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Neutrino Signals from Gravitino Dark Matter with Broken R-Parity

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Neutrino Signals from Gravitino Dark Matter with Broken R-Parity DESY-THESIS-2008-043 December 2008 Neutrino Signals from Gravitino Dark Matter with Broken R-Parity Diplomarbeit zur Erlangung des akademischen Grades Diplom-Physiker des Departments Physik der Universit¨at Hamburg durchgefuhrt¨ unter der Betreuung von Dr. Laura Covi in der Theory Group am DESY, Hamburg vorgelegt von Michael Grefe arXiv:1111.6041v1 [hep-ph] 25 Nov 2011 aus Luneburg¨ Hamburg September 2008 Gutachter der Diplomarbeit Erstgutachter: Dr. Laura Covi Zweitgutachter: Prof. Dr. Jan Louis Abstract The gravitino is a promising supersymmetric dark matter candidate, even without strict R-parity conservation. In fact, with some small R-parity vio- lation, gravitinos are sufficiently long-lived to constitute the dark matter of the universe, while the resulting cosmological scenario is consistent with primordial nucleosynthesis and the high reheating temperature needed for thermal leptogenesis. Furthermore, in this scenario the gravitino is unstable and might thus be accessible by indirect detection via its decay products. We compute in this thesis the partial decay widths for the gravitino in models with bilinear R-parity breaking. In addition, we determine the neutrino sig- nal from astrophysical gravitino dark matter decays. Finally, we discuss the feasibility of detecting these neutrino signals in present and future neutrino experiments, and conclude that it will be a challenging task. Albeit, if de- tected, this distinctive signal might bring considerable support to the scenario of decaying gravitino dark matter. Zusammenfassung Das Gravitino ist auch ohne strikte R-Parit¨at-Erhaltung ein vielversprechen- der Kandidat fur¨ supersymmetrische dunkle Materie. Tats¨achlich sind Gra- vitinos bei leichter R-Parit¨at-Verletzung genugend¨ langlebig um die dunkle Materie im Universum darzustellen, w¨ahrend das daraus resultierende kosmo- logische Szenario mit primordialer Nukleosynthese und der hohen Reheating- Temperatur, die fur¨ thermische Leptogenese ben¨otigt wird, vereinbar ist. Dar- uber¨ hinaus ist das Gravitino in diesem Szenario instabil und k¨onnte daher durch seine Zerfallsprodukte fur¨ eine indirekte Entdeckung zug¨anglich sein. In dieser Diplomarbeit berechnen wir die partiellen Zerfallsbreiten des Gravi- tinos in Modellen mit bilinearer R-Parit¨at-Brechung. Zudem bestimmen wir das Neutrinosignal astrophysikalischer Zerf¨alle von dunkler Materie, die aus Gravitinos besteht. Schließlich diskutieren wir die M¨oglichkeit diese Neutri- nosignale in heutigen und zukunftigen¨ Neutrinoexperimenten zu beobachten und kommen zu dem Schluss, dass es eine sehr herausfordernde Aufgabe ist. Dessen ungeachtet k¨onnte dieses charakteristische Signal eine deutliche Unterstutzung¨ fur¨ das Szenario zerfallender Gravitinos als dunkler Materie darstellen. Contents Contents i List of Figures iii List of Tables iv Preface 1 1 Dark Matter and the Early Universe 4 1.1 BigBangCosmology ....................... 4 1.2 DarkMatter............................ 11 1.2.1 EvidenceforDarkMatter . 11 1.2.2 Particle Dark Matter Candidates . 14 1.2.3 Direct and Indirect Detection of Dark Matter . 15 2 Supersymmetry, Supergravity and the Gravitino 18 2.1 Supersymmetry .......................... 18 2.2 Supergravity............................ 28 2.3 TheGravitino........................... 29 2.3.1 The Free Massive Gravitino Field . 29 2.3.2 Gravitino Interactions . 32 2.3.3 Gravitino Cosmology . 33 3 Gravitino Decays via Bilinear R-Parity Breaking 35 3.1 Bilinear R-ParityBreaking. .. .. .. 35 3.2 Gravitino Decay Channels . 37 3.2.1 Calculation of Decay Widths . 37 3.2.2 Fragmentation of the Z 0, W and h Bosons . 44 3.2.3 Neutrino Spectra from Gravitino Decays . 46 i Contents 4 Neutrinos as a Probe of Gravitino Dark Matter 49 4.1 Neutrino Signals . 49 4.1.1 Neutrino Fluxes . 49 4.1.2 Neutrino Propagation and Neutrino Oscillations . 54 4.2 NeutrinoBackground. 57 4.2.1 Atmospheric Neutrinos . 57 4.2.2 Further Neutrino Background Sources . 59 4.3 ReductionoftheNeutrinoBackground . 60 4.3.1 Electron and Muon Neutrinos . 61 4.3.2 Tau Neutrinos . 62 4.4 DetectionProspects. 63 4.4.1 Water CerenkovDetectorsˇ . 63 4.4.2 Observability in Super-Kamiokande . 65 4.4.3 FutureDetectors . .. .. .. .. 68 4.5 Constraints on the Gravitino Parameters . 69 5 Conclusions 72 A Units and Physical Constants 74 B Notation, Conventions and Formulae 76 C Calculation of Decay Widths 83 C.1 FeynmanRules .......................... 83 C.2 Kinematics ............................ 86 C.3 Gravitino Decay Channels . 87 D PYTHIA Simulation 96 Acknowledgements 101 Revision History 102 Bibliography 103 ii List of Figures 1.1 Concordance model of cosmology and BBN predictions of the light element abundances. 10 1.2 Typical rotation curve of a galaxy and miscellaneous halo den- sityprofiles. ............................ 12 1.3 Comparison of the angular profile of the flux from decaying and annihilating DM. 16 2.1 Renormalization group evolution of the inverse gauge cou- plings in the SM and the MSSM. 19 3.1 Branching ratios of the gravitino decay channels. 42 3.2 Branching ratios of the SM Higgs boson. 45 3.3 Neutrino injection spectra from gravitino decay. 47 4.1 Neutrinofluxesafterpropagation. 57 4.2 Averaged full-sky neutrino fluxes expected at the Super-K site. 61 4.3 Down-going tau neutrino fluxes expected at the Super-K site. 63 4.4 Cross sections of CC tau neutrino interactions. 64 4.5 Neutrino energies and event topologies. 66 4.6 Tau neutrino events expected at Super-K. 67 4.7 Constraints on the gravitino parameter space. 70 iii List of Tables 1.1 Parameters for miscellaneous halo models. 13 2.1 Gauge supermultiplets of the MSSM. 20 2.2 Chiral supermultiplets of the MSSM. 21 2.3 Gravity supermultiplet. 28 2.4 Clebsch–Gordancoefficients. 31 3.1 Branching ratios of the gravitino decay channels. 43 3.2 Decay modes of the Z0 and W bosons, and the τ lepton. 44 3.3 Numbers of neutrinos and antineutrinos from fragmentation. 45 4.1 Halo flux parameters for different halo models. 54 4.2 Neutrino oscillation parameters. 56 4.3 Values for the parameterization of the corona neutrino flux. 60 iv Preface The nature of the dark matter (DM) in the universe is still one of the unsolved mysteries in modern cosmology. Its existence is strong evidence for physics beyond the Standard Model, but until now the only indication for dark matter is based on its gravitational interaction. One of the most favored solutions to the dark matter problem is the introduction of supersymmetry with conserved R-parity. In this framework, the lightest supersymmetric particle (LSP) is stable and therefore a natural DM candidate, if it is also neutral and only weakly interacting. The most extensively studied case is where the LSPs are Weakly Interacting Massive Particles (WIMPs) and the dominant contribution to the dark matter in the universe. One of the most interesting candidates is, in fact, the lightest neutralino, since it can be tested in accelerator, direct detection and indirect detection experiments in the near future [1]. On the other hand, it is also possible that dark matter only interacts grav- itationally, and supersymmetry offers also candidates of this type. In local supersymmetry (i.e. supergravity) the gravitino arises as a natural candidate for dark matter. It is the superpartner of the graviton and has been the first supersymmetric dark matter candidate proposed [2]. The gravitino is also one of the most elusive dark matter candidates, since, as part of the gravity multiplet, all its interactions are suppressed either by the Planck scale (for the spin-3/2 component) or by the supersymmetry breaking scale (for the goldstino component). Nonetheless, a high reheating temperature after the inflationary phase in the early universe leads via thermal gravitino production to a relic abundance that can account for the observed dark matter density in the universe and is compatible with baryogenesis via thermal leptogenesis. Typically, the extremely weak interactions of the gravitino cause severe trouble for the standard cosmological scenario, since they make either the gravitino—if it is not the LSP—or the next-to-lightest supersymmetric par- ticle (NLSP) so long-lived that it decays during or after Big Bang Nucle- osynthesis (BBN). Therefore, the successful prediction of the light element abundances can be spoiled (see for instance [3]). 1 Preface However, it was recently proposed that these problems are easily circum- vented if a small breaking of R-parity is introduced [4]. In that case, the neutralino is too short-lived to play the role of dark matter, whereas the gravitino—if it is the LSP—can still have a sufficiently long lifetime, even exceeding the age of the universe by many orders of magnitude. Since the NLSP decays into Standard Model particles via R-parity violating couplings, the cosmology reduces to the standard, non-supersymmetric case well before the onset of BBN. In collider experiments, late decays of the NLSP can be a signature of this gravitino LSP scenario. Another advantage of models with R-parity violation is the fact that gravitino dark matter is no more invisible in astrophysical experiments: Even if the strongly suppressed couplings rule out an observa- tion in direct dark matter detection experiments, the tremendous number of gravitinos in the Milky Way and nearby galaxies compensates for the suppressed decay rate, possibly making gravitino decay products visible in indirect detection experiments. In fact, it has been found in [5, 6, 7] that gravitino dark matter with a life- time of 1026 s and a mass of 150 GeV can account simultaneously for the ∼ ∼ anomalies in the extragalactic gamma-ray flux, suggested by the Energetic Gamma Ray Experiment Telescope (EGRET) [8], and in the positron frac- tion, suggested by the High Energy Antimatter Telescope (HEAT) balloon experiment [9]. Motivated by this coincidence, we compute in this thesis the neutrino signal in the same scenario, both as a consistency check and to find out whether in this scenario an anomalous contribution to the neutrino flux may be expected in present and future neutrino experiments.
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