scuola di dottorato in scienze della natura e tecnologie ... importante de cette th ese est dedi ee...

Università degli Studi di TorinoScuola di Dottorato in Scienze della natura e Tecnologie Innovative

Université de Paris Diderot-Paris VIIED. 560 Sciences de la Terre et de l’Environnement et Physique de

l’Univers et des Planètes

Dark Matter searches with charged cosmic rays

Andrea Vittino

Advisors: Nicolao FornengoMarco Cirelli

A mio padre

Abstract

The issue of Dark Matter represents one of the most exciting challengesfor physicists. This elusive substance acts as a fundamental ingredientin shaping up the history of the Universe, it makes up more than the80% of the total matter inside it and perhaps its existence can be tracedback to the solution of one of the main problems that affect the StandardModel of particle physics. In the last decades, gravitational evidencesin favor of its existence have been collected in a variety of observations,ranging from the cosmological to the astrophysical scale. At the sametime, all the non-gravitational attempts for a detection have failed inproviding indisputable signals.

Among the different Dark Matter searching strategies, indirect detec-tion is the technique based on the attempt to detect Standard Modelparticles that can be generated in pair annihilation or decay processesand that can reveal their presence in astrophysical or cosmological ob-servables. Among these particles, an important role is played by chargedcosmic rays, which will be the main topic of this thesis. Our explorationis directed towards all the main messengers: antiprotons, positrons andlight anti-nuclei.

Concerning hadronic channels, we show that antiprotons can be effec-tively used as a powerful tool to constrain the parameter space of DarkMatter, while anti-nuclei can be seen as a potential discovery channel,even if the large uncertainty that affects production mechanisms hasto be taken into account. To this purpose, we carry out an in-depthinvestigation of the issues related to anti-nuclei formation through theso-called coalescence mechanism, we illustrate how this process can beeffectively implemented in our computations and we try to assess the

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extent of the uncertainty that it brings to our results. We consider inour analyses anti-deuteron and anti-Helium and for both of them weinvestigate the perspectives of detection with current or soon-to-comeexperiments.Concerning, on the other hand, positrons, we perform a global fit tothe observables that have been recently measured by Ams-02 (namely,e± fluxes and their fraction) within a purely astrophysical framework inwhich electrons and positrons are produced either by primary sourcessuch as Pulsar Wind Nebulæ and Supernova Remnants or through spal-lation reactions of primary cosmic rays against interstellar matter inorder to assess if the presence of a Dark Matter contribution is reallyneeded to explain observations.

All across the different analyses that we conduct, a critical role is playedby the mechanisms of propagation of the potential Dark Matter mes-sengers both in the galactic medium and in the solar neighbourhood.Therefore, an important part of this thesis is devoted to the descriptionof the various aspects of these processes, with the attention being fo-cussed on the impact that they can have on the results that we obtain.

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Sintesi

La materia oscura rappresenta uno dei misteri più affascinanti dellafisica. Questa elusiva sostanza agisce come ingrediente fondamentale neldare forma all’evoluzione dell’Universo, costituisce più dell’80% dellamateria contenuta in esso e la sua esistenza potrebbe essere connessacon uno dei problemi, tuttora irrisolti, che affliggono il Modello Stan-dard delle particelle elementari. Negli ultimi decenni, un gran numerodi osservazioni, su scale che spaziano da quelle astrofisiche a quelle cos-mologiche, ha permesso di accumulare una serie di evidenze puramentegravitazionali in favore della sua esistenza. D’altro canto, tuttavia, tuttii tentativi volti a trovare tracce non gravitazionali della sua presenzahanno fallito nel produrre segnali certi.

Tra le diverse tecniche che vengono normalmente utilizzate a tale fine,la rivelazione indiretta è quella che si basa sulla ricerca di particelledel Modello Standard che possono essere prodotte in annichilazioni odecadimenti di materia oscura e che possono rivelare la loro presenza inosservabili astrofisiche o cosmologiche. Tra i possibili segnali che sononormalmente considerati in questo tipo di ricerca, vi sono i raggi cosmicicarichi, che costituiscono l’argomento di questa tesi. La nostra esplo-razione comprende gli antiprotoni, i positroni e gli anti-nuclei leggeri.

Per quanto riguarda i segnali adronici, mostriamo che gli antiprotonisono uno strumento che può essere usato efficacemente per vincolare lospazio dei parametri della materia oscura, mentre gli anti-nuclei costitu-iscono un promettente canale di scoperta, malgrado la larga incertezzalegata ai loro meccanismi di produzione non possa essere ignorata. Pervalutare il peso di questo fattore, conduciamo un’indagine approfonditadei problemi legati alla formazione degli anti-nuclei attraverso il mec-

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canismo noto come coalescenza, soffermandoci in particolare su cometale processo possa essere implementato nella nostra analisi e quale sial’incertezza legata ai parametri che lo governano. Nella nostra indaginesugli anti-nuclei consideriamo quelli più leggeri, ossia l’anti-deuterio el’anti-elio e per entrambi deriviamo le prospettive di osservazione daparte di esperimenti attuali o futuri.Per quanto riguarda, invece, i positroni, effettuiamo un fit globale delleosservabili recentemente misurate dall’esperimento Ams-02 (ossia i flussidi e± e il loro rapporto) nel quadro di un approccio puramente astrofisiconel quale elettroni e positroni sono emessi da sorgenti primarie comePulsar Wind Nebulæ e Supernova Remnants o attraverso reazioni dispallazione di raggi cosmici primari contro la materia interstellare, alloscopo di determinare se un contributo da parte della materia oscura ènecessario per spiegare le misurazioni.

Nelle nostre indagini, un ruolo particolarmente importante è giocatodai meccanismi di propagazione dei potenziali messaggeri di materia os-cura sia nel mezzo interstellare che nell’ambiente solare. Per questo, unaparte importante della tesi è dedicata alla descrizione dei diversi aspettidi questi processi, con particolare attenzione rivolta all’impatto che essihanno sui nostri risultati.

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Résumé

Parmi les mystères de la physique, l’un des plus intéressants est sansdoute représenté par la matière noire. En fait, cette élusive substanceagit comme ingrédient fondamental pour l’évolution de l’Univers, con-stitue plus de 80% de son contenu de matière et son existence est peut-être liée à la solution d’un des problèmes qui affligent le Modèle Standardde la physique des particules. Au cours de dernières décennies, un grandnombre d’observations astrophysiques et cosmologiques nous a permisd’accumuler des preuves gravitationnelles de son existence. Au mêmetemps, toutefois, toutes les tentatives dans le but de trouver des tracesnon gravitationnelles de sa présence ont échoué à produire un signal in-contestable.

Entre les différentes technique utilisées à cet effet, la détection indirècteest basée sur la recherche de particules du Modèle Standard qui peu-vent être produites lors de l’annihilation ou de la désintégration de lamatière noire et qui peuvent révéler leur présence dans des observablesastrophysiques ou cosmologiques. Cette thèse a pour but celui de décrireles perspectives qui caractérisent cette stratégie de recherche pour ce quiconcerne les rayons cosmiques chargés. Notre investigation comprend lessignaux principaux qui ont été conçus: antiprotons, positrons et anti-noyaux légers.

Pour ce qui concerne les signaux hadroniques, nous montrons que lesantiprotons peuvent être utilisés efficacement pour limiter l’espace despossibles valeurs des paramètres de la matière noire, tandis que lesanti-noyaux représentent un possible moyen de découverte, bien quel’incertitude liée aux mécanismes de leur production ne puisse pas êtresous-éstimée. Pour évaluer l’impact de ce facteur, nous menons une

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analyse approfondie des problèmes liés à la formation des anti-noyaux àtravers le mécanisme connu sous le nom de coalescence en nous concen-trant sur la façon dont ce phénomène est réalisé dans notre modélisationet sur l’incertitude qui entoure les paramètres qui le régissent. Dansnotre analyse nous considérons les anti-noyaux les plus légers, l’anti-deuteron et l’anti-Helium, et pour chacun d’entre eux nous établissonsles perspectives de découverte d’un signal par les expériences actuelleset futures.Pour ce qui concerne, d’autre part, les positrons, nous effectuons unfit global des observables mésurées récemment par l’expérience Ams-02(c’est à dire les flux de e± et leur rapport) sous l’hypothèse que tous lesélectrons et les positrons sont émis par des sources astrophysiques tellesque les Pulsar Wind Nebulæ et les Supernova Remnants ou à travers lescollisions des rayons cosmiques primaires avec le milieu interstellaire,dans le but de déterminer si une contribution de la matière noire estnécessaire pour expliquer les résultats des mésures.

Au cours de notre analyse, un rôle très important est joué par lesmécanismes de propagation des particules que nous étudions dans lemilieu interstellaire et dans l’héliosphère. C’est pour cela qu’une partieimportante de cette thèse est dediée à la description des différents as-pects de ces phénomènes, avec un accent sur l’impact qu’ils ont sur nosrésultats.

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The results that are illustrated in the Chapters 3, 4 and 5 of this thesishave been originally presented in the following peer-reviewed publica-tions:

[1] A. Vittino, N. Fornengo, L. Maccione,“Dark matter searches with cosmic antideuterons: statusand perspectives”,JCAP 09 (2013) 031, [arXiv:1306.4171]

[2] A. Vittino, N. Fornengo, L. Maccione,“Constraints on particle dark matter from cosmic-ray an-tiprotons”,JCAP 04 (2014) 003, [arXiv:1312.3579]

[3] M. Cirelli, N. Fornengo, M. Taoso, A. Vittino,“Anti-helium from dark matter annihilations”,JHEP 08 (2014) 009, [arXiv:1401.4017]

[4] M. Di Mauro, F. Donato, N. Fornengo, R. Lineros, A. Vittino,“Interpretation of AMS-02 electrons and positrons data”,JCAP 04 (2014) 006, [arXiv:1402.0321]

and in the following conference proceedings:

[1] A. Vittino, N. Fornengo, L. Maccione,“Perspectives of dark matter searches with antideuterons”,Proceedings of RICAP - 2013, Roma, Italy, 22 - 24 May 2013,Nucl.Instrum.Meth. A742 (2014) 145-148, [arXiv:1308.4848]

[2] A. Vittino, N. Fornengo, L. Maccione,“The role of antiprotons and antideuterons in dark matterindirect detection”,Proceedings of the 14th ICATPP Conference, Como, Italy, 23-27September 2013, Astroparticle, Particle, Space Physics and Detec-tors for Physics Applications, 225-229 (Ed. World Scientific)

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http://arxiv.org/abs/1306.4171http://arxiv.org/abs/1312.3579http://arxiv.org/abs/1401.4017http://arxiv.org/abs/1402.0321http://arxiv.org/abs/1308.4848

Acknowledgements

I owe my deepest gratitude to my supervisors, Nicolao Fornengo andMarco Cirelli, for their constant support and invaluable help through-out these years. Without their endless patience and encouragement thisthesis would never have existed. Working with them has been an in-credibly enriching experience in both scientific and human terms.

Special thanks go to all the people that have contributed to the workspresented in this thesis: Luca Maccione, Marco Taoso, Fiorenza Donato,Roberto Lineros and Mattia Di Mauro. Collaborating with them hasbeen a real pleasure and has provided me a wonderful opportunity togrow as a scientist. In particular, I thank Mattia, who has been my clos-est companion throughout my PhD, for being not only an indefatigablecollaborator, but also a true friend.

I will be forever indebted to the IDAPP program for giving me theopportunity to spend six wonderful months in Paris. In particular, Ithank Alessandra Tonazzo for her invaluable help with the bureaucracyof this joint PhD. In this regard, I also acknowledge the support fromSylvie Le Houëzec of Paris-7 and from Catherine Cataldi of IPhT. Also,I am extremely thankful to the people at ScienceAccueil, who providedme such a wonderful help in finding an accomodation in Paris.

I wish to express my deep gratitude to the whole BSM and Cosmol-ogy groups at the IPhT. I consider myself very lucky to have had theopportunity to work in such an interesting and exciting environment.In particular, I am thankful to Marco Taoso, Filippo Sala and GaëlleGiesen: without them my stay in Saclay would not have been such abeautiful and enriching experience.

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I am very thankful to Georg Raffelt and Michael Kachelriess, who havevery kindly accepted to refer this work. I also thank Andrii Neronov,Dieter Horns, Pasquale Serpico and Fiorenza Donato who will attendmy thesis defence.

Warm thanks go to all the PhD students, postdocs, friends that havebeen part of the life of our underground office in Torino: Giulio, Ana,Cristiano, Marghe, Andrea, Irene, Mezzas, XXVIB, Paolo, Gianluca,Stefano, Roberto, Mark, Luca, Sofiane (one day, my friend, we will fin-ish our project!). They have made life in an underground bunker notonly bearable, but also enjoyable!

On the personal side, words cannot express the gratitude that I oweto my family for supporting and encouraging me in all of my endeavors.

Lastly, above all, I would like to thank Antonella for her endless loveand for keeping me sane even in my darkest hours. I owe you everything!

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Contents

1 The Dark Matter problem 191.1 The standard cosmological model: a minimal introduction 201.2 Gravitational evidences for the existence of Dark Matter 23

1.2.1 Oort and the stellar motion . . . . . . . . . . . . 231.2.2 Virial theorem and clusters dynamics . . . . . . . 231.2.3 Rotation curves of spiral galaxies . . . . . . . . . 241.2.4 Gravitational lensing and Bullet cluster . . . . . . 25

1.3 Dark Matter Properties . . . . . . . . . . . . . . . . . . . 261.4 Dark Matter candidates and production mechanisms . . 28

1.4.1 Dark Matter candidates . . . . . . . . . . . . . . 281.4.2 The Standard Model of particle physics and its

problems . . . . . . . . . . . . . . . . . . . . . . . 291.4.3 Production mechanisms for each DM candidate . 33

1.5 Detection of WIMPs . . . . . . . . . . . . . . . . . . . . 381.5.1 Direct detection . . . . . . . . . . . . . . . . . . . 391.5.2 Searches at colliders . . . . . . . . . . . . . . . . 451.5.3 Indirect detection . . . . . . . . . . . . . . . . . . 48

2 Charged cosmic rays 572.1 Charged cosmic rays: an introduction . . . . . . . . . . . 57

2.1.1 A bit of history . . . . . . . . . . . . . . . . . . . 572.1.2 CR spectrum, origin and composition . . . . . . . 60

2.2 CRs propagation in the Galaxy: the diffusion equation . 612.2.1 The spatial diffusion coefficient K . . . . . . . . . 622.2.2 The convective velocity ~vc . . . . . . . . . . . . . 632.2.3 Energy losses . . . . . . . . . . . . . . . . . . . . 632.2.4 The momentum diffusion coefficient Kpp . . . . . 64

15

CONTENTS

2.2.5 The source term Q . . . . . . . . . . . . . . . . . 642.2.6 The destruction term D . . . . . . . . . . . . . . 67

2.3 Analytical solution of the transport equation . . . . . . . 682.3.1 The case of antiprotons and anti-nuclei . . . . . . 692.3.2 The case of positrons . . . . . . . . . . . . . . . . 71

2.4 Solar modulation . . . . . . . . . . . . . . . . . . . . . . 752.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . 752.4.2 General formalism . . . . . . . . . . . . . . . . . 772.4.3 The force-field approximation . . . . . . . . . . . 772.4.4 Numerical methods . . . . . . . . . . . . . . . . . 80

3 Dark Matter searches with antiprotons 853.1 Signal and background fluxes . . . . . . . . . . . . . . . 863.2 Statistical analysis . . . . . . . . . . . . . . . . . . . . . 903.3 Bounds from Pamela . . . . . . . . . . . . . . . . . . . 923.4 Prospects for the Ams-02 experiment . . . . . . . . . . . 973.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . 100

4 Dark Matter searches with anti-nuclei 1014.1 Anti-deuteron production in Dark Matter annihilation . . 101

4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . 1014.1.2 The coalescence mechanism . . . . . . . . . . . . 1034.1.3 Different coalescence models . . . . . . . . . . . . 1054.1.4 Tuning of the coalescence momentum . . . . . . . 1084.1.5 Issues of the MC model . . . . . . . . . . . . . . 1094.1.6 Injection spectra and differences between the co-

alescence models . . . . . . . . . . . . . . . . . . 1124.2 Anti-helium production in Dark Matter annihilations . . 115

4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . 1154.2.2 The coalescence mechanism for three anti-nucleons 115

4.3 Propagation mechanisms in the Galaxy and in the helio-sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.4 Astrophysical backgrounds . . . . . . . . . . . . . . . . . 1194.4.1 Anti-deuteron background . . . . . . . . . . . . . 1194.4.2 Anti-Helium background . . . . . . . . . . . . . . 120

4.5 Prospects for DM detection with anti-deuterons . . . . . 1224.5.1 Anti-deuteron interstellar and top-of-atmosphere

fluxes . . . . . . . . . . . . . . . . . . . . . . . . 122

16

CONTENTS

4.5.2 Number of expected events . . . . . . . . . . . . . 1264.6 Prospects of DM detection with anti-Helium . . . . . . . 1294.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . 131

5 The origin of galactic positrons 1395.1 Primary Astrophysical Sources . . . . . . . . . . . . . . . 140

5.1.1 Supernova Remnants . . . . . . . . . . . . . . . . 1405.1.2 Pulsar Wind Nebulae . . . . . . . . . . . . . . . . 142

5.2 Secondary component . . . . . . . . . . . . . . . . . . . . 1445.3 Galactic propagation and solar modulation . . . . . . . . 1455.4 Fit to Ams-02 data . . . . . . . . . . . . . . . . . . . . . 146

5.4.1 Global fit . . . . . . . . . . . . . . . . . . . . . . 1465.4.2 Secondary positrons: can we disfavor the Min and

Max propagation models? . . . . . . . . . . . . . 1495.4.3 A look at the PWNe cut-off energy . . . . . . . . 1505.4.4 A deeper look at the PWNe contribution . . . . . 152

5.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . 1605.6 An update . . . . . . . . . . . . . . . . . . . . . . . . . . 160

6 Conclusions 163

Appendices

Appendix A Energy losses 169A.1 Energy losses for CR nucleons . . . . . . . . . . . . . . . 169

A.1.1 Coulomb interactions . . . . . . . . . . . . . . . . 169A.1.2 Ionization . . . . . . . . . . . . . . . . . . . . . . 170A.1.3 Convection and reacceleration . . . . . . . . . . . 170

A.2 Energy losses for CR leptons . . . . . . . . . . . . . . . . 171A.2.1 Ionization . . . . . . . . . . . . . . . . . . . . . . 171A.2.2 Bremsstrahlung . . . . . . . . . . . . . . . . . . . 171A.2.3 Synchrotron emission . . . . . . . . . . . . . . . . 172A.2.4 Inverse Compton scatterings . . . . . . . . . . . . 172

Appendix B Cross sections for CRs production and prop-agation 175B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 175B.2 Production cross sections . . . . . . . . . . . . . . . . . . 176

B.2.1 Antiprotons . . . . . . . . . . . . . . . . . . . . . 176

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CONTENTS

B.2.2 Anti-nuclei . . . . . . . . . . . . . . . . . . . . . . 178B.2.3 Positrons . . . . . . . . . . . . . . . . . . . . . . 178

B.3 Annihilation cross sections . . . . . . . . . . . . . . . . . 179B.3.1 Antiprotons . . . . . . . . . . . . . . . . . . . . . 179

B.4 Anti-nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . 179

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Chapter 1

The Dark Matter problem

Light thinks it travels faster thananything but it is wrong. No matterhow fast light travels, it finds thedarkness has always got there first,and is waiting for it.

— Terry Pratchett, Reaper Man

In this chapter the issue of Dark Matter will be investigated under thepoint of view of cosmology, astrophysics and particle physics. Its role inthe standard cosmological model will be sketched in Section 1.1, whilethe gravitational evidences for its existence will be listed and describedin Section 1.2. Section 1.3 will be devoted to the study of its prop-erties in relation to astrophysical and cosmological observations, whilein Section 1.4 we will try to understand how the issues that affect thestandard model of particle physics can provide possible hints to solve itsmystery: to this purpose, we will analyse the motivations and the pro-duction mechanisms for some representative examples of Dark Mattercandidates that arise in different theories beyond the standard model.Lastly, in Section 1.5.1, we describe in detail the different ways in whicha particular type of Dark Matter candidates, the so-called WIMPs, canbe detected.

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1.1. THE STANDARD COSMOLOGICAL MODEL: A MINIMAL INTRODUCTION

Figure 1.1: Taken from [3]. The velocity of distant galaxies (units should be km s−1)as a function of their distance from the observer.

1.1. The standard cosmological model: a minimal

introduction

The starting point when building a cosmological model (a theoreticalframework to describe the evolution of the Universe) is represented bythe well-known Einstein equation:

Rµν −1

2Rgµν =

8πGNc4

Tµν + Λgµν (1.1)

This equation relates the geometry of the Universe (expressed throughthe Ricci tensor Rµν, the Ricci scalar R and the metric tensor gµν) toits energy content (which is described by the energy-momentum tensorTµν). The quantity Λ, known as cosmological constant, has been origi-nally introduced to take into account the accelerated expansion of theUniverse.

Another element that has to be considered in the construction ofa cosmological model is represented by the symmetries of the Universe,which can be extremely useful when solving Einstein equation. In partic-ular, a standard hypothesis consists in picturing the Universe as isotropi-cal and homogenous. These two assumptions, which usually go togetherunder the name of cosmological principle, have been probed and con-firmed to a very large extent by measurements of the Cosmic MicrowaveBackground (CMB) [1] and by galaxy surveys [2].

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CHAPTER 1. THE DARK MATTER PROBLEM

The cosmological principle dictates the geometry of the Universe,which can only be described by the Friedmann-Robertson-Walker (FRW)metric, whose line element can be written, in the frame of the comovingcoordinates (t, r, θ, φ), as:

ds2 = − dt2 + a(t)[

dr2

1− kr2+ r2(dθ2 + sin2φ2)

](1.2)

where the spatial curvature parameter k can assume the values -1,0,1for, respectively, an open, flat or closed universe, while the quantitya(t), which is called cosmological scale factor, is introduced to take intoaccount the expansion of the Universe. This phenomenon, firstly de-scribed by Hubble [3], consists in the fact that, apart from a handful ofnear stars and galaxies, the radiation emitted by astrophysical sources ismeasured to be, on average, redshifted proportionally to their distancesfrom Earth. Since redshift is a manifestation of the Doppler effect, alarger redshift corresponds to a larger velocity of the emitting objectand therefore, as shown in Fig. 1.1, the further a galaxy is from theobserver, the faster it moves, compatibly with an expanding Universe.This observation is described by the very popular Hubble law :

v = H0d (1.3)

where the quantity H0 = (67.4 ± 1.4) km s−1 Mpc−1 [1] is the Hubbleconstant. If it is expressed in units of 100 km s−1 Mpc−1, as it oftenoccurs, it is called reduced Hubble constant and denoted by h.

The evolution of the scale factor with time is given by Friedmannequations, which can be found by rephrasing Einstein equation for theFRW metric:

H2(t) =

(ȧ

a

)2=

8πGN3

ρ− ka2

+Λ

3(1.4)

ä

a= − 4πGN

3(ρ+ 3p) +

Λ

3(1.5)

The function H(t) is called Hubble parameter (its present value is theHubble constant H0 of Eq. (1.3)), ρ is the total energy density (matterplus radiation) and p is the pressure of the fluid. In a universe in which

21

1.1. THE STANDARD COSMOLOGICAL MODEL: A MINIMAL INTRODUCTION

k = 0 and Λ = 0 (which usually goes under the name of Einstein-DeSitter universe), the energy density acquires its critical value:

ρc(t) =3H2(t)

8πGN(1.6)

We can use this critical density to express the abundance of eachcomponent i that constitutes the Universe in terms of the dimensionlessvariable:

Ωi =ρiρc

(1.7)

By plugging Eq. (1.7) into the Friedmann equation (1.4), one obtains:

(Ωtot − 1)H2(t) =k

a2(t)(1.8)

where Ωtot =∑

i=m,r,λ Ωi and the labels (m, r, λ) denote, respectively,matter, radiation and dark energy. The dark energy density is definedas Ωλ = Λ/3H

2, while Ωm is given by the sum of the baryonic matterdensity Ωb and the non-baryonic matter density Ωnb. From Eq. (1.8) wecan derive that, in the case of a flat universe (k = 0), we have Ωtot = 1.There are various ways to measure the abundancies Ωi: for example,by analysing the position and relative heights of the peaks in the CMBanisotropies power spectrum measured recently by the Planck Col-laboration [1], one gets for the baryonic abundance the value Ωbh

2 =0.02207± 0.00033 which is much smaller than the total matter densitythat is Ωmh

2 = 0.1423± 0.0029 and this can be seen as a compelling ev-idence in favor of the existence of non-baryonic matter in the Universe.If one considers other cosmological measurements that are strongly af-fected by the values of the parameters Ωi, namely the abundancies oflight elements produced in the primordial nucleosynthesis (BBN) [4], thebaryonic acoustic oscillations (BAO) [5] or Supernova data (SNe) [6], theneed for a large amount of non-baryonic matter finds a further confir-mation.

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1.2. Gravitational evidences for the existence of Dark

Matter

In addition to the cosmological measurements that have been brieflymentioned in the previous Section, a certain amount of gravitationalevidences for the existence of non-baryonic DM in the Universe can befound. The purpose of this Section, that follows quite closely Ref. [7],is to give a brief overview of these observational hints.

One element that is worth noticing is that all these evidences, whichconsist in discrepancies between astrophysical or cosmological observa-tions with respect to theoretical predictions, are purely gravitational;in other words, particle DM has evaded any non-gravitational detectionconceived until now. This has led part of the community to propose avery different way to explain some of these evidences, in terms of theo-ries involving Modifications to the Newtonian Dynamics (MOND). Evenif this kind of approach will not be discussed in this thesis, the readermust always keep in mind that alternatives to the particle DM scenarioexist and an open-minded attitude should always be maintained.

1.2.1. Oort and the stellar motion

The first hint of DM was found in 1932 by the dutch astronomer JanOort [8], who studied the motion of stars in the galactic neighbour-hood: he derived the velocity of stars moving close to the galactic planethrough the measurement of their Doppler shifts. He then inferred theirgravitational potential from their density and their velocities by meansof a thermodynamical approach and he found that this potential wasnot sufficient to keep the stars bound together, thus demanding for thepresence of DM in our Galaxy.

1.2.2. Virial theorem and clusters dynamics

Given a relaxed1 system of elements that interact with a potential pro-portional to 1/r (being r the generic inter-particle distance), the virialtheorem is a simple law that relates the average over time of its total

1A system is relaxed if it has reached an equilibrium in which the velocity distribution of itsconstituents is not altered by collisions that occur among them.

23

1.2. GRAVITATIONAL EVIDENCES FOR THE EXISTENCE OF DARK MATTER

Figure 1.2: Rotation curve of the spiral galaxy NGC3198, taken from [11].

kinetic and potential energies by stating that:

2〈Ekin〉 = −〈Epot〉 (1.9)

The first evidence of DM found by applying the virial theorem datesback to 1933 [9], when Fritz Zwicky measured the velocity of the galaxiesinside the Coma Cluster, together with the radius of the cluster itself(determined from the volume occupied by the galaxies). From theseobservations and by means of the virial theorem, Zwicky inferred themass of the Coma Cluster to be about 400 times greater than the valuethat was expected from the cluster luminosity and therefore he was ledto the conclusion that the majority of the mass of the Coma Clusterhad to be dark.

1.2.3. Rotation curves of spiral galaxies

In spiral galaxies, the velocity of a star that rotates around the center ata distance r, outside of the internal bulge (inside the bulge, motion is notexpected to be Keplerian), can be inferred by requiring its centrifugalacceleration to be equal to the gravitational pull:

v2

r=

GM(r)

r2→ v(r) =

√GM(r)

r(1.10)

24


being M(r) the mass of the portion of the galaxy comprised within aradius r from the galactic center. Therefore, one should expect for thevelocity profile of the galaxy a v(r) ∝ r−1/2 behaviour. As first notedby Vera Rubin and collaborators, this prediction is in strong disagree-ment with observations which usually show a velocity curve that, afterreaching a peak, stays constant while the distance r increases [10, 11],as illustrated in Fig. 1.2. This behaviour can be considered as a stronghint for the existence of a non-luminous matter halo in which galaxiesare embedded.

1.2.4. Gravitational lensing and Bullet cluster

As clear from the Einstein equation (1.1), a fundamental prediction ofgeneral relativity is that the presence of matter has the power to curvespace-time; therefore light, that propagates along the geodesics of thespace-time manifold, is deflected by the presence of matter. This mech-anism is usually called gravitational lensing. Depending on the positionof the source (the object that emits the light) and the mass of the lens(the object that deflects the light), we can be in the strong or weaklensing regime.

In the strong lensing regime, the lens is very massive and close to thesource and thus we have the maximal bending of light and the observerwill see multiple images of the source (this basically happens because, asa result of the strong deformation of the space-time, there is more thanone null geodesic connecting the source to the observer). The stronglensing is usually used to map the mass distribution on not-so-largescales: for example, it has been exploited to measure a mass-to-lightratio of approximately 300 in the Abell370 cluster [12, 13].

Whenever the mass of the lens is not strong enough to produce multi-ple images, we are in the weak lensing regime, in which the distortion ofthe source image can be a stretching (shear) or a magnification (conver-gence). Basically all the sources in the Universe experience weak lensingand thus this mechanism can be used to study the mass distribution onvery large scales [14,15].

A striking evidence of the existence of DM that can be inferred by

25

1.3. DARK MATTER PROPERTIES

Figure 1.3: The merging galaxy cluster 1E0657-558 in a figure taken from [16]. Col-ors indicate the temperature of the plasma from the coolest (in blue) to the hottest(in white), while the green contours indicate the mass distribution inside the clusterreconstructed through the gravitational lensing.

means of gravitational lensing comes from the observation of the 1E0657-558 system shown in Fig. 1.3, which is an example of a very rare processof clusters merging [16]. The important thing to point out is that, in thecollision between the two clusters, the gravitational potential, inferredfrom weak and strong lensing, does not trace the plasma distribution,which is where all the baryons are and that can be inferred from X-rayemission. This means that the center of mass of the system does notcorrespond to the center of the baryonic matter.

1.3. Dark Matter Properties

From cosmological and astrophysical measurements, such as the onesthat have been mentioned in the previous Sections, one can infer someproperties that a good DM candidate must have. In particular:

• DM must be stable on cosmological scales: in fact, as an ingredi-ent of the cosmological standard model, DM particles must havea lifetime greater than the present age of the Universe which is13.8 Gyr [1].

• DM must be invisible, i.e., it must be optically dark, otherwisewe would have detected it through its emission or absorption of

26


radiation. More precisely, the darkness of DM implies that its elec-troweak interactions are very weak, which means that DM parti-cles are either electrically neutral or, at least, their electric chargesand electromagnetic dipole moments must be extremely small. Adynamical consequence of this electrical neutrality is that DM par-ticles are dissipationless, which means that they cannot cool downby emitting photons. The main consequence of this property isthat DM do not collapse to the central disks of galaxies as baryonsusually do.

• DM must be collisionless : apart from interacting extremely weaklywith photons, observations such as the one concerning the bulletcluster, described in the previous Section, are strong indicationsthat DM particles do not interact, or interact very weakly, withbaryons. However, one important point to remark is that theseconstraints do not apply to self-interactions, through which DMcan wash out small scale structures in the halos or erase cusps thatcan appear at the center of galaxies.

• DM must be non-baryonic: as it was underlined in the previousSections, we can count on CMB and BBN measurements to haveprecise and independent estimates of the fraction of the total matterdensity that is represented by baryons. As it was already stated,the huge discrepancy between Ωm and Ωb demands for the presenceof a dominant non-baryonic DM component.

• DM must be non-relativistic at the time of structure formation:once that a collisionless species decouples from the plasma (mecha-nism that will be described in the next Section), it starts to streamfrom overdense to underdense regions, smoothing out, in this way,density inhomogeneities. This mechanism, known as Landau orcollisionless damping, leads to the elimination of clustering belowa scale that is known as the free streaming length which is deter-mined by the velocity of the decoupled species at the time whenperturbations start to grow, that is at the epoch of matter-radiationequality, when the temperature of the Universe is around 1 eV. Ifthe DM is relativistic at this epoch, its free streaming length is verylarge and this leads to a top-down scenario for structures forma-tion, in which clusters at small scales can be generated uniquelyby fragmentations occurring at larger scales. This prediction is in

27

1.4. DARK MATTER CANDIDATES AND PRODUCTION MECHANISMS

contrast with galaxies surveys [2] that favor a bottom-up patternfor structures formation.

1.4. Dark Matter candidates and production mech-

anisms

1.4.1. Dark Matter candidates

The problem with the DM properties listed in the previous Section isthat they do not constrain efficiently enough the vast space of possi-ble DM theories. In fact, it is not too complicated to build a particlephysics model that satisfies all the requirements listed above and canthus provide viable DM candidates. The most widely studied candi-dates, which will also be our reference DM particles in this thesis, areWeakly Interacting Massive Particles (WIMPs), which are particles witha mass around the weak scale, from the GeV to the TeV range, that in-teract at tree level with the Z and the W bosons, but not with photonsand gluons. Examples of WIMPs can arise in different theories of newphysics, such as in Supersymmetry or in Universal Extra Dimensions(UED) theories, an example being represented by Kaluza-Klein DM.In these theories, usually, the stability of the DM candidate is assuredby the introduction of discrete symmetries, such as R-parity in Super-symmetry or KK-parity in UED theories, that prevents it from decaying.

Apart from WIMPs, which have gathered the majority of the com-munity interest in these last decades, the list of good DM candidatesis long. Our goal in this Section is not to give a complete and detailedoverview of all the possible DM candidates but simply to concentrate onsome of them, by stressing the main motivations that particle physics isable to provide in favor of their existence and by describing their pro-duction mechanisms in the Early Universe.

Before moving on to the discussion, we must warn the reader thatpicturing DM in connection with the main unresolved issues in parti-cle physics is certainly tantalizing but not strictly necessary. In fact,recent years have seen a flourishing of theories inspired by a minimalattitude towards the DM mystery. These scenarios are characterisedby a straightforward approach in which extra multiplets are added to

28


the Standard Model in order to account for DM. If this multiplet is ascalar, one can for example define the so-called scalar singlet [17] andinert doublet [18] models, in which the stability of the DM candidate isusually assured by the introduction of an unbroken Z2 symmetry. Onthe other hand, as shown in Ref. [19], true minimality is achieved in thecase in which the additional field is a SU(2)L fermionic quintuplet: inthis case, in fact, the stability of the DM candidate is naturally assuredby an accidental symmetry, i.e., by the fact that decay modes consistentwith renormalizability do not exist.

1.4.2. The Standard Model of particle physics and its prob-lems

The Standard Model of particle physics (hereafter, SM) is the theorythat describes elementary particles and their interactions. This theoryhas been verified to a spectacular level of precision, in particular bycollider experiments, like Lep, Tevatron and Lhc. However, despiteits many successes, when it comes to the issue of DM, the SM fails topredict a viable candidate: in fact, the only possible DM particle in theframework of the SM is the neutrino, which, as we will see in the fol-lowing, can only account for a small fraction of the total DM abundance.

Apart from the issue of DM, there are other possible cracks in theSM building: for example, it cannot account for neutrino masses and itis plagued by some theoretical conundrums such as the gauge hierarchyproblem or the strong-CP violation. These issues have pushed a largepart of the community to look for more general theories beyond the SM.

Our purpose in this section is to see how this quest to extend the SMcan possibly shed some light to solve the DM problem. In particular,we will see that some directions that one can take when going beyondthe SM can lead to interesting DM candidates with different propertiesand different production mechanisms.

The gauge hierarchy problem and supersymmetry

One of the questions that has puzzled physicists so far regards the small-ness of the Higgs mass with respect to the Planck mass MPl. More

29


technically, the Higgs mass is given by:

m2h = m2h0 + ∆m

2h (1.11)

where mh0 is the bare mass (the mass at tree level), while the quantity∆mh represents the corrections due to diagrams in which fermions loopappear; at one loop, this quantity is:

∆m2h ≈λ2Y

16π2Λ2uv (1.12)

where λY represents the fermion Yukawa coupling terms, with λY ≈O(1) for the top quark, while the ultra-violet cutoff Λuv stands for thescale up to which the SM is assumed to be a valid description of nature.Thus, if we assume no new physics all the way up to the Planck scale,the only way in which such a small mass of the Higgs boson can beachieved is by imposing a very fine-tuned cancellation between the baremass and its one-loop corrections which seems a highly unlikely solution.

One elegant way to solve the gauge hierarchy problem is representedby supersymmetry (SUSY) [20], which consists in defining a new sym-metry realized by the operator Q that associates to every SM particle aso-called superpartner ; the particle and its superpartner have the samequantum numbers but differ in spin by a factor 1/2 :

Q|fermion〉 = |boson〉 Q|boson〉 = |fermion〉 (1.13)

Because of this difference in the spins, the contribution to the Higgs massfrom every SM particle is cancelled at all orders by the one that comesfrom its superpartner if the two particles have exactly the same mass.This obviously cannot be true since no supersymmetric partner has everbeen observed in the same mass range of SM particles: supersymmetryhas to be broken, the masses of particles and superparticles are differentand the correction to the Higgs mass becomes:

∆m2h ≈λ2Y4π2

(m2SUSY −m2SM

)ln

(ΛuvmSUSY

)(1.14)

being mSM and mSUSY the masses of the SM particle and of its super-partner, respectively. If the scale of SUSY is close to the weak scalethen ∆m2h ≈ O(1) even for Λuv ≈ MPl. If, on the contrary, the SUSYscale is higher, then we need a certain degree of fine tuning to explain

30


the small mass of the Higgs boson.

In the framework of SUSY, several DM candidates have been pro-posed: the most widely studied, which for many years has been consid-ered the archetype of a WIMP, is the lightest neutralino, a fermion whichis the lightest mass eigenstate composed by a mixture of bino B̃, neutralwino W̃ and neutral higgsinos H̃u and H̃d [21, 22]. Another example ofsupersymmetric WIMP is represented by the sneutrino [23, 24] whichis the scalar superpartner of neutrino. Finally, a non-WIMP candidatewith spin 3/2 is the gravitino, the superpartner of the graviton [25,26].

Neutrino masses and sterile neutrinos

SM assumes neutrinos to be massless, in order to satisfy the gauge in-variance requirements of the theory. However, the fact that neutrinooscillates can be seen as a very robust evidence that they must havemass. One possibility to give mass to neutrinos is represented by the in-troduction in the SM lagrangian LSM of right-handed majorana fermionsNα which are singlets with respect to SM interactions. The completelagrangian of the model can be written as:

L = LSM + N̄αi/∂Nα − (λNiβL̄iβφ̃ + h.c.)−1

2MαβN̄

cNβ (1.15)

where the terms λNiβ represent the neutrino Yukawa couplings, Mαβis the Majorana mass matrix and Lβ represents the leptonic doublets(β = e, µ, τ). The number of sterile neutrinos is not fixed by the sym-metries of the theory: one possibility that is often considered is to havethree of them, in analogy with the number of quarks/leptons genera-tions. The neutrino mass eigenstates, which are a mixture of left andright-handed components, can be found by diagonalizing the matrix:

m =

(0 λiβ〈φ〉

λ∗αj〈φ〉 Mαβ

)(1.16)

This matrix has two groups of eigenvalues: mν ≈ λ2/M , which areassociated to active neutrinos and are given predominantly by linearcombination of left-handed components, and MN ≈ M , that, on theother hand, correspond to the masses of sterile neutrinos defined asmixtures in which right-handed components dominate.

31


As one can easily understand, there are two ways to explain thesmallness of active neutrinos masses: the first one, that is the seesawmechanism [27], consists in assuming λ ≈ O(1) and very large M , evenat the grand unification scale; the other way consists, on the contrary,in assuming very small Yukawa couplings thus enabling for light sterileneutrinos, which can represent good DM candidates. In particular, ifM is at the EW scale, we are in the so-called νMSM framework [28,29]in which the sterile neutrino is a particle in the O(10) keV range andinteresting links can be established between DM and baryogenesis [29].

The strong-CP problem and the QCD axion

The QCD part of the SM lagrangian contains the term:

θQCDg2

32π2GaµνG̃aµν (1.17)

where G is the gluon field strength, g is the strong interactions couplingand θQCD is defined as:

θQCD = θQCD + arg(det(Mq)) (1.18)

being Mq the quark mass matrix and θQCD the QCD phase. This termcontributes to observables, such as the electric dipole moment of theneutron, that are CP-violating. The fact that these observables areheavily constrained implies the very strong bound θQCD < 10

−10 [30].This strong limit has no plausible explanations in the SM context.One suggestive way of solving this problem has been suggested by Pecceiand Quinn in [31, 32]: they postulated a new U(1)PQ global symmetrythat must be spontaneously broken. The Nambu-Goldstone boson as-sociated to the breaking of U(1)PQ is the axion a. One can show thatbecause of the presence of the axion field, the following term appear inthe lagrangian:

caa

fa

g2

32π2GaµνG̃aµν (1.19)

where ca is a constant and fa is the scale at which U(1)PQ is broken.This term and the one in Eq. (1.17) represent a potential for the axionthat vanishes when:

a → 〈a〉 = − θQCDfaca

(1.20)

32


and, concerning the CP-violating term, we have:

θQCD → θQCD +ca〈a〉fa→ 0 (1.21)

Besides representing a very clever way to evade the strong-CP prob-lem, axions represent also a good DM candidate.

1.4.3. Production mechanisms for each DM candidate

The case of WIMPs: thermal freeze-out

The standard scenario of WIMP production assumes that, for a largepart of the Universe early history, WIMPs were kept in thermal equilib-rium with the other constituents of the thermal bath through particle-antiparticle collisions such as:

DMDM↔ XX̄ (1.22)

where X denotes every particle of the bath apart from the DM ones.We assume that there is no asymmetry between DM and DM. As longas DM is in thermal equilibrium with the rest of the thermal bath, thecommon rate for the DM production and the annihilation processes is:

Γ = 〈σannv〉neq (1.23)

where σann is the DM pair annihilation cross section, v is the relativevelocity of the annihilating WIMPs, neq denotes the number density ofWIMPs in thermal equilibrium and the brackets represent the averagingover the WIMP thermal distribution. As a rough criterion, we canassume that DM particles are in thermal equilibrium with the plasmaof the early Universe as long as:

Γ & H (1.24)

where H is the Hubble rate, already seen in Section 1.1, that denotesthe velocity at which the Universe expands. As the Universe expands,Γ becomes smaller since particles are more and more diluted. At thefreeze-out temperature Tf , Γ = H and after that moment, WIMPs aredecoupled, which means that:

Γ . H (1.25)

33


i.e. the Universe has expanded to a point in which DM is so diluted thatthe pair annihilation and pair production processes are no more efficientenough and the WIMPs number density simply scales as a(T )−3, beinga(T ) the Universe scale factor introduced in Section 1.1 (in other words,the number of DM particles per comoving volume remains constant).

To get a more quantitative information about the freeze-out mech-anism, we can address to the Boltzmann equation which describes theevolution of the WIMPs number density n (we are assuming that DMhas no chemical potential):

dn

dt= −3Hn− 〈σannv〉(n2 − n2eq) (1.26)

The term 3Hn accounts for the dilution due to the expansion ofthe Universe, while the second term 〈σannv〉n2 represents the rate atwhich WIMPs undergo pair annihilation processes and the third term〈σannv〉n2eq corresponds to the rate of WIMPs pair production in the XX̄annihilation process. As one can derive from statistical mechanics, thenumber density of a particle species with mass m in thermal equilibriumwith a thermal bath characterized by a temperature T is:{

neq ≈ T 3 m� T relativistic limitneq ≈ (mT )3/2e−m/T m� T non−relativistic limit

(1.27)

The present value of the relic density of a species can be found bysolving the Boltzmann equation. For a detailed description of the calcu-lation we address the reader to Ref. [33]. The evolution of the comovingnumber density of a species, and the dependence of the relic density on〈σannv〉 are shown in Fig. 1.4.

Obviously, the relic density will be affected by the time at which thedecoupling takes place; for a hot relic, which is a species that decoupleswhen it is relativistic (m� Tf), the relic density is:

Ωh2 = 7.83× 10−2[geff/g∗s(Tf)](m/eV) (1.28)

34


Figure 1.4: Taken from Ref. [34]. Comoving number density of a species as a function oftime. Solid line refers to a species in thermal equilibrium, while dashed lines denote thenumber density after the freeze-out (different lines are for different values of 〈σannv〉).

where geff = g if the species is a boson or geff = (3/4)g if it is a fermion,being g the number of degrees of freedom, while:

g∗s =∑

i=bosons

gi

(TiT

)3+

7

8

∑i=fermions

gi

(TiT

)3(1.29)

If we consider the case of a neutrino species, its density as a hot relicis:

Ωνν̄ =mν

91.5 eV(1.30)

The requirement that the neutrino relic density is less than the DMdensity gives a rather weak bound on the neutrino mass, as found byGershtein and Zeldovich in Ref. [35]. Anyway, the current bounds onneutrino masses, e.g.

∑νmν ≤ 0.39 eV found in Ref. [36] by a joint

analysis of Planck and WMAP measurements, are too strong to allow

35


SM neutrinos to account for more than a negligible part of the total DM.

On the other hand, a species that decouples in the non-relativisticregime is known as cold relic. Its density can be written as:

ΩDMh2 ≈ 1.07× 10

9 GeV−1

Mpl

xDM,f√g∗(xDM,f)

1

〈σannv〉f≈ 3× 10

−27cm3 s−1

〈σv〉(1.31)

where the subscript f denote quantities evaluated at the freeze-outand xDM,f = mDM/Tf . As one can notice, the annihilation cross sec-tion for which the relic density happens to be in the right ballpark is〈σannv〉 = 3 × 10−26 cm3 s−1, usually called thermal cross section. Thisvalue of the cross section naturally occurs in the case of WIMPs andthis, some years ago, gave rise to the term WIMP miracle. Anyway as ithas been shown for example in Ref. [37], the correct relic density is notpeculiar only of the electroweak scale: a WIMPless miracle is possible.We remark, at this point, a small caveat: the picture of the freeze-outmechanism that we have sketched here ignores some complications thatcan occur when dealing with real particle physics models: as an exem-ple, we mention resonances, thresholds and co-annihilations which aredescribed in detail in Ref. [38].

For completeness, we can consider the scenario in which the DM par-ticle under consideration is a SuperWIMP(SWIMP) [25], i.e., a particlethat is much less interacting than a WIMP, as it can be the case forgravitinos or axinos. These particles can be produced by the decay ofWIMPs after the freeze-out. If we assume that every WIMP producesexactly one SWIMP, the SWIMP relic density is given by:

ΩSWIMP =mSWIMPmWIMP

ΩWIMP (1.32)

One point that is worth noticing about SWIMPs is that their progenitordoes not necessarily need to be neutral: in fact, they can also be pro-duced by charged particles, as long as they have the right abundance;for example, in the case of SUSY, a SWIMP such as the gravitino canbe the result of the decay of a charged slepton or a chargino.

Lastly, another class of particles that are much more weakly interact-ing than WIMPs is represented by Feebly Interacting Massive Particles

36


(FIMPs) [39]. They can be produced through the so-called freeze-inmechanism: in this scenario the FIMP χ of mass m is not in equilib-rium with the thermal bath because of its feeble interactions. Its initiallynegligible abundance2 is increased by occasional collisions or decays ofparticles living in the thermal bath, with the peak of this productionprocesses taking place when the temperature of the Universe T dropsbelow m. The abundance of χ then remains constant (“freezes-in”)as a result of the fact that the production rate for smaller tempera-tures becomes suppressed. This occurs because the particles in the baththat can take part in the FIMP production processes are the ones withmasses M > T , which are non-relativistic particles whose abundance issuppressed.

Production mechanisms for sterile neutrinos

As discussed in detail in Ref. [40], the easiest way to produce sterile neu-trinos is through the so-called Dodelson-Widrow (DW) mechanism [41].The idea is very simple: basically, as seen in Section 1.4.2, sterile neu-trinos are not completely sterile, but are defined as mixtures that con-tain a small active component; the key point at the base of the DWmechanism is that active neutrinos can be produced easily in the EarlyUniverse plasma and this mechanism can build up a small quantity ofsterile neutrinos thanks to the active-sterile mixture. Then, their inter-actions are so small that they do not annihilate again.

From the constraints that can be derived by looking for imprints ofthe N → νγ reaction in the X-ray band [42], we know that the DWmechanism is not sufficient to provide the right amount of sterile neu-trinos that compose all the DM of the Universe. Anyway, some othermechanisms can give their contribution: for example, in the case of alepton-antilepton asymmetry in the Early Universe, we can have the so-called Shi-Fuller (SF) mechanism [43]. Without entering into too muchdetail, the idea is that in an environment with such an asymmetry, therecan be a situation similar to the MSW effect in matter, which meansthat it may exist a temperature of the plasma for which active-steriletransitions could be resonant and, thus, enhanced.

2As explained in Ref. [39], the smallness of the initial FIMP abundance is a necessary conditionfor the freeze-in condition to work. A way to make it negligible can be, for example, inflation.

37

1.5. DETECTION OF WIMPS

Another possibility is that sterile neutrinos, like superWIMPs, canbe the result of the decay of a heavier particle, in particular a scalarsinglet (that can also be the inflaton as seen in Ref. [44]).Finally, sterile neutrinos can be produced in a quasi-traditional freeze-out mechanism if we consider that they can be not sterile at all undera gauge group larger than the SM, that breaks down to the SM at acertain temperature.

Production mechanisms for axions

Apart from being produced thermally with the freeze-out mechanisms,axions can be produced non-thermally by a mechanism known as vac-uum re-alignment (for a review, see Ref. [45]). The main idea is that,while today we expect θQCD = 0 to conserve CP, in the Early Universe,i.e. at a temperature T for which TPQ > T > ΛQCD, axions are charac-terised by random initial states and there are no reasons to expect θQCDto be zero: in fact, at such a temperature, the Peccei Quinn symmetry isalready broken and the axion field has acquired a vacuum expectationvalue, but T is still above the QCD energy scale. Therefore, we saythat the axion field is misaligned with respect to the minimum of itspotential θQCD = 0.

When the temperature of the Universe reaches the QCD energy scaleΛQCD, non-perturbative instanton effects become important and gen-erate an effective potential whose curvature at the minimum assignsa temperature-dependent mass to the axion field: in practice, the ax-ion field starts to roll around the minimum of this effective potential(which obviously is θQCD = 0, in order to solve the strong-CP problem)and these oscillations correspond to a zero-momentum, therefore deeplynon-relativistic, axion condensate that fills the Universe. In this wayaxions are a cold DM candidate despite their very small mass.

1.5. Detection of WIMPs

Among the DM candidates that we have briefly illustrated in the previ-ous Section, we single out here the case of cold WIMPs, which will bethe central focus of all the investigations that will be conducted in therest of the thesis.

38


Figure 1.5: Taken from Ref. [48]. Current (as of January 2014) limits on WIMP-nucleon spin independent scattering cross section, together with perspectives for futureexperiments and predictions from some theoretical models.

In particular, this Section will be devoted to a very brief sketch ofthe techniques that can be adopted to detect WIMPs: Section 1.5.1 de-scribes direct detection, while Sections 1.5.2 and 1.5.3 provide an outlineof the perspectives offered respectively by collider searches and indirectdetection with photons, neutrinos and cosmological measurements. Asalready remarked, indirect searches with charged cosmic rays, that rep-resent the core of the thesis, will be analysed in excruciating detail inChapters 3, 4 and 5.

1.5.1. Direct detection

The idea behind DM direct detection [46] is that WIMPs can be visiblethrough their scatterings off SM particles. From N-body simulations, weknow that the velocity of DM in the Earth vicinity is around 200 km s−1

and therefore these scatterings occur always in a deeply non-relativisticregime, similarly to the collision between two billiard balls.

The differential event rate for the scattering of a DM particle against

39


Figure 1.6: Taken from Ref. [48]. Current (as of January 2014) limits on WIMP-neutron (left panel) and WIMP-proton (right panel) spin dependent scattering crosssections.

a nucleus N can be written as [47]:

dR

dER=

ρ0mDMmN

∫ ∞vmin

vf(v)dσDM,NdER

(ER, v)dv (1.33)

being ρ0 the local DM density, f(v) the DM velocity distribution inthe detector frame and dσDM,N/dER the cross section for the scatteringprocess. The lower bound of the integral, labeled vmin, is defined asthe minimal velocity that the WIMP must have in order to make thenucleus recoil with the energy ER:

vmin =

√mNER2µ2N

(1.34)

where the quantity µN is the reduced mass of the WIMP-nucleus sys-tem: µN = mDMmN/(mDM +mN), while the cross section dσDM,N/dERcan be defined as the sum of a spin independent and a spin dependentcomponent:

dσDM,NdER

=

(dσDM,NdER

)SI

+

(dσDM,NdER

)SD

(1.35)

If the dependence from ER and v is made explicit, one can obtain :(dσDM,NdER

)SI,SD

=mN

2µ2Nv2σSI,SD0 F

2SI,SD(ER) (1.36)

where σSI,SD0 , that are usually the quantities in terms of which directdetection constraints, like the ones shown in Figs. 1.5 and 1.6, are ex-

40


Figure 1.7: From Ref. [50]. All the most relevant direct detection experiments groupedby the detection technique that they use.

pressed, represent the cross sections for the zero transferred momen-tum case while the functions FSI,SD(ER) are the form factors that en-code the dependence of the cross sections on the transferred momentumq =√

2mNER.

The key element of the direct detection technique is represented bythe discrimination between the DM signal, which, typically, has an ex-pected interaction rate below 1 event per 10 kg of target material perday, and the background, e.g. natural radioactivity and cosmic rays in-teractions, which is responsible for millions of events per kg per day. Theways in which this huge background can be reduced and disentangledfrom the few expected signal events are numerous and varied: first, tosuppress the scattering of neutrons with the target material, which canbe the result of a radioactive decay or have cosmic origins, direct detec-tion experiments are usually located hundreds of meters undergroundand they are usually shielded by materials that are rich in hydrogen(for example the polyethylene), which are able to reduce neutrons en-ergy to a level such that they are no more able to produce a scatteringabove the threshold. Secondly, taking advantage of the fact that WIMPsare weakly interacting and thus they are expected to interact at most

41


Figure 1.8: Taken from Ref. [51]. The annual modulation as seen by Dama andDama/Libra.

once inside the detector, direct detection experiments usually discardall the multiple scattering events. Another good technique of discrimi-nation comes from the knowledge that WIMPs must interact uniformlythroughout the detector: all the surface interactions, i.e. those interac-tions that take place at the surface of the detector, where the scatteringsdue to strongly interacting particles are more likely to happen, are dis-carded. Finally, since WIMPs are expected to interact mostly with theatoms nuclei, while all the background events, apart from those due toneutrons, are against electrons, a good way to separate the backgroundfrom the signal is represented by distinguishing between nuclear recoilsand electron recoils. We mention here, however, that, as suggestedby [49], electron recoils could be the imprint of a DM particle with amass in the sub-GeV region.

Apart from these basic techniques, each experiment operating in thedirect detection domain use a peculiar way to detect WIMP-nucleonscatterings and to suppress the background. According to the techniqueused among the ones sketched in Fig. 1.7, an experiment usually fallsinside one of these general categories:

• Threshold detectors (Simple, Coupp, Picasso): these detec-tors make use of superheated liquids (such as Freon) which are usu-ally tuned in their temperature and pressure in such a way that theenergy deposited by a nuclear recoil can cause a nucleation (whichbasically means that nuclear recoil events can form bubbles in theliquid). The advantage of threshold detectors is that they can havevery large masses without being too expensive, since they do not

42


require photon shielding or cryogenics.

• Noble liquid detectors (Lux, Xenon, Xmass, Zeplin, WArP,ArDM, Deap, MiniCLEAN): these detectors use as target a no-ble liquid, such as liquid Xenon (Lux, Xenon, Xmass, Zeplin) orliquid Argon (WArP, ArDM, Deap, MiniCLEAN). This kindof target can be ionized and subsequently scintillate when a recoiltakes place: basically, the recoil generates ionization and excitationprocesses in the liquid gas and this triggers the production of ex-cited dimers that subsequently de-excitate through the emission ofphotons with a very precise wavelength that depends on the kind ofrecoil that has originated the process. Thus, electron and nuclearrecoils can be discriminated since they produce differently shapedpulses. Noble liquids detectors are currently the most sensitive ex-periments to spin independent interactions.

• Cryogenic detectors (Texono, CoGeNT, Edelweiss, CDMS,Cresst): these detectors generally use ultrapure Germanium, keptat very low temperature, as target material. Some of these detec-tors (like Texono and CoGeNT) only measure the ionizationof the energy depositions, while others (in particular Edelweissand CDMS) can also measure the energy deposited in the form ofphonons, which are the vibrations of the crystal lattice. Measure-ments of this kind usually translate into measuring a very small (atthe level of the µK) increase in the temperature of the detector.Differently with respect to other experiments, Cresst measuresthe phonons and the scintillation light.

• Highly radiopure NaI detectors (Dama, Dama/Libra, Na-iad, Anais): these detectors make use of sodium iodine scintil-lators to detect single scattering events. They do not distinguishbetween the DM signal and the background on an event-by-eventbasis, but they take advantage of the fact that the signal is expectedto exhibit a significant annual modulation, while the backgroundis not expected to modulate. This modulation takes place becausethe velocity of the WIMPs in the Earth frame changes in the courseof the year as a result of the Earth revolution around the Sun andthus the count rate in a direct detection experiment should show apeak in June and a minimum in December.

43


Figure 1.9: Examples of constraints on SUSY parameters (in the MSSM scenario)derived by ATLAS (left panel, taken from Ref. [60]) and CMS (right panel, taken fromRef. [61].

As shown in Fig. 1.8, the Dama and Dama/Libra experimentshave seen such a modulation with a compelling evidence that nowhas reached the level of 9.3σ [52]. This effect, if interpreted interms of WIMP scattering on nuclei, is at tension with most of theconstraints found by other experiments, unless one assumes thatthe modulation is due to DM scatterings off electrons [49], in whichcase the tension is alleviated. Until now, attempts to explain themodulation effect in terms of backgrounds [53–55] have not beenconvincing [56–59]. While waiting for future developments, it is fairto consider the question of the Dama excess still open.

• Directional detectors (Newage, Mimac, Drift, DMCTP):gaseous detectors kept at a sufficiently low pressure can make therecoil tracks long enough to be imaged and thus give informationsabout the direction of the scatterings. The idea is that by knowingthe arrival direction of the scattering particles one should be able todistinguish between a DM signal and the background: in fact, thesignal is expected to be correlated with the WIMP wind, i.e. withthe motion of the Earth with respect to the galactic center, whilethe background is expected to be isotropic. Besides, directionaldetectors can provide a complete information about the WIMPvelocity distribution.

44


Figure 1.10: Taken from Ref. [63]. CMS and ATLAS constraints on DM-nucleon crosssection derived from mono-W and mono-Z searches, compared with direct detectionbounds.

1.5.2. Searches at colliders

Collider searches present different pros and cons with respect to directand indirect searches: among the advantages, the most remarkable oneis that they do not suffer from those astrophysical uncertainties, which,as we have seen in the previous Section and as we will see in the next one,usually plague direct and indirect searches. On the other hand, amongthe possible disadvantages of this detection technique, we must mentionthe fact that DM searches at a given collider can only reach DM massesbelow a certain threshold related to the center of mass energy at whichthe machine operates and thus direct and indirect searches could be theonly instrument to look for DM in these large mass regions. Another,often neglected, source of uncertainty that afflicts collider searches, isthat, given a certain potential signal, one cannot really establish if itcomes from the true DM of the Universe or from a generic other parti-cle, which is stable only on collider timescales.

Because of its extremely elusive nature, once produced in a collider,DM is expected to leave the detector unseen, its only possible signaturebeing a missing energy /E. In a lepton collider a precise measurement of/E can be carried out, since the energies of the beams are well-known,

45


while in a hadron collider only the transverse component /Et can beprecisely determined. This happens because, for this class of machines,collision processes take place at the partonic level and partons that donot participate to the reaction end up in the poorly covered forwardregion of the detector carrying with them an unknown fraction of thebeam energy.

DM searches in the framework of BSM theories

In a given SM extension, such as SUSY or UED theories, the DM can-didate usually comes with a much longer list of heavier other particles.These particles can be electromagnetically charged or coloured and thusthey are expected to interact with SM particles much more strongly thanthe WIMP itself. Therefore, when looking for DM imprints in collidermeasurements within one of these theoretical frameworks, the expectedsignatures that one should hunt for are cascade decays that start fromthese WIMP “siblings”.Considering, as an example, the case of SUSY searches at LHC, possi-ble signal events are represented by decay chains triggered by squarks orgluinos that lead to the production of both WIMPs and SM particles.Thus the final imprint of this class of reactions in the detector consistsin a mixture of jets, missing transverse energy, leptons and sometimesphotons. The exact rate of each one of these components obviously de-pend on the parameters of the theory.

The SM background for this kind of signals is represented by theevents that generate neutrinos (missing energy) plus jets: the dominantcontribution is expected to be given by W/Z + jets, tt̄ and QCD mul-tijet production. By comparing this expected background with collidermeasurements, one is able to constrain the parameter space of the the-ory under consideration, as shown, for example, in Fig. 1.9 in the caseof SUSY.

DM searches in a simplified framework

This Section, which closely follows Refs. [62, 63], is devoted to the de-scription of the approach that one has to adopt if he does not want torestrict his investigations to a particular theoretical model.

46


The basic idea is to reduce to the maximal possible extent the quan-tity of assumptions about the nature of the DM particles. The best wayto assume this point of view is to adopt the effective field theory ap-proach developed in Ref. [64]. This method is based on the assumptionthat the DM particle is the only particle outside of the SM that canbe produced at the collider. In addition, the DM field is assumed tobe odd under some Z2 symmetry, under which all the SM particles areeven; therefore any DM-SM interaction must involve an even number ofDM particles. Besides, this effective field theory approach can be fol-lowed only in the case in which the DM field in uncharged under the SMgauge group which means that no tree level couplings to gauge bosonsare allowed. Lastly, we remark that, recently, great emphasis has beenput on the validity of this method [65,66]: basically, one should alwaysremember that this approximation is correct only if the mediator of theinteraction between the DM and the SM particles is heavier than theenergy that is transferred in the interaction process. Otherwise, effectsfrom a UV-complete theory must be taken into account.

Given these premises, following Ref. [64], one can build the completelist of operators describing the interaction between the DM particle andthe hadronic sector of the SM. Then, constraints such as the ones shownin Fig. 1.10, are usually expressed by assuming the DM-nucleon inter-action to be expressed by one of those operators.

The channels in which this effective searches for DM are usually per-formed are:

• Mono-photon searches (1 photon and large /Et): the dominantbackground process in this channel is represented by Z(→ νν) + γ,but one has to consider also other possible backgrounds such asW/Z + γ and W/Z + jet final states if the jet coming from thegauge boson decay is mis-identified as a photon.

• Mono-jet searches (1 jet and large /Et): this channel has manypotential sources of backgrounds: Z → νν, W + jets, single top ortop pair production, diboson or multijet events.

• Mono-W/Z searches: in this channel, three possible final statescan be present, since gauge bosons can decay into hadronic or lep-tonic final states:

47


(i) W/Z → jet + /Et in which the dominant background processesare Z → νν + jet and W/Z + jets with decays from non-reconstructed leptons.

(ii) W → lν + /Et with backgrounds given by multijet events, top-quark, Z boson and diboson production.

(iii) Z → ll + /Et where the dominant background is given by di-boson production.

An additional channel, which is the result of a searching strategythat is different from the ones that are listed above, is represented bysearches through Higgs boson measurements. In particular, the mea-surement that is usually considered is the H → invisible branchingratio: the search for invisible decays of the Higgs is usually performedin events with a ZH final state, that can be tagged because of the de-cay of the Z boson into ll or bb̄. Another possibility is represented byevents in which the Higgs is produced through the Vector Boson Fusion(VBF) mechanism. Constraints to the invisible Higgs decay branchingratio are usually given by combining the upper limits derived from theevents mentioned above with the measurements of all the visible branch-ing ratios, such as H → γγ, H → qq, etc...

1.5.3. Indirect detection

The key point about DM indirect detection is that, after the freeze-out,WIMPs can still undergo pair annihilation reactions (even if the fre-quency of these events is sufficiently small to have practically no impacton the relic density) or decays, if they are not stable particles. Theseprocesses can lead to the production of SM particles that can be de-tected in the cosmic ray flux3 or can have had a non-negligible impacton the history of the Universe.

The purpose of this Section, which follows very closely Ref. [67] towhich we address the reader for further details, is to give a brief overviewof the main indirect detection channels except for charged cosmic rays,which will be treated in much more detail in the rest of the thesis.

3Here, as it will be manifest in the following, we adopt a general definition of cosmic rays thatinclude also neutral particles such as neutrinos and photons.

48


Figure 1.11: The two currently most discussed claims for DM detection in the gamma-ray channel. The excess at the GC, in the left panel, is taken from Ref. [75], while the130 GeV line signal that appears in the right panel is taken from Ref. [82].

Indirect detection with photons

DM annihilation or decay can lead to the production of photons eitherpromptly, i.e. directly from the annihilation or decay process itself or,in a more indirect way, as the result of the emission of DM-generatedelectrons and positrons through Inverse Compton Scattering (ICS) onambient light or synchrotron radiation when propagating across mag-netic fields.The prompt emission from an angular direction dΩ originates a differ-ential flux which can be written as [68]:

dφγdΩdE

= �r�4π

(ρ�mDM

)2J∑i

〈σv〉idN iγdE

annihilating DM

dφγdΩdE

=r�4π

ρ�mDM

J∑i

ΓidN iγdE

decaying DM

(1.37)

where the quantity dN iγ/dE represents the differential energy spectrumof the photons produced per annihilation in the i channel (i = qq̄, l+l−,etc.). The spectra for the different annihilation or decay channels aresummed after being convoluted by the quantities 〈σv〉i or Γi which repre-sent, respectively, the DM thermally averaged annihilation cross sectionand decay width for the final state i. The parameter � is a statisticalfactor that is equal to 1/2 if DM is a Majorana particle or to 1/4 if it isa Dirac particle, while the quantities r� and ρ� represent, respectively,the distance of the Earth from the center of the Galaxy and the local

49


Figure 1.12: Constraints coming from the analysis of the dwarf spheroidal emission,in the gamma-ray band (left panel, taken from Ref. [99]) and in the radio band (rightpanel, taken from [100]).

DM density. Lastly, J , which is usually called J-factor, is defined as theintegration along the line of sight of all the intervening DM: it obviouslyvaries according to the direction of the gamma-ray source that we areconsidering:

J =

∫l.o.s.

ds

r�

ρ(r(s, θ))

ρ�(1.38)

being θ the angle between the direction of the line of sight and theEarth-Galactic Center axis, while r(s, θ) =

√r2� + s

2 − 2r�s cosθ.Concerning, on the contrary, the secondary gamma-ray emission throughICS or synchrotron emission by electrons and positrons produced in DMannihilation or decay events, the spectrum is given by:

dφ

dEγdΩ=

1

Eγ

∫l.o.s.

dsj(Eγ, r(s, θ))

4π(1.39)

where the emissivity j is defined as:

j(Eγ, r) =

∫ mDM/2me

dEePICS/Sync(Eγ, Ee, r)dnedEe

(r, Ee) (1.40)

where the function PICS/Sync corresponds to the differential power emit-ted in the form of photons through ICS and synchrotron processes (weaddress the reader to Ref. [68] for their detailed expressions), while thefunction dne/dEe is the propagated electron/positron spectrum emittedby DM annihilation or decay.

50


Another secondary process that is expected to be relevant, in particu-lar for DM masses aroundO(10) GeV is represented by the bremsstrahlunginteraction of DM-generated electrons and positrons with the electro-magnetic field generated by the interstellar gas. As recently shown inRef. [69], the role of this process is not only limited in shaping the DMγ-ray spectrum, but it also involves the modification of the e± spectrum,thus affecting the subsequent emission through ICS and synchrotron.

An important thing to point out is that photons that are producedby DM annihilation or decay through different mechanisms have a dif-ferent frequency: in fact, while photons from prompt emission and ICSare in the gamma-ray band, the ones that are emitted in the form ofsynchrotron radiation from electrons/positrons with energies around theGeV/TeV scale propagating in magnetic fields with O(µG) intensities,as for the case of the Milky Way halo, are characterised by frequenciesin the MHz/GHz range, i.e. in the radio band, with the possibility toreach the X-ray band only in the case in which the DM under consider-ation is really heavy or the magnetic field is really strong, as in the caseof the Galactic Center.

Photons produced by DM annihilation or decay are expected to bemore visible in those astrophysical targets for which the density of DMis high and/or the background radiation is low. Targets with high DMdensities are, for example, the Milky Way Galactic Center (GC) or smallregions just outside it as the Galactic Ridge(GR), Globular Clusters(GloC), Dwarf spheroidal Galaxies of the Milky Way (dSph), while tar-gets in which the signal-to-noise ratio is expected to be large or, at least,the background is supposed to be better under control, are the galactichalo at high latitudes, the dSph and the whole Universe itself, which isexpected to be characterised by an isotropic flux of redshifted photon,usually defined as extragalactic flux.

The most recent claim for a DM detection in gamma rays data con-cerns the GC region [70–75], in which a significant excess over the ex-pected background has been found. This excess seems to be well com-patible with a DM particle with mass around 30-40 GeV annihilatinginto the bb̄ channel with a thermal cross section or, if also secondaryemission from DM-produced electrons (e.g. ICS and bremsstrahlung)

51


is included [76, 77], with a DM with mass around 10 GeV annihilatingdemocratically into leptons with a cross section slightly smaller thanthe thermal one. However, this DM interpretation of the excess seemsto be in a certain tension with bounds found in other channels [77, 78];also, one must consider that astrophysical explanations of the excessare possible: for example, photons can be produced by hadronic [79],or leptonic [80] populations generated in burst-like events in the pasthistory of the Galaxy.

Concerning another claim of DM detection in the GC region, a cou-ple of years ago Refs. [81] and [82] pointed out a possible line emissioncompatible with a 130 GeV DM from the GC region. This claim for aline is supported also by the template analysis of Ref. [83] and evidencefor lines have been found also from galaxy clusters in the analysis ofRef. [84]. This has stimulated a lot of model-building activity in thecommunity (as an example, see Refs. [85–89], but the complete list ismuch longer). The Fermi-LAT Collaboration has investigated the linesignal in Ref. [90], pointing out that a similar line feature can be seenalso in the low incidence angle Earth’s limb data and thus the hypoth-esis that the signal is the result of an instrumental systematic gain pace.

Lastly, in 2011, another potential hint of DM has appeared in termsof an excess in the radio measurements at frequencies ranging from 3 to90 GHz performed by the balloon-borne Arcade 2 experiment [91]. Af-ter a careful background subtraction, DM candidates compatible withthe excess are light WIMPs annihilating or decaying into leptons: inparticular, for DM particles with mass around 10 GeV a thermal an-nihilation cross section fits the data very well. Very recently, however,Ref. [92] has stressed the strong tension between these candidates andthe positron fraction measured by Ams-02.

Apart from these claims of detection, in recent years there have alsobeen plenty of analyses putting constraints on DM parameter space byusing gamma-rays data from various experiments and targets: Ref. [93]uses H.E.S.S. observations of the GC and dwarf spheroidal togetherwith radio data from the GC to constrain DM annihilation cross sec-tion, while, to pursue the same purpose, Refs. [94, 95] focus only onthe GC region. H.E.S.S. and Fermi-LAT measurements of gamma-

52


rays emitted by dwarf spheroidal lead to the constraints presented inRef. [96–99], while a very recent analysis of radio emission from dwarfspheroidals in the Local Group is carried out in Ref. [100]. These con-straints are shown in Fig. 1.12. Concerning, on the contrary, galacticdiffuse gamma-rays, analyses can be found in Refs. [101–107]; Ref. [108]presents a study in which the extragalactic gamma-ray flux, togetherwith H.E.S.S. data of the Fornax cluster emission are used to constrainthe properties of decaying DM. Finally, Refs. [109, 110] present multi-wavelength and multi-messenger analyses in which several observationsat various frequencies are used to investigate DM properties.

Indirect detection with neutrinos

Neutrinos, just like photons, have the advantage of propagating straightfrom the source to the detector, because of their very weak interactions.The way in which neutrinos are detected is however different with re-spect to gamma-rays and the choice of the targets is often limited bythe location of the detector. Imprints of DM-generated neutrinos areexpected to appear in the form of Cherenkov emission of charged par-ticles (in particular, muons) that neutrinos should produce while goingthrough the detector. As one can easily understand, the main sourceof background related to this detection technique comes from cosmicmuons that can impact the detector from above. This is why neutrinotelescopes usually select only upgoing tracks, which are those tracks thatare originated from neutrinos that have crossed the Earth.

The possible targets at which telescopes look for DM-generated neu-trinos are, just like for the gamma-rays, the GC (Icecube in Ref. [111])or the Galactic Halo (this was done, for example, by the IcecubeCollaboration in Ref. [112]) or the satellite galaxies. An interestingcase, proposed for the first time in Ref. [113, 114] and computed inRefs. [115–121], is represented by the neutrino flux produced by DMannihilation in the Sun (Icecube in Ref. [122], Antares in Ref. [123],the Baksan Underground Scintilator Telescope in Ref. [124]): the ideais that DM particles can interact with the nucleus of a massive celestialbody if this nucleus is placed along their orbits. As a result of repeatedscatterings, WIMPs velocity can be sensibly reduced and, if it happensto become lower than the escape velocity, DM particles can be trappedinside the celestial body and, as particles accumulate, a DM overdensity

53


Figure 1.13: Upper left panel: taken from Ref. [111]; bounds on 〈σv〉 derived fromIcecube neutrino searches from the GC. Upper right panel: taken from Ref. [112].Constraints on the annihilation cross section in different channels derived from theIcecube search for neutrinos from the Galactic Halo. Lower left and right panels:taken from Ref. [123], these panels show the limits imposed on the Spin Indipendent(SI) and Spin Dependent(SD) DM-nucleon cross sections by the searches for neutrinosfrom DM annihilation in the Sun by various telescopes (e.g. Icecube, Antares andBaksan).

is built. Annihilation processes that takes place in this overdense regionproduce a neutrino flux which can be written as [121]:

dφνdEν

=Γann4πd2

dNνdEν

(1.41)

where d is the Earth-Sun distance, Γann is the DM annihilation ratein the Sun and dNν/dEν is the neutrino energy differential spectrumper annihilation, after all effects, such as hadronization, energy lossesin matter and oscillations, have been taken into account. We remarkthat the same formalism can be used to compute the neutrino signalproduced by DM trapped at the center of the Earth (as discussed, forexample, in Ref. [117]).

54


Figure 1.14: Right panel: taken from Ref. [128]. Bounds on the DM annihilation crosssection into the e+e− channel as a function of the DM mass and of the � parameter,which rules the velocity-dependence of 〈σv〉 (see Ref. [128] for details). Left panel :taken from Ref. [136]. CMB constraints found using WMAP7 + ACT data on DMannihilating into muons (x signs) and electrons (diamonds signs).

In Fig. 1.13 some relevant constraints coming from the neutrino channelare shown.

Indirect detection with cosmological measurements

Constraints on DM parameter space from cosmological measurementsusually refer to phases of the history of the Universe which take placemuch later with respect to the DM freeze-out mechanism described inSection 1.4.3. Th

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