Unstable Gravitino Dark Matter Prospects for Indirect and Direct Detection
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Unstable Gravitino Dark Matter Prospects for Indirect and Direct Detection Dissertation zur Erlangung des Doktorgrades des Departments Physik der Universit¨at Hamburg vorgelegt von Michael Grefe aus L¨uneburg Hamburg 2011 Gutachter der Dissertation: Prof. Dr. Laura Covi Prof. Dr. Jan Louis Prof. Dr. Piero Ullio Gutachter der Disputation: Prof. Dr. Laura Covi Prof. Dr. Wilfried Buchm¨uller Datum der Disputation: 6. Juli 2011 Vorsitzender des Pr¨ufungsausschusses: Prof. Dr. G¨unter H. W. Sigl Vorsitzender des Promotionsausschusses: Prof. Dr. Peter H. Hauschildt Dekan der Fakult¨at f¨ur Mathematik, Informatik und Naturwissenschaften: Prof. Dr. Heinrich Graener Abstract We confront the signals expected from unstable gravitino dark matter with observa- tions of indirect dark matter detection experiments in all possible cosmic-ray channels. For this purpose we calculate in detail the gravitino decay widths in theories with bilin- ear violation of R parity, particularly focusing on decay channels with three particles in the final state. Based on these calculations we predict the fluxes of gamma rays, charged cosmic rays and neutrinos expected from decays of gravitino dark matter. Although the predicted spectra could in principal explain the anomalies observed in the cosmic- ray positron and electron fluxes as measured by PAMELA and Fermi LAT, we find that this possibility is ruled out by strong constraints from gamma-ray and antiproton observations. Therefore, we employ current data of indirect detection experiments to place strong constraints on the gravitino lifetime and the strength of R-parity violation. In addition, we discuss the prospects of forthcoming searches for a gravitino signal in the spectrum of cosmic-ray antideuterons, finding that they are in particular sensitive to rather low gravitino masses. Finally, we discuss in detail the prospects for detecting a neutrino sig- nal from gravitino dark matter decays, finding that the sensitivity of neutrino telescopes like IceCube is competitive to observations in other cosmic ray channels, especially for rather heavy gravitinos. Moreover, we discuss the prospects for a direct detection of gravitino dark matter via R-parity violating inelastic scatterings off nucleons. We find that, although the scat- tering cross section is considerably enhanced compared to the case of elastic gravitino scattering, the expected signal is many orders of magnitude too small in order to hope for a detection in underground detectors. Zusammenfassung Wir konfrontieren die erwarteten Signale von instabiler Gravitino-Dunkler-Materie mit Beobachtungen von Experimenten zur indirekten Suche nach dunkler Materie in allen m¨oglichen Kan¨alen kosmischer Strahlung. Zu diesem Zweck berechnen wir in allen Einzelheiten die Gravitinozerfallsbreiten in Theorien mit bilinearer Verletzung der R- Parit¨at, wobei wir uns insbesondere auf Zerfallskan¨ale mit drei Teilchen im Endzus- tand konzentrieren. Auf der Basis dieser Berechnungen sagen wir die Flusse¨ von Gam- mastrahlen, geladenen kosmischen Strahlen und Neutrinos vorher, die aus Zerf¨allen Gravitino-Dunkler-Materie erwartet werden. Obwohl die vorhergesagten Spektren prinzip- iell die beobachteten Anomalien in den von PAMELA und Fermi LAT gemessenen Flussen¨ von Positronen und Elektronen in der kosmischen Strahlung erkl¨aren k¨onnten, beobachten wir, dass diese M¨oglichkeit auf Grund starker Einschr¨ankungen aus den Beobachtungen von Gammastrahlen und Antiprotonen ausgeschlossen ist. Daher verwenden wir aktuelle Daten von Experimenten zur indirekten Suche nach dunkler Materie um starke Schranken an die Gravitinolebensdauer und die St¨arke der R- Parit¨ats-Verletzung zu setzen. Des Weiteren diskutieren wir die Erfolgsaussichten kom- mender Suchen nach einem Gravitinosignal im Spektrum von Antideuteronen in der kosmischen Strahlung, wobei wir beobachten, dass sie insbesondere fur¨ niedrige Grav- itinomassen empfindlich sind. Schließlich er¨ortern wir ausfuhrlich¨ die Erfolgsaussichten ein Neutrinosignal aus Zerf¨allen Gravitino-Dunkler-Materie zu messen, wobei wir fest- stellen, dass die Sensitivit¨at von Neutrinoteleskopen wie IceCube insbesondere fur¨ den Fall schwerer Gravitinos zu Beobachtungen in anderen Kan¨alen kosmischer Strahlung konkurrenzf¨ahig ist. Daruber¨ hinaus besprechen wir die Erfolgsaussichten fur¨ eine direkte Entdeckung Gravitino-Dunkler-Materie uber¨ R-Parit¨ats-verletzende inelastische Streuungen an Nuk- leonen. Wir stellen fest, dass, obwohl der Streuwirkungsquerschnitt gegenuber¨ dem Fall elastischer Gravitino-Streuungen deutlich erh¨oht ist, das erwartete Signal um viele Gr¨oßenordnungen zu klein ist als dass man eine Entdeckung in unterirdischen Detek- toren erhoffen k¨onnte. F¨ur Melanie Contents Contents i List of Figures iii List of Tables vi 1 Introduction 1 2 Cosmology and Dark Matter 6 2.1 BigBangCosmology ............................. 6 2.2 EvidencefortheExistenceofDarkMatter . 15 2.3 ConstraintsonDarkMatterProperties . 19 3 Supersymmetry and Supergravity 21 3.1 Supergravity.................................. 22 3.2 The Minimal Supersymmetric Standard Model . 27 3.3 Bilinear Breaking of R Parity ........................ 34 4 Gravitino Decays 42 4.1 The Massive Gravitino and its Interactions . 42 4.2 Gravitino Cosmology . 45 4.3 GravitinoDecayChannels . .. .. 48 4.3.1 Two-BodyDecays........................... 48 4.3.2 Three-BodyDecays.......................... 52 4.3.3 Gravitino Branching Ratios . 59 4.4 Spectra of Final State Particles from Gravitino Decays . ... 63 5 Indirect Detection of Gravitino Dark Matter 76 5.1 IndirectSearchesforDarkMatter . 76 5.2 Probing Gravitino Dark Matter with Gamma Rays . 82 5.3 Probing Gravitino Dark Matter with Cosmic-Ray Antimatter . .. 87 5.3.1 Positrons and Electrons . 89 5.3.2 Antiprotons .............................. 95 5.3.3 Antideuterons............................. 100 i Contents 5.3.4 Bounds on the Gravitino Lifetime from Charged Cosmic Rays . 103 5.4 Probing Gravitino Dark Matter with Neutrinos . 104 5.4.1 Neutrino Fluxes . 105 5.4.2 NeutrinoandMuonSpectra . 109 5.4.3 RatesandBounds .......................... 117 5.5 Constraints on the Gravitino Dark Matter Parameter Space . .... 124 6 Direct Detection of Gravitino Dark Matter 128 6.1 DirectSearchesforDarkMatter. 128 6.2 Gravitino Dark Matter with Bilinear R-Parity Violation . 131 7 Conclusions and Outlook 137 Acknowledgments 141 A Units and Physical Constants 142 B Notation, Conventions and Formulae 144 C Feynman Rules 149 D Kinematics of Scattering and Decay Processes 153 E Calculation of Gravitino Decay Widths 158 E.1 Two-BodyDecays............................... 158 E.2 Three-BodyDecays.............................. 160 E.2.1 ψ3/2 γ∗/Z∗ ν f f¯ ν ....................... 160 → + → E.2.2 ψ W ∗ ℓ− f f¯ ℓ− ....................... 166 3/2 → → ′ E.2.3 ψ h∗ ν f f¯ ν .......................... 170 3/2 → → F Calculation of Gravitino–Nucleon Cross Sections 173 F.1 Inelastic Gravitino–Nucleon Scattering via Higgs Exchange . ... 173 F.2 Inelastic Gravitino–Nucleon Scattering via Z Exchange . 175 F.3 Inelastic Gravitino–Nucleon Scattering via Photon Exchange . .... 179 Bibliography 181 ii List of Figures 2.1 Timeline of the thermal early universe. 10 2.2 BBN predictions of the light element abundances and ΩΛ Ωm plane of theconcordancemodelofcosmology. .− . 14 2.3 WMAP 7-year temperature anisotropy map and angular power spectrum. 15 2.4 Rotation curve of the Milky Way and the Bullet cluster. 17 2.5 Energy content of the universe at the time of the CMB emission and today. 19 3.1 Renormalization group evolution of the inverse gauge couplings in the standard model and in the minimal supersymmetric standard model. .. 22 3.2 Schematic particle content of the minimal supersymmetric standard model. 28 4.1 Branching ratios of the gravitino decay channels in the decoupling limit. 61 4.2 Branching ratios of the gravitino decay channels in the decoupling limit for the case of a suppressed photon channel. 63 4.3 Spectra of stable final state particles from gravitino decay in the channel ψ Zν ................................... 67 3/2 → i 4.4 Spectra of stable final state particles from gravitino decay in the channel ψ W e................................... 68 3/2 → 4.5 Spectra of stable final state particles from gravitino decay in the channel ψ Wµ................................... 69 3/2 → 4.6 Spectra of stable final state particles from gravitino decay in the channel ψ W τ................................... 70 3/2 → 4.7 Spectra of stable final state particles from gravitino decay in the channel ψ hν ................................... 70 3/2 → i 4.8 Fermion spectra from gravitino decay in the channel ψ W ∗ℓ f f¯′ ℓ . 72 3/2 → i → i 4.9 Fermion spectra from gravitino decay in the channel ψ Z∗ν f f¯ ν . 73 3/2 → i → i 4.10 Fermion spectra from gravitino decay in the channel ψ3/2 γ∗/Z∗νi ¯ → → f f νi...................................... 74 5.1 Density profiles for different dark matter halo models and angular de- pendence of the line-of-sight integral for dark matter annihilations and decays...................................... 79 iii List of Figures 5.2 Diffuse gamma-ray flux from gravitino dark matter decays compared to the measured extragalactic gamma-ray background. ... 84 5.3 Bounds on the gravitino lifetime from gamma-ray observations. .... 86 5.4 Contribution to the cosmic-ray positron fraction from gravitino decays compared to measurements and the expectation from astrophysical pri- maryandsecondaryproduction.. 92 5.5 Cosmic-ray electron flux from gravitino