framgått att indirekt detek-tion är mer lämpat att studera med solen som källa, än jorden.

Contents

1 Introduction 2

2 Background Material 52.1 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Relic Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Investigation 73.1 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.3 Analytical Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3.1 Direct detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3.2 Indirect detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.4.1 Direct Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.4.2 Indirect Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Summary and Conclusions 21

1

Chapter 1

Introduction

New discoveries in theoretical and experimental physics build upon each other, theoreticalderivations and predictions may be the basis of experimental discoveries and experimentaldata may give rise to new theories; the case of dark matter is certainly the latter. Thefirst convincing experimental evidence for dark matter (DM) was made by Fritz Zwicky[1] who discovered that the velocity of galaxy clusters exceeded the predicted velocitybased on total mass of the galaxy using classical Newtonian physics. Calculating therotational velocity of a galaxy with radius r gives v(r) ∝

√M(r)/r where M(r) is the

total mass inside the radius r. If r > rgalaxy we can predict that v(r) ∝ 1/√r, however the

velocity profile of most galaxies is essentially constant out to the far edges of the visiblegalaxy [2, 3]. This would indicate a mass density inverse proportional to the square ofthe radius in turn giving a mass M(r) ∝ r, however at some point the mass has to fall ofto zero. In our study we will simulate the direct and indirect detection using a programcalled "micrOMEGAs".

In order to further understand and analyse DM we must first introduce a conceptused in cosmology, the density parameter Ω. The density parameter is the result ofsolving a specific form of the Einstein equations, called the Friedmann equations, withdifferent cosmological geometries [4]. Ω is used to define the density as a fraction of thecritical density Ω = ρ/ρcrit, where ρcrit is the density in which the universe will expandforever. A universe with Ω = 1 is called a flat universe and recent measurements by thePlanck satellite shows strong evidence suggesting that our universe is approximately aflat universe Ωtot ≈ 1 [5]. The total density Ωtot = ΩΛ + ΩM includes the dark energyΩΛ = 0.6825 and the total mass ΩM = 0.3175, this includes the DM as well as the nucleonsand electrons, the so-called ”baryonic” matter. The baryonic matter ΩB = 0.049 whichgives ΩDM = Ωχ = ΩM − ΩB = 0.2685, where χ denotes the dark matter [6]. Thebaryonic matter only makes up a small fraction of the total mass and it is therefore ofgreat interest to study the dark matter and the underlying theory behind it.

Today there are many suitable DM candidates that satisfy all of the following nec-essary criteria: they must be stable enough to survive for the lifetime of the Universe,have a weak interaction with electromagnetic radiation and give a density parameterclose to the expected value ΩDM = 0.2685. Candidates that fulfil these criteria includeaxions, sterile neutrinos, supersymmetric DM and Weakly Interactive Massive Particles(WIMPs) [7]. However it is also worth noting that, while observations indicate the exis-tence of DM, the DM has never been observed directly and the idea of DM stems froman acceptance that the Newtonian gravitational theory still holds on a galactic scale. A

2

modified gravitational theory can explain the velocity profile of galaxies but gives rise toother unresolved issues [7].

Of the DM candidates, the most popular candidate is the WIMP [8]. One of themost important characteristics of a good DM candidate is if the theoretical relic densityresembles the experimentally derived value of ΩDM = 0.2685. Notably, when consideringWIMPs as thermal relics out of the early universe their present relic density adds up to:

ΩDMh2 ≈ 3× 10−27cm3s−1

σannν. (1.1)

Studies have shown that ΩDMh2 roughly equates to 0.1 giving the self-annihilation cross

section, σannν, a value of 3 × 10−26cm3s−1[9], which is on par with that of the weakinteraction [10]; this coincidence have come to be known as the ”WIMP miracle”.

When searching for DM there are primarily two methods, direct and indirect detec-tion. Direct detection of DM is the study of the energy dependent elastic DM-nucleiscattering and is based on the DM halo inside the Milky Way [11], assumed to be com-prised of WIMPs. As the Earth moves through the halo a flux of WIMPs is created ofthe order of 105(100GeV/mχ) where mχ is the mass of the WIMP [7]. Direct detectionaims to see the rate (M) and energies (ER) of the recoils from the WIMPs elasticallyscattering of other particles’ nuclei, and with the current estimates of the WIMPs massgives the recoil energy of 1 to 100 keV [12].

As opposed to direct detection, indirect detection instead aims at detecting the by-products from the annihilation of DM. The products include charged particles and theirrespective anti-particle, for instance electrons and positrons, or different types of radiationsuch as gamma rays. [11]. The indirect detection of DM through its annihilation productsis of great importance for ruling out or favouring some DM models [7]. Indirect detectionfrom the Sun assumes an equilibrium between the captured WIMPs and outgoing flux ofannihilation product as the Sun moves through the milky way and the DM halo. WIMPsinteract only weakly with the nuclei of the Sun, however they occasionally scatter andloose enough momentum to be gravitationally bound, and over the lifespan of the Sunit is reasonable to assume that such an equilibrium has been reached [7]. Even thoughindirect detection requires astrophysical data, such as the velocity distribution and localDM density, it is of minimal uncertainty. This is due to the averaging over billions ofyears of gathering WIMP through nuclei scattering.

We will be simulating the direct and indirect detection using a program called ”mi-crOMEGAs” (version 4.1) using a model based on supersymmetry (SUSY) called minimalsupersymmetric extension of the Standard Model (MSSM). Supersymmetric DM candi-dates are amongst the most popular and best-motivated proposals that naturally fulfilsall the necessary conditions in an elegant matter; however it is worth noting that super-symmetric particles has never been found despite extensive search in the LHC [7]. TheMSSM is a supersymmetric model that takes only the Lightest Supersymetric Particle(LSP) that are required for SUSY models are taken into consideration which are sta-ble WIMPs category [7, 13]. The LSP in the MSSM model that are considered as DMcandidates varies depending on the model parameters, it includes the neutrally chargedsneutrino with spin zero, neutralino with spin 1/2 and the gravitino with spin 3/2. Thesneutrino’s mass is ranging from a few GeV to several TeV, recent results have indicatedthat the large nuclei interaction would exclude the sneutrino as a candidate [14]. TheLSP candidate that is most widely considered is the neutralino, which is the WIMP con-

3

sidered in the simulation. The final candidate, the gravitino, is mainly considered in anextended model called next-to-lightest supersymmetric particle (NLSP) which is not thefocus of this study. Using micrOMEGAs we can simulate the indirect detection of theDM annihilation spectrum from γ, e+, p, ν and ν, these are the common stable StandardModel particles used in indirect detectors.

4

Chapter 2

Background Material

2.1 SupersymmetryTo understand the need for Supersymmetry (SUSY) we must first understand how itcame to be. SUSY is an attempt to go beyond the standard model (BSM) in explainingthe problems the that arise when closing to the TeV threshold with the SM [15]. TheSM mainly differentiates particles into two kinds, fermions which are the foundationof matter with half integer spin and gauge bosons being the force mediating particleswith full integer spin. SUSY aims to solve the problems in the SM by creating theirsymmetric counterparts called its superpartner. What separates the SM particle fromits superpartner is the difference in its spin value by 1/2 [16]. This means that for everyfermion, there is an gauge boson superpartner and vice versa.

The aforementioned extension of SUSY, MSSM, aims to simplify this by creating onesuperpotential from which all fields of the SM can be derived [17], whereas in SUSYthere are not any limit to the amount of potential fields. The minimal in MSSM is thusbecause of it assumes the minimal amount of superfields, resulting in that all SM groupsi.e. the fermions and gauge bosons, get their gauge or scalar and fermionic superpartnerrespectivley. The Higgs boson also gets two spin 1/2 counterparts called the Higgsino.

The MSSM also has another important attribute, as it preserves R-parity [18]. Withthe preservation of R-parity, this ensures the stability of the LSP and if it is electricallyneutral, makes it a promising DM-candidate [15]. As aforementioned, the LSP is mostlikely to be a neutralino, which are made out of linear combinations of the neutralgauginos, winos and binos. These combinations can create a total of four combination,where the lightest one is expected to be the LSP.

2.2 Relic DensityIt is assumed that WIMPs were in thermal equilibrium in the early universe [4]. As theuniverse expanded however, WIMPs along with virtually all other particles fell out ofthis equilibrium, also known as decoupling. As almost all particle today has decoupled,studying thermal relics and their density is of interest to determine their abundance inpresent time.

To determine the relic density of a generic particle we use a modified Boltzmann

5

equation as an expression for the particle number density [17]

dn

dt+ 3Hn = −〈σannν〉(n2 − (neq)2), (2.1)

where n is the particle number density, H Hubble’s constant, σann the self annihilationcross section, ν its speed and

neq = g(mT2π ) 32 e−

mT (2.2)

is the number density at thermal equilibruim in the Maxwell-Boltzmann approximationfor a massive particle moving at non-relativistic speeds with mass m and temperature T .Solving this equation yields the final expression for relic density as

ΩXh2 ≈ 1.07× 109GeV −1

MP

m

TF√g∗

1a+ 3bTF

m

, (2.3)

where MP is the Planck mass, TF the freeze-out temperature, h = H0100

kms

1Mpc

where H0is the Hubble constant and a and b are constants depending on the mass of the particle.An approximation to this is commonly used [17]

ΩXh2 ≈ 3× 10−27cm3s−1

σannν, (2.4)

which is the more familiar notation, out of which we discovered the ”WIMP-miracle”.

6

Chapter 3

Investigation

3.1 ProblemWe will simulate the DM direct detection of heavy (131Xe, 127I and 73Ge) and lightnuclei (23Na) scattering and indirect detection spectrum from γ, e+, p, ν and ν of thesupersymmetric model MSSM using micrOMEGAs_4.1 and study the difference of twomodel parameters.

3.2 ModelTwo model parameters were used in the study given by the following table’s labelled”MSSM1’ and ’MSSM2’ in the results.

Table 3.1: Parameters used in the model labeled ”MSSM1” in the results. All parametersuses the SUSY Les Houches Accord (SLHA) convention [19, 20]

Parameter value [GeV] Parameter value [GeV]mu 350 MG1 200MG2 400 MG3 800Ml1 500 Ml2 500Ml3 500 Mr1 200Mr2 200 Mr3 200Mq1 1000 Mq2 1000Mq3 1000 Mu1 300Mu2 300 Mu3 300Md1 300 Md2 300Md3 300 At -1000Ab 0 Al 0MH3 1000 tb 10Am 0

7

Table 3.2: Parameters used in the model labeled ”MSSM2” in the results. All parametersuses the SUSY Les Houches Accord (SLHA) convention [19, 20]

Parameter value [GeV] Parameter value [GeV]mu 19 MG1 80.7MG2 161.3 MG3 483.9Ml1 400 Ml2 400Ml3 400 Mr1 400Mr2 400 Mr3 400Mq1 3400 Mq2 3400Mq3 3400 Mu1 3400Mu2 3400 Mu3 3400Md1 3400 Md2 3400Md3 3400 At 830Ab 0 Al 0MH3 1577 tb 37.38Am 0

3.3 Analytical Calculations

3.3.1 Direct detectionThe direct detection of the elastic scattering rates on nuclei is computed by the eventrate given in terms of kg−1day−1keV−1, this is given by the expression [7]

dM

dER= ρ0

mNmχ

∫ ∞vmin

vf(v)dσWN

dER(v, ER)dv, (3.1)

where ρ0 is the local WIMP density in the galaxy, recent studies have shown ρ0 = (0.30±0.05) GeVcm−3 [21]. The function f(v) is the velocity distribution, micrOMEGAs stan-dard velocity distribution model is the commonly used Maxwellian distribution (Gaus-sian) [22], further modulation can be done through Earth’s rotation around the Sun andultra-fine structure shown in [7]. mN is the mass of the nucleus and mχ is the mass ofthe WIMP. vmin is the minimum velocity required to cause elastic scattering of energyER which can be derived from

ER = µ2Nv

2(1− cos(θ))mN

, (3.2)

vmin =√ERmN

2µ2N

, (3.3)

where µN = mχmNmχ+mN is the reduced mass of the WIMP-nucleus scattering, note that

we are using non-relativistic expressions. The WIMPs cross section must also be takeninto account during non-relativistic setting, as they differ between spin-dependent andspin-independent.

8

Spin-independent

The spin-dependent cross section of a WIMP with velocity v is given by [22]

dσSINdER

= σSI0Θ(Emax(v)− ER)F 2

N(q)Emax(v) , (3.4)

where Θ(x) is the Heavyside function, FN(q) is the nucleus form factor which is a functionof q =

√2ERMN and Emax is the maximum recoil energy given by 3.2

Emax = 2µ2Nv

2

mN

. (3.5)

Integrating 3.4 over all velocities gives the distribution of states at the recoil energy

dNSI

dER= 2Mdett

π

ρ0

Mχ

F 2N(q)(λpZ + λn(A− Z))2I(E), (3.6)

where ρ0 is the DM density near the Earth, Mdet is the mass of the detector and t is theexposure time,

I(E) =∫ ∞vmin

f(v)v

dv (3.7)

and FN is the form factor given by the Fourier transform of the nucleus distribution,

FN(q) =∫e−iqxρN(x)d3x, (3.8)

where ρN normalized such that FN(0) = 1. In micrOMEGAs the nucleus distribution isgiven by a Fermi distribution function

ρN(r) = cnorm

1 + e(r−RN )/a (3.9)

Spin-dependent

The spin-dependent cross section is given by [22]

dσSDNdER

=16µ2

χ

2JN + 1(S00(q)a20 + S01(q)a0a1 + S11(q)a2

1)Θ(Emax(v)− ER)Emax(v) (3.10)

Sij is the nuclei structure function which takes the spatial distribution as well as themagnitude of the spin into account. They are normalized by

S00(q) = C(JN)(Sp + Sn)2

S11(q) = C(JN)(Sp − Sn)2

S01(0) = 2C(JN)(Sp + Sn)(Sp − Sn) (3.11)

where C(JN) = (2JN+1)(JN+1)4πJN .

Integrating 3.10 over all velocities gives the distribution of states at the recoil energy

dNSD

dER= 8Mdett

2JN + 1ρ0

Mχ

(S00(q)a20 + S01(q)a0a1 + S11(q)a2

1)I(E) (3.12)

For a further analysis as well as the list of the spin-dependent form factors used inmicrOMEGAs see ref [22].

9

3.3.2 Indirect detectionIn micrOMEGAs the indirect detection of charged particles is modulated as a energydiffusion process as they move from the DM annihilation source to the Earth, the particlesare scattered through inverse Compton scattering and deflected by the galactic magneticfield. The energy distribution is described by the progagation equation

∂

∂z(VCψa)−∇ · (K(E)∇ψa)−

∂

∂E(b(E)ψa) = Qa(x, E), (3.13)

where ψa = dndE

is the number density of particles/(volume · energy), a expresses theparticle type and Qa is the production rate through DM annihilation given by

Q(x, E) = 12〈σv〉

(ρ(x)mχ

)2dNν

dEν. (3.14)

K(E) is the diffusion coefficient, assumed homogeneous, b(E) is the energy loss rate andVC is the convective velocity in the z axis. The first term in Eq. 3.13 describes the energyloss of the galactic magnetic field and magnetic turbulence, the second term is the lefthand side is the energy transfer of the convection-diffusion and the final term on the lefthand side is the energy loss of inverse Compton scattering and diffusive retardation [23].The equation is solved using two-zone disk model with the z direction parallel to thegalactic wind. For a further analysis of the geometry see ref [24, 25].

Positrons

For positrons the main contribution to the propagation equation 3.13 is the diffusion andenergy loss term,

−∇ · (K(E)∇ψe+)− ∂

∂E(b(E)ψe+) = Qe+(x, E). (3.15)

Assuming that K(E) is homogeneous and that the energy loss rate b(E) is dominated bysynchrothon radiation and inverse Compton scattering the above equation can be writtenas a heat equation after substituting

ψ(E, r, z) = N(t, r, z)/b(E), (3.16)

t(E) = −∫ K(E)

b(E) dE, (3.17)

giving the propagation equation

( ∂∂t−∇2)N(t, r, z) = σv

2m2χ

ρ2(e, z)(fe+(E)b(E)K(E)

) ∣∣∣∣E=E(t)

. (3.18)

This equation can be solved using Green’s functions and a full 3D integration over thethe cylinder coordinated r, z, θ giving the positron density in the Sun. This is computedin micrOMEGAs using monte carlo integration. For a complete derivation see ref [23].

10

Anti protons

The source term for anti protons 3.14 has a positive contribution from the DM annihi-lations as well a negative from the anti protons annihilation with the cosmic medium,mainly H and He. As the anti proton moves through the medium with a velocity vp theannihilation rate with H and He is given by

Γtot = σannpH vpnH + σannpHevpnHe, (3.19)

where the annihilation cross sections of anti protons and nuclei N σannpN can be foundin [26, 27]. The particle densities are set to nH = 0.9cm−3 and nHe = 0.1cm−3. Thepropagation equation 3.13 then becomes[

−K(E)∇2 + Vc∂

∂z+ 2(Vc + hΓtot(E))δ(z)

]ψp(E, r, z) = σv

2ρ2(r, z)M2

χ

fp(E). (3.20)

A similar approach of using Green functions and a final 3D integration over the cylindercoordinates as with the positrons is taken except for an important difference that theenergy loss is negligible. The full solution of the above equation is given in [22]

3.4 Results

3.4.1 Direct DetectionThe direct detection event rate given in terms of kg−1day−1keV−1, note that the numberof events per kg per day for an energy interval is the integral over the energy interval.The figures show the theoretical predictions for the two sets of parameters Table 3.1and Table 3.2 with both spin-dependent and spin-independent cross sections taken intoaccount. The result is separated into heavy and light nuclei:

11

Heavy Nuclei

0 20 40 60 80 100 120 140 160 180 20010

−13

10−12

10−11

10−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

E[keV]

dM/d

E

Distribution of recoil energy of 131Xe

MSSM1MSSM2

Figure 3.1: Theoretical predictions of the distribution over recoil energy, the figure showsnumber of events per day per kilogram of detector material 131Xe.

12

0 20 40 60 80 100 120 140 160 180 20010

−13

10−12

10−11

10−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

E[keV]

dM/d

E

Distribution of recoil energy of 127I

MSSM1MSSM2

Figure 3.2: Theoretical predictions of the distribution over recoil energy, the figure showsnumber of events per day per kilogram of detector material 127I.

0 20 40 60 80 100 120 140 160 180 20010

−13

10−12

10−11

10−10

10−9

10−8

10−7

10−6

10−5

10−4

E[keV]

dM/d

E

Distribution of recoil energy of 73Ge

MSSM1MSSM2

Figure 3.3: Theoretical predictions of the distribution over recoil energy, the figure showsnumber of events per day per kilogram of detector material 73Ge.

13

Light Nuclei

0 20 40 60 80 100 120 140 160 180 20010

−15

10−14

10−13

10−12

10−11

10−10

10−9

10−8

10−7

10−6

10−5

E[keV]

dM/d

E

Distribution of recoil energy of 23Na

MSSM1MSSM2

Figure 3.4: Theoretical predictions of the distribution over recoil energy, the figure showsnumber of events per day per kilogram of detector material 23Na.

3.4.2 Indirect DetectionThe indirect detection spectra calculated for γ, e+, p, ν and ν given by dN/dE distri-bution in each figure. The result is separated for detections from the Sun and Earthrespectively with the detectors at the Earth’s surface.

14

WIMP annihilation from the Sun

0 20 40 60 80 100 120 140 160 180 20010

−25

10−20

10−15

10−10

E[GeV]

dN/d

E

Photon flux for angle of sight 0.10[rad] and cone angle 0.03[rad]

MSSM1MSSM2

Figure 3.5: Theoretical prediction for the γ energy spectra with the detector angle ofsight 0.10[rad] and cone angle 0.03[rad].

0 20 40 60 80 100 120 140 160 180 20010

−18

10−16

10−14

10−12

10−10

10−8

10−6

E[GeV]

dN/d

E

positron flux [cm2 s sr GeV]−1

MSSM1MSSM2

Figure 3.6: Theoretical prediction for the e+ flux from the Sun

15

0 20 40 60 80 100 120 140 160 180 20010

−24

10−22

10−20

10−18

10−16

10−14

10−12

10−10

10−8

10−6

E[GeV]

dN/d

E

antiproton flux [cm2 s sr GeV]−1

MSSM1MSSM2

Figure 3.7: Theoretical prediction for the p flux from the Sun

0 20 40 60 80 100 120 140 160 180 20010

1

102

103

104

105

106

107

108

109

E[GeV]

dN/d

E

nu flux from Sun [1/Year/km2/GeV]

MSSM1MSSM2

Figure 3.8: Theoretical prediction for the ν flux from the Sun given by Year−1km−2GeV−1

16

0 20 40 60 80 100 120 140 160 180 20010

1

102

103

104

105

106

107

108

109

E[GeV]

dN/d

E

nu−bar from Sun [1/Year/km2/GeV]

MSSM1MSSM2

Figure 3.9: Theoretical prediction for the ν flux from the Sun given by Year−1km−2GeV−1

17

WIMP annihilation from the Earth

The muon flux from the Earth

0 10 20 30 40 50 60 70 80 90 10010

−5

10−4

10−3

10−2

10−1

100

E[GeV]

dN/d

EUpward muons[1/Year/km2/GeV]

MSSM1MSSM2

Figure 3.10: Theoretical prediction for the µ flux from the Sun given byYear−1km−2GeV−1

18

3.5 DiscussionWe have analysed the direct and indirect detection of two sets of parameters given byTable 3.1 and 3.2. From the results we find that the sets give two distinct curves withdifference in order of magnitude and maximum energy, using experimental data it wouldtherefore be possible to exclude one of the sets of parameters in favour of the other. Notethat we are only studying a super symmetric model and further simulations has to bemade in order to compare a SUSY model with a non-SUSY model.

The results we have acquired can be used for an analysis of direct and indirect detec-tion data as well as an estimation to the detector size necessary for a significant numberof events. When comparing the indirect detection of the Sun, Fig 3.8 and Fig 3.9, andthe Earth, Fig 3.10, we find that the flux of annihilation particles is orders of magnitudehigher from the Sun. Therefore, indirect detectors aimed at detecting the annihilationparticles from the Sun rather than the Earth would have a reduced cost, less detectormaterial, and increased accuracy.

For the direct detection (Fig 3.1, 3.2, 3.3 and 3.4) we simulated the effect of differentnuclei - ranging from light nuclei, 23Na Fig 3.4, to heavier nuclei, 131Xe Fig 3.1, 127IFig 3.2 and 73Ge Fig 3.3. The lighter nuclei is used to study spin-dependent while heavynuclei are more sensitive to spin-independent interactions. Active detectors using lightnuclei include Simple, Picasso and Tokyo/NaF, and for heavy nuclei Edelweiss, DAMA,CDMS, Warp and Xenon. It is possible to combine two elements to detect both the SDand SI nuclei scatterings, detectors using this technique is NAIAD and DAMA/LIBRAusing Na and I. There are also detectors using a model-independent approach by studyingthe annual cycles of the DM flux, such as the previously mentioned DAMA/LIBRA.

The indirect detection was simulated as the flux of γ, e+, p, ν and ν from the Sun,generated by DM annihilation. The detection of gamma-ray has had some unexplainedresults. The detector EGRET observed an excess gamma-rays, however if this is causedby dark matter is still unknown [28]. In addition, the Fermi Gamma-ray Space Telescopefound strong evidence for a tentative gamma-ray line that could be caused from darkmatter annihilations [29]. Furthermore, the PAMELA detector has observed a largerpositrons flux from the sun than expected, however no excess anti-proton flux has beendetected; this might lead to constraints to the properties of the DM candidates [7]. Thereare also several high-neutrino detectors such as AMANDA, IceCube and ANTARES.

In the future we might expect a higher level of sensitivity and a wider energy range forthe direct and indirect detectors. The model-independent direct detector DAMA/LIBRAhas had several upgrades to the sensitivity compared with its predecessor DAMA/NaIand will now take into account several second-order effects [7]. The previous detectorDAMA/LIBRA showed a clear annual signature and the results of its successor has beensimilar, although a conclusive analysis has not been made [30, 31]. The results of directdetectors are dependent on the amount of detector material, it is therefore possible togain a higher level of sensitivity by increasing the detector size. An increased size wouldimply several engineering challenges, however a conceptual design has already been madefor a ton-scale detector of size 18×20×17 m3 [7]. A similar approach is taken for indirectdetectors, recently the neutrino detector IceCube had its size doubled in order to increasesensitivity [7, 32].

Another pivotal moment in the search for DM, is finding evidence for SUSY. Recentdiscoveries such as the Higgs boson at 125 GeV falls in line with the SUSY prediction

19

of it being lighter than 135 GeV [33]. Results from the ATLAS Collaboration at CERNstudying the chargino and neutralino decay into the Higgs have yielded results in linewith the Standard Model (SM) and a simplified SUSY model [34]. Other studies have alsoaimed at excluding mass ranges for scalar particles under the assumptions of a minimalsupersymetric scenario [35]. As the Large Hadron Collider (LHC) recently reopened inthe search for high energy SUSY particles, we may very well be standing on the precipiceof unlocking some of the secrets of dark matter [7].

20

Chapter 4

Summary and Conclusions

There are two main ways of experimentally detecting DM, direct and indirect detection.In this report we have studied the theoretical simulations of direct and indirect detectionusing a program called ”micrOMEGAs”. The direct detection the DM-nuclei elasticscattering is simulated and the event rate is determined for different scattering energies.Indirect detection aims at detecting the DM annihilation by-products and the simulationwas done for the standard model by-products γ, e+, p, ν and ν.

We have made predictions of the direct and indirect detection for two sets of pa-rameters for the MSSM and there is a clear difference to the two results in the orderof magnitude as well as the maximum energy. It would therefore be easy to rule outone set of parameters in favour of the other for this particular model using experimentaldata. Our predictions also showed a preference to look for DM-annihilations from theSun rather than the Earth.

21

Bibliography

[1] F. Zwicky. Die Rotverschiebung von extragalaktischen Nebeln. Helvetica PhysicaActa, 6:110–127, 1933.

[2] Manuel Drees and Gilles Gerbier. Mini-Review of Dark Matter: 2012. 2012.

[3] Jaan Einasto. Dark Matter. Encyclopedia of Life Support Systems (EOLSS), As-tronomy, 2009.

[4] Mark Trodden and Sean M. Carroll. TASI Lectures: Introduction to Cosmology.page 82, 2004.

[5] P.A.R. Ade et al. Planck 2013 results. XVI. Cosmological parameters. As-tron.Astrophys., 571:A16, 2014.

[6] Pierre Salati. Dark Matter Annihilation in the Universe. Int.J.Mod.Phys.Conf.Ser.,30:1460256, 2014.

[7] Gianfranco Bertone, Dan Hooper, and Joseph Silk. Particle dark matter: Evidence,candidates and constraints. Phys.Rept., 405:279–390, 2005.

[8] Marco Taoso, Gianfranco Bertone, and Antonio Masiero. Dark Matter Candidates:A Ten-Point Test. JCAP, 0803:022, 2008.

[9] E Komatsu, K M Smith, J Dunkley, C L Bennett, B Gold, G Hinshaw, N Jarosik,D Larson, M. R. Nolta, L Page, D N Spergel, M Halpern, R S Hill, a Kogut, M Limon,S S Meyer, N. Odegard, G S Tucker, J L Weiland, E Wollack, and E LWright. Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: CosmologicalInterpretation. The Astrophysical Journal Supplement Series, 192(18):57, 2010.

[10] Gianfranco Bertone. The moment of truth for WIMP dark matter. Nature,468(7322):389–393, 2010.

[11] J. L. Feng. Dark Matter Candidates from Particle Physics and Methods of Detection.araa, 48:495–545, September 2010.

[12] G. Belanger, F. Boudjema, A. Pukhov, and A. Semenov. micrOMEGAs_3: Aprogram for calculating dark matter observables. Comput.Phys.Commun., 185:960–985, 2014.

[13] G. Bélanger, F. Boudjema, a. Pukhov, and a. Semenov. MicrOMEGAs: A programfor calculating the relic density in the MSSM. Computer Physics Communications,149(2):103–120, 2002.

22

[14] Toby Falk, Keith A. Olive, and Mark Srednicki. Heavy sneutrinos as dark matter.Phys.Lett., B339:248–251, 1994.

[15] Stephen P. Martin. A Supersymmetry primer. Adv.Ser.Direct.High Energy Phys.,21:1–153, 2010.

[16] Hitoshi Murayama. Supersymmetry phenomenology. pages 296–335, 2000.

[17] Gianfranco Bertone, Dan Hooper, and Joseph Silk. arXiv : hep-ph / 0404175v2 13Aug 2004 Particle Dark Matter : Evidence , Candidates and Constraints. Interac-tions, pages 1–144, 2007.

[18] V. Barger and R. J. N. Phillips. Supersymmetry Phenomenology. page 15, 1993.

[19] SUSY Les Houches accord: Interfacing SUSY spectrum calculators, decay packages,and event generators. pages 1–34, 2004.

[20] SUSY Les Houches Accord 2. Computer Physics Communications, 180(1):8–25,2009.

[21] Lawrence M. Widrow, Brent Pym, and John Dubinski. Dynamical Blueprints forGalaxies. Astrophys.J., 679:1239–1259, 2008.

[22] G. Bélanger, F. Boudjema, a. Pukhov, and a. Semenov. Dark matter direct detectionrate in a generic model with micrOMEGAs_2.2. Computer Physics Communica-tions, 180(5):747–767, 2009.

[23] G. Bélanger, F. Boudjema, P. Brun, a. Pukhov, S. Rosier-Lees, P. Salati, and a. Se-menov. Indirect search for dark matter with micrOMEGAs-2.4. Computer PhysicsCommunications, 182(3):842–856, 2011.

[24] D. Maurin, F. Donato, R. Taillet, and P. Salati. Cosmic rays below z=30 in adiffusion model: new constraints on propagation parameters. Astrophys.J., 555:585–596, 2001.

[25] F. Donato, D. Maurin, P. Salati, A. Barrau, G. Boudoul, et al. Anti-protons fromspallations of cosmic rays on interstellar matter. Astrophys.J., 563:172–184, 2001.

[26] L. C. Tan and L. K. Ng. Parametrization of p invariant cross section in p−p collisionsusing a new scaling variable. Phys. Rev. D, 26:1179–1182, Sep 1982.

[27] L C Tan and L K Ng. Calculation of the equilibrium antiproton spectrum. Journalof Physics G: Nuclear Physics, 9(2):227, 1983.

[28] F.W. Stecker, S.D. Hunter, and D.A. Kniffen. The Likely Cause of the EGRET GeVAnomaly and its Implications. Astropart.Phys., 29:25–29, 2008.

[29] Christoph Weniger. A Tentative Gamma-Ray Line from Dark Matter Annihilationat the Fermi Large Area Telescope. JCAP, 1208:007, 2012.

[30] Jonathan H. Davis. Fitting the annual modulation in DAMA with neutrons frommuons and neutrinos. Phys.Rev.Lett., 113:081302, 2014.

23

[31] J. Klinger and V.A. Kudryavtsev. Muon-induced neutrons do not explain the DAMAdata. Phys.Rev.Lett., 114(15):151301, 2015.

[32] T. and DEYOUNG. Status of the icecube neutrino telescope. International Journalof Modern Physics A, 20(14):3160–3162, 2005.

[33] Nathaniel Craig. The State of Supersymmetry after Run I of the LHC. page 72,2013.

[34] Gev Higgs. âĹŽ and a neutralino Search for direct pair production of a charginoand a neutralino decaying to the 125 GeV Higgs boson in. pages 0–33, 2014.

[35] ATLAS Collaboration. Search for Scalar Bottom Quark Pair Production withthe ATLAS Detector in pp Collisions at sqrt[s]=7 TeV. Physical Review Letters,108(18):181802, 2012.

24