Introduction Motivation WIMP models. WIMP models. Sebastian Belkner. University of Bonn - University of Cologne. June 24, 2016

Transcription

1 WIMP models Sebastian Belkner University of Bonn - University of Cologne June 24, / 27

2 A brief history of the universe 2 / 27

3 Outline 1 Motivation On galactic scales On cosmological scales 2 WIMP models General workframe SM+D and extra dimension SUSY 3 / 27

4 Evidence for DM Motivation On galactic scales 4 / 27

5 On galactic scales The DM halo From Newtonian dynamics, velocities v(r) are expected to be GM(r) v(r) = r. M(r) = 4π ρ(r)r 2 dr, ρ(r) 1 r beyond optical disc. Rotation curve implies ρ(r) 1 r 2 5 / 27

6 On galactic scales The DM halo Newtonian dynamics is not working on large scale? MACHOs the answer? Scan milky way for light anomalies, not suffienctly many found. There must be something, non light emitting "dark" (or blue?!) which only interacts weakly. 6 / 27

7 On cosmological scales Evidence for DM Motivation On cosmological scales 7 / 27

8 On cosmological scales The CMB CMB isotropic up to T 10 5 K. Extraordinary black body spectrum corresponding to T 2.726K. Expand Temperature anisotropy in terms of spherical harmonics, δt T = l,m a l,my l,m. 8 / 27

9 On cosmological scales The CMB Calculate expectation value C l = a l,m 2 = 1 2l+1 m a l,m 2, plot l(l+1)c l 2π against l. Radiation and gravitation led to oscillation of the hot early universe soup. 9 / 27

10 On cosmological scales The CMB First peak tells us about the curvature of the universe. Ratio of first and second peaks height gives information about the fraction of baryonic matter. 9 / 27

11 On cosmological scales The CMB Fit cosmological model (ΛCDM), find best parameters. Leads to Ω b h 2 = ± and Ω M h 2 = In accordance with BBN predictions, < Ω b h 2 < / 27

12 WIMP models The WIMP sector General workframe SM+D and extra dimension SUSY 11 / 27

13 General workframe Properties Term WIMP is given to a dark matter particle that fell out of thermal equilibrium with the hot dense plasma of the early universe Lifetime τ χ >> τ U Stringent constraints: in general electrically neutral and uncoloured Interaction with the SM weak, but still sizeable. σ = g 4 eff M 2 WIMP 12 / 27

14 General workframe Properties To avoid overclosing, M WIMP 1.8TeV g eff Thus mass near weak scale. Correct relic density, Ω χ h In general rather large masses, cold DM needed. Hot DM leads to a top down formation of the universe, which we don t observe. 12 / 27

15 General workframe WIMP miracle Assume full thermal equilibrium, self-annihilation cross section n χ σ(χχ SM)ν χ > expansion rate H decoupled when n χ σ(χχ SM)ν χ < expansion rate H Evolution of number density given by Boltzmann equation, one finds Ω X cm 3 /s σν 13 / 27

16 General workframe WIMP miracle Freeze out at T F m χ /20. Leads to weak scale self annihilation cross section of about σ(χχ SM)ν χ cm 3 s / 27

17 SM+D and extra dimension WIMP models The WIMP sector General workframe SM+D and extra dimension SUSY 14 / 27

18 SM+D and extra dimension A SM DM candidate? Use Ω ν cm 3 /s σν m νi 93eV. Ω ν h 2 i Assume m ν < 2.05eV and m ev 2 (constraints from solar and atmospheric neutrinos). leads to Ω ν h / 27

19 SM+D and extra dimension A SM DM candidate? using CMB and large structure data reduces value to Ω ν h Hence, neutrinos are essentially ruled out as DM candidates, total relic density is too small. Further, neutrinos are hot DM 15 / 27

20 SM+D and extra dimension Scalar singlet WIMP Simplest WIMP model Add real singlett scalar field via discrete Z 2 symmetry. Renormalizability demands only coupling to higgs. Unbroken Z 2 no mixing with higgs avoid possible fast decays. Ruled out already. 16 / 27

21 SM+D and extra dimension Extra dimension by using Einsteins general relativity in five dimensions, Kaluza and Klein could recover both GR and Maxwell eqn s. Assume extra dimension δ is compactified of some size R, M Planck M EW. Hence, solves hierarchy problem. Another motivation is String and M-theory, they need additional dimensions. Universal extra dimension, allow every particle to propagate through δ Upon compacitifaction, quantized momenta for all fields propagating through δ, p 2 1 R / 27

22 SM+D and extra dimension Universal extra dimension Fourier expansion Kaluza Klein [KK] states Each SM particle is associated with an infinite tower of KK states with masses n R Introduce KK parity stable ligthest KK-particle (LKP). In most models, LKP is first excitation of the photon (more precisely, hypercharge gauge boson B). 18 / 27

23 SUSY WIMP models The WIMP sector General workframe SM+D and extra dimension SUSY 19 / 27

24 SUSY Introduction Relates fermions to bosons and vice versa, Q Fermion = Boson, Q Boson = Fermion. MSSM, introduce an additional Higgs field and fermionic partners to all SM gauge and higgs fields, associate scalar partners to all fermions. 20 / 27

25 SUSY Introduction Solves hierarchy problem, which is linked to the big difference in the electroweak and planck scale Scalar mass 1-loop correction, δm α 2π Λ2. mass correction cancels via postulating new particles with similar masses but different spin. fermion loop = - boson loop, hence the contributions cancel, δm α 2π (m2 B m2 F ) 21 / 27

26 SUSY Introduction Grand unification 21 / 27

27 SUSY Introduction Names spin 0 spin 1/2 SU(3) C, SU(2) L, U(1) Y squarks, quarks Q (ũ L dl ) (u L d L ) ( 3, 2, 1 6 ) ( 3 families) u ũr u R ( 3, 1, 2 3 ) d d R d R ( 3, 1, 1 3 ) sleptons, leptons L ( ν ẽ L ) (ν e L ) ( 1, 2, 1 2 ) ( 3 families) e ẽr e R ( 1, 1, 1) Higgs, higgsinos H u (H u + Hu) 0 ( H u + H u) 0 ( 1, 2, ) H d (Hd 0 H d ) ( H d 0 H d ) ( 1, 2, 1 2 ) Table : Chiral supermultiplets in the MSSM. The spin-0 fields are complex scalars, and the spin-1/2 fields are left handed two component Weyl fermions. Taken from [7]. Names spin 1/2 spin 1 SU(3) C, SU(2) L, U(1) Y gluino, gluon g g ( 8, 1, 0) winos, W bosons W ± W 0 W ± W 0 ( 1, 3, 0) bino, B boson B0 B 0 ( 1, 1, 0) Table : Gauge supermultiplets in the MSSM. Taken from [7]. 22 / 27

28 SUSY Sneutrino SUSY particle of the neutrino. Interesting mass range between 550 to 2300 GeV Sneutrinos have full weak strength vector couplings to the Z, cross section for scattering on protons well above experimental constraints. Cure by enlarging mass predicted relic density is well above the observation. 23 / 27

29 SUSY Neutralino Introduce R-parity, +1 for SM particles, 1 for SUSY particles. First introduced to suppress proton decay. Choose basis ψ 0 = ( B, W 0, h 0 d, h 0 u) Neutralino-mass part of the lagrangian reads (ψ 0 ) T M χ ψ 0 + h.c., M χ non-diagonal Diagonalize interaction eigenstates (after SSB) with matrix N to find mass eigenstates. χ 0 1 = N 11 B + N 12 W 3 + N 13 h0 d + N 14 h0 u. Gaugino and higgsino fraction, f g = N N2 12, f h = N N / 27

30 SUSY Neutralino Find the right mixture! Pure binos do not pair-couple to any SM particle. As a consequence, such scenarios tend to severely overclose the universe. Pure higgsinos, on the other hand, tend to annihilate too efficiently into SM gauge bosons through s-channel Higgs exchange. To increase the predicted relic abundance, choose either heavy or light higgsino. Mixed bino-higgsino explains relic abundance in the universe, ( well-tempered neutralino). 25 / 27

31 SUSY Myriad possibilities There are several other (more or less exotic) models on the market CHAmps, WIMPzillas, Q-balls, primordial black holes,... Possible explanation is the mixture of different models. 26 / 27

32 SUSY Sources Gianfranco Bertone, Dan Hooper and Joseph Silk, Particle Dark Matter: Evidence, Candidates and Constraints, arxiv:hep-ph/ v2 Katherine Garrett and Gintaras Dũda, Dark Matter: A Primer, arxiv: v2 [hep-ph] Manuel Drees, Gilles Gerbier, Mini Review of Dark Matter: 2012, arxiv: v1 [hep-ph] Manuel Drees, WIMPs: An Introduction, Matthew Low and Lian-Tao Wang, Neutralino Dark Matter at 14 TeV and 100 TeV, arxiv: v2 [hep-ph] N. Arkani-Hamed, A. Delgado and G. F. Giudice, Nucl. Phys. B 741(2006) 108 [hep-ph/ ] Stephen P. Martin, A supersymmetric primer, [arxiv:hep-ph/ ] Xiao-Gang He, Tong Li, Xue-Qian Li, Jusak Tandean and Ho-Chin Tsai, The Simplest Dark-Matter Model, CDMS II Results, and Higgs Detection at LHC arxiv: v3 [hep-ph] G. Bélanger, C. Delauna, A. Goudelis, Neutralino dark matter and naturalness of the electroweak scale arxiv: v1 [hep-ph] 27 / 27

33 Additional stuff Appendix 1 / 1