ACTA UNIVERSITATIS UPSALIENSIS Uppsala Dissertations from the Faculty of Science and Technology 70

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ACTA UNIVERSITATIS UPSALIENSIS

Uppsala Dissertations from the Faculty of Science and Technology 70

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Anna Davour

Search for low mass WIMPs with

the AMANDA neutrino telescope

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Dissertation presented at Uppsala University to be publicly examined in Häggsalen, Ång- strömlaboratoriet, Lägerhyddsvägen 1, Polacksbacken, Uppsala, Friday, June 15, 2007 at 13:00 for the degree of Doctor of Philosophy. The examination will be conducted in English.

Abstract

Davour, A. 2007. Search for low mass WIMPs with the AMANDA neutrino telescope. Acta Universitatis Upsaliensis. Uppsala Dissertations from the Faculty of Science and Technology.

125 pp. Uppsala. ISBN 978-91-554-6909-2.

Recent measurements show that dark matter makes up at least one fifth of the total energy density of the Universe. The nature of the dark matter is one of the biggest mysteries in current particle physics and cosmology.

Big Bang nucleosynthesis limits the amount of baryonic matter that can exist, and shows that the dark matter has to be non-baryonic. Particle physics provides some candidates for non-baryonic matter that could solve the dark-matter problem, weakly interacting massive particles (WIMPs) being the most popular. If these particles were created in the early Uni- verse a substatial relic abundance would exist today. WIMPs in our galactic halo could be gravitationally bound in the Solar System and accumulate inside heavy bodies like the Earth.

Supersymmetric extensions to the Standard Model give a viable WIMP dark matter candidate in the form of the lightest neutralino. This thesis describes an indirect search for WIMPs by the neutrino signature from neutralino annihilation at the core of the Earth using the AMANDA detector. As opposed to previous dark matter searches with AMANDA, this work focuses on the hypothesis of a relatively light WIMP particle with mass of 50-250GeV/c²

The AMANDA neutrino telescope is an array of photomultiplier tubes installed in the clear glacier ice at the South Pole which is used as Cherenkov medium. Data taken with AMANDA during the period 2001-2003 is analyzed. The energy threshold of the detector is lowered by the use of a local correlation trigger, and the analysis is taylored to select vertically upgoing low energy events. No excess above the expected atmospheric neutrino background is found.

New limits on the flux of muons from WIMP annihilations in the center of the Earth are calculated.

Keywords: dark matter, WIMP, neutrino detection, AMANDA, supersymmetry Anna Davour, Department of Nuclear and Particle Physics, High Energy Physics, Box 535, Uppsala University, SE-75121 Uppsala, Sweden

urn:nbn:se:uu:diva-7913 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7913)

Printed in Sweden by Universitetstryckeriet, Uppsala 2007

Distributor: Uppsala University Library, Box 510, SE-751 20 Uppsala www.uu.se, acta@ub.uu.se

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To the memory of Martin

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Acknowledgements

Exhausted by the work on this thesis I look back on my years as PhD student at the Department of Radiation Science (which lately was renamed the De- partment of Nuclear and Particle Physics) and the AMANDA group working on our own shiny Icehenge. Now there is only a ﬁnal short, sharp shock of the thesis defense (51 days and counting!) before I leave for a new gold coast as (hopefully) a doctor of philosophy. Before giving this work to the printer I want to write down my thanks to the people who have made my research possible, and who have meant a lot for me during this time.

First of all I want to thank my supervisor Olga Botner, for support and advice and for careful scrutiny of every digit of my results and every bin of my plots.

Carlos Perez de los Heros has been a great help with disentangling all the odd pieces of software used in the AMANDAcollaboration, and has been very available for practical advice. Allan Hallgren has contributed a lot to the dis- cussions of my work. Jan Conrad, before he defended his thesis and vanished, gave me a thorough introduction to conﬁdence intervals and other statistical matters (of which I sadly forgot a lot).

Daan Hubert has given feedback all along the progress of my work. I thank him for the e-mail correspondence, and most important for a lot of Monte Carlo.

Johan Lundberg has been a great ofﬁcemate (to the extent that he has shown up in Uppsala at all . . . ). Thanks for the nice, creative and constructive discus- sions! Lately the group has been joined by Martino and Olle who gilded my last time with cheerful chat. We’ll meet again and talk about our memory of whiteness.

I also want to thank Inger Ericson for taking care of practical things and helping me to keep my sanity in the years of rice and salt.

Agnes Lundborg and Karin Schönning kindly agreed to proofread my thesis, and had lot of comments which immensely improved the text. Without you it would not have been as fun to write.

Fandom, and especially Upsalafandom, has been a social resort and stress relief in good and bad times. Thank you all, for tea, sympathy and a sofa — and for beer, and for books, and for reading my assorted writings. Let’s go to the multicoloured Mars in a ginger bread space craft!

Of course I also have to mention my parents, my siblings, and the rest of my great big family who stand behind me.

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There are so many people who have helped me to keep on track in my pri- vate and professional life during these years. From the Paciﬁc edge to the wild shore, from Uppsala to Antarctica and back again, from computer troubles to child care to teaching in course lab — I cannot mention you all. Please do feel included in my gratefulness.

Finally: Andreas, my husband, for always standing by my side and for keeping my nose above the water in difﬁcult times. Rebecka, my daughter, for reminding me of what’s really important in life.

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1. Introduction

The universe is under no requirement to make sense, though a doctoral thesis is.

Gregory Benford: Eater

The topic of this thesis is the search for dark matter particles in the form of weakly interacting massive particles (WIMPs) accumulated inside the Earth.

This is one example of how particle physics research today is connected with cosmology and astrophysics.

One hundred years ago relativity and quantum mechanics were just being born in the minds of a few experts. This was the heroic time of brave ideas, which led to a golden age of discoveries in the inner of the matter and in the far reaches of space. At the end of the 20:th century we had established an inventory of the building blocks of matter, the fundamental particles and interactions, called the standard model of particle physics.

At the same time, we had also collected an inventory of the properties of the whole Universe, a concordance model ﬁtting the observations of energy density, expansion and structure.

Our knowledge of the world now ranges from the constituents of the atomic nucleus (lengths of ∼ 10⁻¹⁸ meters) to the size of the observable Universe (∼ 10²⁶meters). This is an impressive range of orders of magnitude!

Newton at his time identiﬁed the force that makes things fall to the ground with the force keeping the planets in orbits around the Sun. Since then we have successfully worked with the assumption that the laws of physics are the same here on Earth and in outer space. The ﬁeld of inquiry concerning the smallest parts of the matter is intertwined with the questions about the oldest and the largest. This is astroparticle physics, which addresses questions about things like the reactions inside stars, the processes in supernovae and gamma ray bursts, and the creation and composition of particles after the big bang.

One of the most salient questions in this ﬁeld today is that of the dark matter.

This is the context of this search for low mass WIMPs with the AMANDA neutrino telescope.

A search for low mass WIMPs...

We now have strong reasons to believe that about 1/4 of the total energy density of the Universe comes in the form of dark matter. Still, this dark matter is unidentiﬁed and only indirectly observed.

At present it is commonly believed that the dark matter consists of new, as yet unidentiﬁed particles — WIMPs. Such particles arise in some extensions

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to the standard model of particle physics. The most studied is the lightest particle occurring in supersymmetric models. The mass of this particular type of WIMP depends on various parameters of supersymmetry, but it falls in the range∼GeV/c²-TeV/c².

In previous searches for WIMPs with AMANDA(Antarctic Muon And Neu- trino Detector Array) the sensitivity for the higher end of the mass spectrum has been better than for the lower end. In this work the part of the parameter space where the WIMPs have low mass (50-250 GeV/c²— masses lower than 50 GeV/c² are excluded by collider experiments) has been the focus of the search in an effort to improve this.

...with the AMANDA neutrino telescope

The AMANDAdetector is a neutrino telescope, designed to detect high energy neutrinos from astrophysical sources. Earlier generations of neutrino detectors focused on reactor neutrinos or neutrinos from the Sun. While the solar neutrinos have energies of <15 MeV the energies of interest for doing extrasolar neutrino astronomy are typically∼100 GeV and higher.

Astronomy has historically been using observations of light from stars and other astronomical objects to gather information about the Universe. High energy neutrino astronomy is expected to be complementary to observations in other kinds of radiation. Where photons are absorbed by dust and gas, and cosmic rays (mostly protons but also heavier atomic nuclei) are deﬂected in magnetic ﬁelds, neutrinos can pass right through and keep a direction pointing back to their source. Neutrinos can carry information about enigmatic highly energetic phenomena, like the processes in active galactic nuclei or gamma ray bursts. High energy neutrinos might for example be related to the origin of the highest energy cosmic rays, which is not yet understood.

The most interesting discoveries would of course be the ones we don’t predict, the surprises that may reveal themselves when we open this new observational window. We might imagine e. g. sources invisible in gamma rays because of screening matter hiding them from us.

To investigate the neutrino as cosmic messenger we therefore need neutrino telescopes. These are very different from other types of telescopes: they need to be very large in order to capture some of the weakly interacting neutrinos.

To reach the necessary volume a neutrino telescope needs to be constructed using materials existing in nature. AMANDA is located deep in the Antarctic glacier at the South Pole, using the ice as detector medium.

The performance of AMANDA has been studied using neutrinos created by cosmic rays interacting in the atmosphere, and the observations of atmospheric neutrinos have been extended in the high energy end. Together with the surface array SPASE (South Pole Air Shower Experiment) AMANDAhas contributed to studies of cosmic ray composition. Data has been used for de- termining limits on the diffuse neutrino flux and high energy flux from galactic plane, the neutrino flux from point sources and from annihilation of dark mat- 4

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ter particles. AMANDAalso monitors our Galaxy for neutrinos from supernova bursts.

AMANDA has shown that it is possible to build a working neutrino telescope, but the most interesting physics goals are still out of reach. Now Ice- Cube is under construction, a larger array that will instrument one km³of ice and be powerful enough to probe the current theoretical models. The ﬁrst Ice- Cube modules were installed in 2005, and the whole array will be ﬁnished 2011 with planned of 4800 optical modules deployed on 80 vertical strings.

The thesis is organized as follows: Chapter 2 gives a background to the dark matter search, outlining the evidence for unseen matter in the Universe, what suggestions there are about its nature, and different attempts to detect it. In the following chapter 3 the detection of neutrinos originating from dark matter particle interactions is discussed, and also the main backgrounds in a neutrino detector.

In chapter 4 the AMANDAdetector is explained in some detail, and the data used for the dark matter search is described.

Chapter 5 presents the simulations of the signal we are looking for and the background of neutrinos and muons from the atmosphere.

The heart of the thesis is in the chapters 6 and 7, where the data analysis is outlined and the results are presented. The focus of my own work has been on developing the data ﬁlter and analysis strategy for low energy events, doing the ﬁrst analysis utilizing the special low energy trigger.

Some technical details about the analysis may be found in the appendices.

Finally there is also a summary in Swedish.

Throughout the thesis masses have been given in units of energy (GeV), according to the convention of putting c= 1.

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2. Dark matter

“Gravity equals mass,” said Retrograde Sinopessen.

“It does?” said Hockenberry,

hearing how stupid he sounded but not caring.

“I always thought it was what held things down.”

Dan Simmons: Olympos

An early example of the detection of mass by the gravitational inﬂuence it exerts is the discovery of Neptune in 1846. The orbit of Uranus showed anoma- lies that were concluded to be caused by a previously unknown planet. Like- wise, it is by the gravitational inﬂuence that we have concluded the existence of dark matter.

How much mass is there in the Universe, and in what form? This chapter outlines the theoretical and observational motivation to search for dark matter, and discusses some aspects of the possible detection.

2.1 A very short introduction to cosmology

To explain the case for dark matter, we need some background information on cosmology.

Our knowledge of the Universe has increased with the development of observational techniques and space-borne instruments. In just a few decades cosmology has gone from a highly speculative ﬁeld to remarkably precise observational science.

It has been known since the 1920’s that the Universe is expanding. Dis- tant galaxies move away from us with a velocity v depending on distance d according to Hubble’s law [1] v= H0· d. H0 is known as the Hubble con- stant, but should more correctly be called the Hubble parameter since it varies with time. Often the dimensionless parameter h= H0/100 km s⁻¹ Mpc⁻¹ is quoted instead of H₀. Because objects on average move away from us, light gets Doppler shifted towards longer wavelengths – therefore astronomical dis- tances are normally measured in units red-shift z:

z= λobserved− λemitted

λemitted . (2.1)

The rate of expansion tells us about the energy content of the Universe.

Matter exerts gravitational attraction, which would work to slow down the expansion. Nevertheless, it turns out that the expansion is neither constant

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nor slowing down. In the 1990’s observations of supernovae of type Ia [2]

indicated that the expansion is actually accelerating. To account for this the cosmological constant Λ is introduced¹ in the equations describing the expanding Universe. The mechanism behind this constant is not understood and goes under the name “dark energy”.

Another effect of gravity described by the theory of general relativity is the bending of space-time, which causes light to be deﬂected in gravitational ﬁelds. The effect is often called gravitational lensing: heavy objects act as lenses, making distant objects appear closer or brighter.

The expansion implies that the Universe has been smaller and hotter. Very early in the history of the Universe the temperature was so high that neutron decay was in equilibrium with neutron creation by interactions of electrons with protons. At this time there were about equally many neutrons and protons. As the expansion continued, the probability that particles would collide and interact fell, and at a certain point almost no more neutrons could be created. Now, the existing nucleons could cluster together and form light atomic nuclei without immediately breaking up again. This is called Big Bang nu- cleosynthesis. The only neutrons surviving from this era are those that were bound in nuclei, since the average lifetime of an isolated neutron is about 15 minutes

When the temperature fell below the point where electrons can be bound in atoms the Universe became transparent to photons. (This event is called recombination, despite the fact that it was the first combination of electrons and nuclei into atoms.) This radiation is still filling the Universe, but now extremely red-shifted. This is the cosmic microwave background (CMB) radiation (denoted by “afterglow light” in figure 2.1).

The small ﬂuctuations in the CMB carry important information about the formation of the Universe, and therefore of its properties. The relative angu- lar sizes and magnitude of the variations are connected to the local density variations when the radiation decoupled. Analysis of this pattern gives us very good measures of the cosmological parameters.

The energy density of the Universe is usually denoted by the density param- eterΩ = ρ/ρc, whereρcis the critical density, deﬁning the boundary between a universe which would expand forever and one that would eventually collapse due to gravitational attraction (in case ofΛ = 0).

The combined knowledge today leads to a consensus concordance model of the important parameters of the Universe. In this model, denoted byΛCDM, the Universe has a geometry very close to ﬂat, and most of the energy density is in the cosmological constant term ΩΛ. The largest part of the remaining energy density is in the form of cold dark matter (CDM). Cold means that

1Originally the cosmological constant was introduced by Einstein in his equations of general relativity to make a static universe possible in the presence of matter. When the expansion was discovered the cosmological constant was for a long time believed to be unnecessary. So this is actually an old term reintroduced again.

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Figure 2.1: A schematical representation of the history of the Universe. It shows the rapid expansion known as inﬂation, the afterglow pattern (cosmic microwave background, CMB) from recombination of atoms, the slow but steady expansion and the stars and structures that developed. WMAP is the instrument that mapped the CMB and provided data for the best calculations of the cosmological parameters today. Im- age credit: NASA/WMAP Science Team.

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the matter particles are on the average moving slowly, with sub-relativistic velocities.

To the best of our knowledge today, the totalΩ is unity or very close to unity. According to ref [3]:

Ωtot= 1.003 ± 0.010. (2.2)

The total energy density is the sum of the matter densityΩM(including dark matter, neutrinos, and the ordinary baryonic matter in stars and interstellar gas and plasma) and the dark energy densityΩ_Λ.

2.2 Evidence for dark matter

The ﬁrst attempts to quantify the amount of mass in galaxies and galaxy clusters were made from estimates of the numbers of constituent stars. From models of stars and from their mass-to-luminosity ratio an estimate of the total mass was achieved. Zwicky suggested already in the 1930’s that mass estimates from luminous matter need to be compared with other methods [4].

He used measurements of the spread in red shifts (velocities) for galaxies in a galaxy cluster known as the Coma cluster, together with the the virial theorem²to infer the existence of invisible matter. He realized that the mass of this dark matter was much larger than the mass of the observed luminous matter in the cluster. He was also a proponent of the idea of using gravitational lensing for another type of measurement of the masses of galaxies [5, 6].

Mapping of rotational velocities in spiral galaxies provides even stronger in- dications of dark matter. Outside the galaxy disk the orbital velocities of stars would be expected to fall off as v_orb∝ r^−1/2in accordance with Kepler’s third law, but measurements show that the velocities are approximately constant as a function of distance (see ﬁgure 2.2). It seems that galaxies are contained in a dark matter halo extending outside the visible disk [7].

Dark matter is also needed to account for the structure formation of the Uni- verse. Matter is clustered in galaxies, galaxy clusters and even larger structures. The formation of these structures can be modeled in large computer simulations (see for example [9]). To agree with the structure mapped in large galaxy surveys (e.g. [10, 3], see ﬁgure 2.3) models require an amount of dark matter of the same order of magnitude as independently observed from the cosmic microwave background.

The Bullet cluster

Recent observations of the galaxy cluster 1E0657-56, known as the Bullet cluster, provide new support for dark matter. Data from the orbiting Chandra

2Recall that the virial theorem relates the kinetic energy of a system to the total potential energy.

For a gravitationally bound system the virial theorem states that< T >= −¹₂ < V >, i.e. the average of the kinetic energy T is half of the average of the negative potential energy.

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Figure 2.2: Measured curve of the rotational velocities in the galaxy NGC 6503 as a function of distance from the center, with curves showing the contribution from the disk and gas, and from the dark matter halo inferred to explain the observation. Figure from [8].

Figure 2.3: Large-scale structure mapped in Sloan Digital Sky Survey (SDSS). The ﬁgure is taken from [10] and shows the distribution of right ascension and red-shift z for galaxies within 6^◦of the equator (slightly less in the Galactic South, corresponding to the right half of the ﬁgure; this is why this half appears less populated).

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X-ray observatory is combined with optical images [11] and give strong evidence that while we cannot exclude modiﬁcations to Newtonian dynamics it still must be mostly dark matter that makes up the mass of this cluster.

The Bullet cluster is the result of two clusters which passed through each other. In a galaxy cluster, most of the visible matter is not located in the stars in the galaxies, but in X-ray emitting intergalactic plasma clouds. The distances between the galaxies are much larger than their size, which means that they will pass essentially unaffected far away from each other when the two clusters merge. The plasma, on the other hand, interacts electromagnetically and experiences a pressure. Since the dark matter only interacts weakly it is expected to follow the distribution of galaxies and be separated from the plasma.

The mass distribution of this region can be mapped by observing the gravitational lensing effect on objects behind the cluster, see ﬁgure 2.4. From the mass density curves it can be seen that the most of the mass is where the galaxies are, and outside the region of luminous plasma. The mass of the galaxies themselves cannot account for the lensing effect. It looks indeed like we have a situation where the dark matter is separated from the luminous matter. There- fore this observation is seen as strong evidence for dark matter.

Figure 2.4: The mass density curves mapped with gravitational lensing, superimposed on the optical (left) and X-ray (right) images of the Bullet cluster, showing that most of the mass is clearly located outside the X-ray luminous plasma clouds where most of the visible matter is located. Figures from [11].

2.3 The amount of dark matter in the Universe

Data from the Wilkinson Microwave Anisotropy Probe (WMAP)[12], mapping the primordial ﬂuctuations in the microwave background radiation, provides some of the best measurements of the cosmological parameters.

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The ﬁt to the WMAP results give

Dark matter density ΩDM = 0.20^+0.02_−0.04 (2.3) Baryon density ΩB = 0.042^+0.003_−0.005 (2.4) Dark energy density Ω_Λ = 0.76^+0.04_−0.06. (2.5) For comparison, it can be mentioned that attempts to estimate the mass of luminous objects arrive at [13]

Ωlum≈ 0.01. (2.6)

To summarize: on all scales, from galaxies to the whole Universe, there are observations indicating that there must be more mass than can be accounted for by luminous matter alone.

2.4 What is the dark matter?

Big Bang nucleosynthesis calculations together with observations of the relative abundance of light elements give constraints on how much baryonic matter there can be. This gives ΩBh² of the same order of magnitude as other measurements, and this result clearly shows that we cannot explain all of the dark matter with cold massive objects of ordinary matter (such matter clumps in galactic halos are called MACHOs, Massive Compact Halo Objects).

Massive neutrinos have also been considered candidates. Neutrinos are nowadays believed to have a small but nonzero mass, since ﬂavour oscillations are observed [14, 15] and these are related to mass differences between different neutrino types. The cosmological constraints on the neutrino masses are very strict: the sum of the masses of the three neutrino ﬂavors is less than 0.62 eV [16]. Because of their small mass neutrinos constitute what is called hot dark matter, as they decouple from the radiation equilibrium in the early Universe at relativistic energies and move with large velocities. Hot dark matter cannot account for structure formation in the Universe and therefore can only be a small part of the total amount of dark matter [17].

So it turns out that known types of matter cannot account for the mass in the Universe. However, there are motivations from particle physics to search for particles that occur in extensions to the standard model.

A weakly interacting massive particle, WIMP, would have the right properties to ﬁt the description of dark matter. Interactions on the weak scale makes the particle difﬁcult to detect, which explains why we have not seen it. It is also possible to calculate the relic abundance of this type of particle from the production in energetic particle reactions in the hot early Universe. The resulting density agrees approximately with the dark matter density.

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2.4.1 Supersymmetry and the neutralino

The most popular candidate for cold dark matter comes from supersymmetric extensions to the standard model. Supersymmetry was proposed in order to solve the hierarchy problem, which is the problem of the large differences between the scale of the coupling constant for gravity and the electroweak interaction. This creates difﬁculties in the calculation of Higgs mass, where the ﬁrst order perturbative corrections become proportional to the square of a cut-off scale, which is the energy scale where new physics becomes important.

If the standard model holds up to the scale where gravity becomes important at∼ 10¹⁹GeV, the corrections to the Higgs mass will be of this order, some 16 orders of magnitude larger than the largest expected Higgs mass. This seems to require ﬁne-tuning of the masses, or some new symmetry that removes the large correction terms.

In supersymmetric models there is a symmetry between fermions and bosons, such that all fermions have a bosonic superpartner and all bosons have a fermionic one as shown in table 2.1. The new particles that enter the theory in the supersymmetric framework have to be taken into account in the calculation of masses, and these additional terms exactly cancel the divergent corrections from standard model particles.

Supersymmetry also introduces a common scale for uniﬁcation of the forces in the standard model. The coupling constants of the fundamental interactions vary with the magnitude of the momentum transfer. The size of the coupling constants evolve to a uniﬁed value at very large momentum transfers if supersymmetry is introduced.

In supersymmetric models particles are usually assumed to possess a symmetry called R-parity, represented by a quantum number deﬁned as

R≡ (−1)^3B^+L+2s, (2.7)

where B is the baryon number, L is the lepton number and s spin. R-parity was ﬁrst introduced in the theory to suppress the rate of proton decay which would otherwise occur as a consequence of the theory at a rate excluded by experimental observation. Standard model particles have R= 1 and their su- persymmetric partners have R= −1. If R-parity is conserved it means that su- persymmetric particles cannot decay into only standard model particles, and therefore the lightest supersymmetric particle (LSP) is stable and a viable dark matter candidate.

In the MSSM (minimal supersymmetric model) the LSP is the lightest neutralino. Four neutralinos arise as linear combinations of the superpartners of the gauge bosons and the Higgs bosons:

χ˜i⁰= Ni1B˜+ Ni2W˜³+ Ni3H˜₁⁰+ Ni4H˜₂⁰, i= 1 − 4. (2.8) 14

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Table 2.1: Standard model particles and their superpartners in the MSSM (from ref [18]).

Standard model particles and ﬁelds Supersymmetric partners Interaction eigenstates Mass eigenstates

Symbol Name Symbol Name Symbol Name

q= u,d,s,c,t,b ^quark q˜L, ˜qR squark q˜1, ˜q2 squark l= e, µ,τ ^lepton ˜lL, ˜lR slepton ˜l1, ˜l2 slepton ν = νe,ν_µ,ν_τ neutrino ν˜ sneutrino ν˜ sneutrino

g gluon g˜ gluino g˜ gluino

W^± W-boson W˜^± wino

H⁻ Higgs boson H˜₁⁻ higgsino



 χ˜₁^±_,2 ^chargino

H⁺ Higgs boson H˜₂⁺ higgsino

B B-ﬁeld B˜ bino

W³ W³-ﬁeld W˜³ wino

H₁⁰ Higgs boson

H˜₁⁰ higgsino











χ˜₁⁰_,2,3,4 ^neutralino

H₂⁰ Higgs boson

H˜₂⁰ higgsino

H₃⁰ Higgs boson

The lightest neutralino ˜χ₁⁰is the dark matter particle that is searched for in this thesis. In the following no other neutralinos will be discussed, and the ˜χ₁⁰ will for simplicity be abbreviated toχ and referred to only as the neutralino.

Neutralinos are of the Majorana type (particle and antiparticle are identical) and therefore they can annihilate with each other, creating standard model particles. There are many possible annihilation channels [19]. Cold dark matter particles are by deﬁnition non-relativistic, and in the non-relativistic limit the most important neutralino annihilation channels are [18]:

χχ → c ¯c,b¯b,t¯t,τ ¯τ,W⁺W⁻,Z⁰Z⁰,Z⁰H₁⁰,Z⁰H₂⁰,H1⁰H₃⁰,H2⁰H₃⁰,H^±W^±. (2.9) The annihilations can be detected by signatures of long lived secondaries from these annihilation products. Various observational efforts have targeted for example gamma rays, neutrinos, positrons or antiprotons.

It can be noted that the branching ratio directly into neutrinos is zero in this limit.

There are also annihilation channels with smaller branching ratios (loop level) intoγγ or Zγ, which are interesting because of the possibility to detect monoenergetic gammas directly indicating the mass of the neutralino.

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Observational constraints

Measurements from particle collider experiments can provide constraints to the available parameter space for supersymmetry. These constraints are highly model dependent, and do not easily translate to for example mass of the neutralino. They are therefore difﬁcult to summarize, but can be applied when calculating the parameters within a given supersymmetric scenario.

Given the most common assumptions the values constrained by collider experiments and cosmology arrive at a lower limit of m_χ> 46 GeV [20]. The upper limit of the mass is about 10 TeV, since a heavier WIMP would give a mass density too large to ﬁt with cosmological observations.

In the discussion of detection we will see that in many cases the most favored masses are of the order of 100 GeV.

2.4.2 Other candidates: axions and Kaluza-Klein states

One of the problems of quantum chromodynamics (QCD), the theory of strong interactions, is that it seems to predict violation of the CP-symmetry (invari- ance under charge and space inversion) which is not observed in experiments.

In an attempt to solve this, a symmetry is introduced which implies the existence of an extremely light particle called axion, which could be a dark matter candidate. Although not as compelling as the neutralino the axion is still often discussed in this context, and some theorists argue that there could be a comparable amount of WIMPs and axions, both contributing to the total dark matter density [21].

Another much discussed candidate arises from the concept of extra dimensions. It is possible that there are other spatial dimensions than the three we are used to, but which are compactified to small scales (high energies). These are motivated as a means of addressing the hierarchy problem (discussed above in connection with supersymmetry), or occur in attempts to construct a theory of quantum gravity and unification of interactions. Particles could occur as a series, called a tower, of Kaluza-Klein states sharing properties with their standard model counterpart but with extra mass arising from their momentum in the extra dimensions. (The momentum is quantized by the confinement of the compactified scale.) The lightest Kaluza-Klein particle is an interesting dark matter candidate, discussed for example in [22] and [23].

Axions and Kaluza-Klein matter are at this time the only serious competi- tors to the neutralino for the attention as dark matter candidates. In the following only WIMP dark matter in the form of neutralinos will be discussed.

2.5 WIMPs in the Solar System

Since the Solar System is in motion around the center of the Galaxy, it is expected that it is moving through the Galactic dark matter halo. WIMPs in 16

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the halo can scatter gravitationally or by weak interactions and be captured in bound orbits around the Sun.

A WIMP passing through matter can undergo weak scattering and lose energy. Over time, the energy loss through multiple scatterings makes WIMPs sink to the bottom of the gravitational well. In this way dark matter particles can accumulate inside planets or the Sun.

In gravitational scattering on a planet the speed with respect to the planet is conserved, while the direction changes. Such scatterings can throw WIMPs into bound orbits around the Sun, and over time the local WIMP density in the system is enhanced. The velocity distribution will be deﬁned by the combined diffusion by the gravitational ﬁelds of all of the planets.

The local distribution of WIMPs at the Earth is depleted by gravitational scattering throwing WIMPs originally in bound orbits out of the system, or into the Sun where they are captured by weak scatterings and sink to the core.

This solar depletion effect suppresses the WIMP capture rate in the Earth (as compared to earlier calculations) for WIMP masses above 100 GeV. Calcula- tions of the capture rate by the Sun and the Earth have recently been published by Lundberg and Edsjö [24].

The capture of low mass WIMPs is not affected by this solar depletion effect, and this result further motivate the focus on low masses in the search for WIMPs in the Earth.

2.6 WIMP search

Dark matter search is a very active ﬁeld, with numerous running and planned detectors and experiments. The attempts can be divided into direct detection of the dark matter particles, and indirect detection of annihilation products.

There is also the possibility to discover dark matter by producing the particles in collider experiments.

It is commonly believed that if supersymmetry exists it will be discovered at the Large Hadron Collider (LHC) at CERN, which will start physics runs at the end of 2007. Astrophysical observations bring complementary constraints, and these active and passive detections can be combined to better determine the more than 100 parameters of supersymmetry [25].

2.6.1 The Galactic dark matter halo

Not only would we like to know if there is a WIMP in the form of a neutralino and identify its properties, there is also much to learn about the local distribution of dark matter in the halo of our own Galaxy.

The usual assumptions about the Galactic dark matter halo are [22]:

• ρ ∝ r⁻²(accounting for the ﬂat rotation curve)

• local density of ρ0= 0.3 GeV cm⁻³

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• isothermal proﬁle (meaning that the velocity dispersion is constant with radius)

• Maxwell-Boltzmann velocity distribution with a characteristic velocity v0

= 270 km s⁻¹

Of course, the properties of the halo have large effects on the prospects of detection. One of the much discussed uncertainties is the density of dark matter at the center of the Galaxy. At large distances the distribution is known from the rotation curve, but at the center the dark matter proﬁle is more dif- ﬁcult to determine. It is generally expected that the density grows for small values of the radius and accumulate close to the center. The possible density is limited by the annihilation of the WIMPs [26].

There might also be substructures in the halo which would affect the results of the searches, as the Solar System moves through regions of higher and lower dark matter density. For example, the amount of WIMPs captured inside the Sun will depend on accumulation throughout the history of the So- lar System, while the present rate of WIMPs scattering in detectors depends on the local halo density at this time.

2.6.2 Direct detection

The idea of direct detection is to detect WIMPs by measuring the energy deposited in weak elastic scatterings on atomic nuclei. A WIMP with mass of tens of GeV scattering on a nucleus would typically transfer an energy of the order of keV, which can be detected through a signature of phonons (measured with bolometers, bubble chambers), photons (scintillators) or charge (ionization detectors).

Detectors are mounted deep underground to avoid background induced by cosmic rays. A difﬁcult type of background consists of neutrons from natural radioactivity. A nuclear recoil induced by a neutron is indistinguishable from elastic WIMP-scattering, and therefore this background needs to be carefully controlled.

There are many detectors running or being developed at the time, utilizing different techniques. The parallel efforts accelerate the detector development and it is important that the various instruments have different systematic uncertainties which will be valuable for evaluating an observation.

One way of identifying a WIMP signal would be to observe the slight vari- ation in event rate over the year that would be the effect of the Earth’s motion through the galactic halo. Depending on the location in the orbit around the Sun, the Earth moves faster or slower through the ambient WIMP population.

Therefore the average relative velocity of the WIMPs with respect to the Earth is expected to vary slightly over the year. The cross section of the weak scattering depends on the energy, which means that the number of interactions per unit time depends on the season. The predicted annual modulation is about 5-10%.

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The NaI scintillation detector DAMA [27] created some excitement and controversy in the dark matter community by claiming discovery by observation of this annual modulation. The DAMA results indicated a WIMP mass of about 50 GeV and cross section 5· 10⁻⁴²cm².

By now other collaborations with detectors such as CDMS [28], CRESST [29] and ZEPLIN [30] have probed the region of the parameter space favored by DAMA and failed to see anything, as shown in ﬁgure 2.6.2.

ZEPLIN-I uses liquid xenon as scintillator, and can discriminate between different particles through the scintillation time-constant, which depends on the energy loss per unit length.

CDMS (Cryogenic Dark Matter Search) uses cryogenic solid state detectors sensitive to ionization charge and phonons. These can discriminate between recoiling electrons from gamma and beta backgrounds and recoiling nuclei from WIMP interaction by pulse shape and ratio of ionization to phonon yield.

CRESST (Cryogenic Rare Event Search with Superconducting Thermome- ters) is using cryogenic calorimeters to detect the nuclear recoils. The second generation detector CRESST-II is using CaWO4crystals as absorber, in which the deposited energy is divided between phonons and scintillation light.

The mentioned detectors are examples of the techniques used for direct detection. Another interesting prospect is to use a direction sensitive detector which could distinguish a daily modulation caused by the relative motion through the WIMP halo as the Earth turns. One project developing along these lines is DRIFT [31], a low pressure gas detector in test run at the Boulby mine.

This detector will have high resolution in space and in energy, to be able to reconstruct the direction of a nuclear recoil.

It can be noted that all of the mentioned detectors are sensitive primarily to spin-independent scattering. The strength of the coupling for spin-dependent and spin-independent interactions depends on the nature of the WIMP. In the case of the neutralino the relative strength of spin-dependent and spin- independent interactions is determined by the parameters of supersymmetry and by the composition of the neutralino (cf equation 2.8)[23]. It is possible that it interacts almost only spin-independently, or only spin-dependently.

Scenarios with primarily spin-dependent couplings are much less constrained, and the strongest limit is placed with the NaI scintillator detector NAIAD [32].

A class of detectors sensitive to spin-dependent couplings are bubble chambers, sensitive to the local rate of energy loss of the recoiling nucleus. One such project is PICASSO [33]. In this detector superheated freon droplets are dispersed in a gel. The droplets boil and expand at small added energy. An expanding droplet induces a measurable vibration in the surrounding gel, which can be recorded by piezoelectric sensors.

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061125102301

http://dmtools.brown.edu/

Gaitskell&Mandic

10¹ 10² 10³

10^-43 10^-42 10^-41 10^-40

WIMP Mass [GeV]

Cross-section [cm2 ] (normalised to nucleon)

Figure 2.5: The current upper limits on spin-independent scattering cross section from (top to bottom) CRESST, ZEPLIN-I and CDMS. The ﬁlled region is the parameter space favored by DAMA (see text for details). The ﬁgure was generated with the script at http://dmtools.brown.edu.

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2.6.3 Indirect detection

WIMPs could also be detected by signs of annihilation. Regions where the WIMP density is higher are particularly interesting since the annihilation rate is proportional to the square of the dark matter density. In section 2.5 we discussed how WIMPs can become gravitationally bound and accumulate in the Solar System. In the same way the dark matter particles can be accumulated for example in the center of our Galaxy.

Calculations of the annihilation rate depend on the original distribution of neutralinos, their cross-section for elastic scatterings through which they lose energy, the mass and the age of the object accumulating neutralinos. These conditions will decide the density and the distribution of the denser neutralino population, and given the annihilation cross section deﬁne the annihilation rate.

Galactic center

One possibility to observe annihilations from the direction of the Galactic center would be through gamma radiation, a continuous spectrum from secondary annihilation products or monoenergetic gammas fromχχ → γγ or χχ → γZ.

The astrophysics of the region at the galactic center is complicated. There is the black hole Sagittarius A^∗ [34] surrounded by a supernova remnant, and a region of hydrogen plasma. Gamma rays can be generated in various processes here. Signatures of WIMP annihilation would be the energy spectrum with a cut-off at the WIMP mass, and absence of variations in time.

The gamma ray telescope EGRET, taking data on the satellite borne Comp- ton Gamma Ray Observatory between 1991 and 2000, has observed a source of gamma radiation in the direction of the galactic center [35], which may have a contribution from WIMP annihilations.

Several ground-based gamma ray telescopes are giving data on the flux from the same direction. Among these H.E.S.S. [36] (with an energy threshold of 160 GeV) has reported the most significant signal. The signal has no cut-off and fits to a power-law spectrum E^−2.25. If the origin is solely from dark matter annihilations the data implies a WIMP mass of 10 TeV. There has also been an attempt to find a dark matter contribution hidden in a power-law background in this data sample, but with no success [37].

The Gamma-ray Large Area Space Telescope (GLAST) [38], to be launched in late 2007, will have lower threshold than the ground-based gamma observatories and better spatial resolution than EGRET, and will contribute to the ability to identify different contributions to the gamma spectrum.

While the Galactic center has been studied in gamma radiation, no ﬂux of neutrinos from this source have been observed. The Galactic center is located in the southern sky and therefore not visible to AMANDA, which ob- serves the other hemisphere using neutrinos that pass trough the Earth. The

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ANTARES [39] neutrino telescope being constructed in the Mediterranean Sea will have a sensitivity enough to detect this signal if the whole excess observed by EGRET is due to WIMP annihilation [22].

Another detection possibility would be synchrotron radiation from secondary electrons and positrons in the magnetic ﬁeld around the Galactic center.

Halo clumps

In addition to the source close to the Galactic center, EGRET has observed a diffuse gamma flux from all directions which is 60% higher than theoret- ically predicted. Careful analysis of the data shows that the excess can be explained by dark matter annihilations in the galactic halo if the annihilation rate is enhanced by a factor of 20 [40] as compared to the expectation from conventional assumptions about the halo and the annihilations. This enhance- ment could be attributed to clumping of the dark matter distribution on small scales. A problem that has been pointed out [41] is that if all of the excess is due to dark matter there would be a flux of antiprotons exceeding the flux detected in balloon experiments.

HEAT was a balloon borne antimatter detector flown between 1995 and 2000. It detected a positron fraction (flux of positrons to total positron and electron flux) which is compatible with expectation from nuclear interactions in interstellar space [42], but a contribution from dark matter cannot be ruled out.

Center of large celestial bodies

As described in section 2.5 neutralinos (or other WIMPs) tend to accumulate the interior of bodies like the Sun or Earth. Most of the annihilation products will be absorbed before reaching a detector close to the surface of the Earth, but neutrinos can escape. Several neutrino detectors have been able to put upper limits on the muon flux from neutrinos coming from the direction of the center of the Sun or Earth, as shown in figure 2.6. In this figure it can be noted that in the case of the Earth, the most interesting prospects of detection come from scenarios with WIMP mass of less than 100 GeV, because higher masses are disfavored by direct detection searches.

At the South Pole, the sun never sets more than 23^◦below the horizon. This means that a search for a signal from the Sun involves nearly horizontal particle tracks. In the earlier stages of AMANDA the detector had smaller radius and was therefore not well suited to ﬁnd and reconstruct horizontal tracks.

The sensitivity for WIMP signals from the Sun became competitive when the detector was completed [43].

Searches for a WIMP signal from the Earth, which is aligned with the detector geometry, started already earlier [44, 45]. For high masses AMANDA

has the best limit on muon ﬂux from the center of the Earth.

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1 10 10² 10³ 10⁴ 10⁵

10 10² 10³ 10⁴

E^th_µ = 1 GeV σSI> σSIlim CDMS 2005

0.05<Ωχh2< 0.2

Neutralino Mass (GeV) Muon flux from the Earth (km-2 yr-1 )

BAKSAN 1978-95 BAIKAL 1998-99 MACRO 1989-98 AMANDA 1997-99

SUPER-K 1996-2001 IceCube best-case

1 10 10² 10³ 10⁴ 10⁵

10 10² 10³ 10⁴

σSI> σSIlim CDMS 2005 E^th_µ = 1 GeV

0.05<Ωχh2< 0.2

Neutralino Mass (GeV) Muon flux from the Sun (km-2 yr-1 )

BAKSAN 1978-95 MACRO 1989-98 SUPER-K 1996-2001

AMANDA-II 2001 IceCube (best case)

Figure 2.6: Limits on the muon ﬂux from the Earth (top) and from the Sun (bottom).

Markers in the ﬁgure show predictions for cosmologically relevant MSSM models, the dots representing models excluded by the CDMS direct detection[28] and the crosses representing the models that are not excluded in direct detection attempts. The years in the legend refer to the data taking periods. The most important limits from different indirect detection projects are plotted, and the predicted sensitivity of the IceCube detector is also indicated.

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Baikal [46] is a Cherenkov array operated in the Lake Baikal. The first version of the detector consisted of almost 200 optical modules on 8 strings at one kilometer depth, and in this configuration started taking data in April 1998. The limit shown in figure 2.6 is obtained in an analysis of data from 1998-1999. (There is a more recent limit from data taken between 1998 and 2002, which lies between 1.7·10³ and 1.2·10³ km²/year for masses from 60 GeV to 1000 GeV [47]. This limit is given for a muon threshold of 10 GeV and therefore not directly comparable to the other limits, and that is why it is not included in the figure.)

Baksan [48] is an underground scintillator detector that has been running since 1978, detecting upward going muons.

MACRO [49] was a modular detector, operated in its complete conﬁgura- tion 1995-2000. It was located deep underground in Gran Sasso, Italy.

Super-Kamiokande [14] is a closed water Cherenkov detector operated underground in the Kamioka-Mozumi mine in Japan. It has an inner detector with over 11 thousand photomultipliers and and outer detector acting as a cosmic ray veto counter.

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3. Neutrino detection

The earth is just a silly ball

To them, through which they simply pass John Updike: Cosmic Gall

The previous chapter outlined the case for dark matter and sketched some of the attempts to detection.

Since this thesis concerns an attempt to ﬁnd WIMPs inside the Earth by detecting a signature of neutrinos resulting from their annihilation, we will now delve into the details of neutrino detection. This chapter discusses neutrino interactions and their detector signatures, and also the muon and neutrino ﬂuxes that are always present in the detector and constitute the background to our search.

3.1 Neutrino interactions

Neutrinos are detected through their weak interactions with matter.

Weak interaction cross sections increase with energy. Low energy neutrinos, up to energies of the order of 100 TeV, pass unhindered through the Earth, and the whole planet can be used as a ﬁlter to separate neutrino induced events from muons generated by cosmic rays. At PeV energies the cross sections are large enough that the Earth becomes opaque to neutrinos, and to search for neutrinos with E_ν EeV it is necessary to look for events from the horizon or from above [50].

The weak interaction is mediated by charged or neutral currents (exchange of W^±or Z⁰bosons). In a neutral current (NC) interaction the outgoing lepton is still a neutrino. In this case the only signature visible will be the hadronic shower at the interaction point. In a charged current (CC) interaction the neutrino is converted to a charged lepton corresponding to the neutrino ﬂavour (see ﬁgure 3.1).

Leptons of different flavors give different signatures in the detector. An electron loses energy quickly and generates an electromagnetic cascade which coincides with the initial hadronic cascade. In case of a ν_τ interacting there will be aτ which has a lifetime of 0.29 ps. A tauon with an energy of 1 PeV traverses about 50 m before decaying, creating a second particle cascade in addition to the cascade at the first interaction point. Tauon events of high energies could be identified by these two correlated particle showers, a “double bang”. In order to clearly resolve the two showers they need to be separated

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ν ν

W,Z

N X,N’

l,

Figure 3.1: Simplified picture of a neutrinoν interacting with a nucleon N. In case of interaction by exchange of a charged current W a charged lepton l is created, and in case of exchange of a neutral Z current the outgoing lepton is still a neutrino. At the energies of interest in AMANDA( 20 GeV), the target nucleon will fragment and the nucleus break up, giving rise to a hadronic shower, a short and localized cascade of particles (only the first branch of the fragmentation is indicated in the figure).

by∼ 100 meters. Identifying ultra high energy tauons by this signature seems feasible for IceCube, with its larger volume.

Muons are lighter than tauons and have a much longer mean life time, 2.2µs. The most important neutrino detection channel exploited in A^MANDA is muons generated byνµin CC interactions. If the muon energy is sufﬁciently large, the muon leaves a long, straight track.

The muon track can be detected and used for accurate reconstruction of the direction of the muon, and through this we gain information about the direction of the original neutrino. The mean difference in the direction of the muon and the parent ν_µ is 0.7^◦/(E_ν/TeV)⁰^.7 [51]. Typical precision in the reconstruction of the direction in AMANDA is a few degrees (depending on muon energy and on the angle with respect to the detector) [52].

In searches for point sources muon events are best suited for analysis. Typ- ical precision in the reconstruction of the direction of cascades is 30-40^◦[53].

Nevertheless, cascade like events have been studied in AMANDA to search for and put limits on the diffuse ﬂux of high energy neutrinos [54]. Cascade events also have the advantage that they can be reconstructed with better energy resolution than muon events since they are localized and often contained in the detector.

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3.2 Muons in ice and the Cherenkov effect

High energy muons are long lived in the detector frame because of time dila- tion, and they generally stop due to energy loss before decaying. The range of muons in ice is therefore limited by the interactions with matter rather than by their lifetime. At low energies ionisation and atomic excitation are the dominant processes, but at higher energies photonuclear and radiative processes (pair production and bremsstrahlung) dominate. The average muon energy loss can be parametrised as [55]

−dE

dx = a(E) + b(E) · E, (3.1)

where a(E) and b(E) can be considered constant for energies above

∼ 10 GeV. In ice a 0.26GeVmwe⁻¹and b 0.36 · 10⁻³mwe⁻¹ [56].¹The term a describes the energy losses due to ionization and atomic excitation, and dominates the energy loss below a critical muon energy of about 700 GeV. Above this energy the photo-nuclear and radiative processes like e⁺e⁻ pair production and bremsstrahlung dominate, described by the term b· E.

When a charged particle moves in a refractive medium with a velocity higher than the speed of light in that medium, Cherenkov light will be emitted. The Cherenkov effect is caused by the local change in the electromagnetic ﬁeld as the particle passes through the matter. This makes the atomic electrons oscillate slightly, acting as small antennas, and thus creating electromagnetic radiation. The electromagnetic wave fronts from the individual atoms are too weak to be noticeable on a macroscopic scale, but if the particle moves faster than the waves there is constructive interference at a certain angle, resulting in the typical Cherenkov light cone (ﬁgure 3.2).

The Cherenkov angle isθC= arccos(_βn¹ ), where n is the index of refraction and β is the velocity expressed as the fraction of the light speed in vacuum (v/c). Ice has n ≈ 1.33 and β very close to 1, which gives an emittance angle of 41^◦.

The number of photons per unit path length and wave length is described by the Frank-Tamm formula [57], here expressed for a particle with unit charge:

d²N

dxdλ =2πα

λ² · (1 − 1

β²n²) (3.2)

whereα is the ﬁne-structure constant.

Because of the optical properties of the ice and the glass housing of the detector modules in AMANDA the wavelength region between 300 nm and 500 nm is most favorable for detection. Integrating equation 3.2 between these

1mwe stands for meters water equivalent, a unit often used in applications of radiation shielding and in other cases when it is of interest to compare the energy loss of radiation in different materials.

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θ

c

µ

Figure 3.2: The Cherenkov light cone, with the Cherenkov angleθCindicated.

limits gives the result that about 200 photons are emitted per centimeter of track length. The muon energy loss from this process is nevertheless negligible compared to the loss from the other processes.

3.3 Particle background to the WIMP search

A WIMP signal will have to be found against an abundant background of other particles giving signals in the detector. These particles are created by cosmic rays hitting the atmosphere where they interact and produce mesons, which in turn interact or decay producing large particle showers.

Most of the particles in these showers are absorbed before reaching AMANDA, which is shielded by about 1500 m of ice. The only particles that reach the detector are neutrinos and high energy muons.

The most important channel for production of muons and muon neutrinos are the decay of charged pions and kaons,

p+ X → π^±+Y

→ µ^±νµ( ¯νµ) (3.3) p+ X → K^±+Y

→ µ^±ν_µ( ¯ν_µ) where pion decay is the dominant contribution [58].

Muons with energies of up to 10 GeV decay throughµ^±→ e^±+ νe( ¯νe) + ν¯µ(νµ) before reaching the ground, and will contribute to the ﬂux of electron neutrinos at these energies. The decay chain gives rise to two muon neutrinos 28