Lecture II: Dark Matter Candidates and WIMPs

1. Lecture II: Dark Matter Candidates and WIMPs

2. Dark Matter Candidates • Particle physicists would like to believe that DM is a kind of particles or many difference kinds of particles • These particles must have the following properties • Electrically neutral • No electromagnetic interactions (non-luminous) • No strong interaction • Otherwise, will see them already through the strong interaction process with ordinary matter (like cosmic ray) • Long life time • Longer than the lifetime of the universe, otherwise would have disappeared long ago

3. DM candidates in SM? • Electroweak symmetry breaking：Higgs particle has not been found • Neutrino is a possible candidate, but too light curve • A new particle！

4. Particles that live long • Electron: lightest charged particle (charge conservation) • Proton: baryon number symmetry breaking interaction is small. • Neutrinos: lightest fermion • Photon and graviton: cannot decay due to energy-momentum conservation • What make the dark matter stable? • Some symmetry which prevent its decay • Or the decay interaction is very very weak

5. Dark Matter Candidates • MACHOS • Primodial Black Holes • Mirror Matter • Axions (10-6 eV) • WIMPs (weakly interacting massive particles), WIMPzillas (1016 GeV)

6. Particle relics • Consider a stable particle X, which interacts with SM particle Y through, , , when temp is much higher than Mx, the creation and annihilation are equally efficient, therefore, DM particle exist in large quantity along with SM particles. • As the temp drops below Mx, the creation becomes exponentially suppressed. In the thermal equilibrium, the number density is if they remain in thermal eq. indefinitely, the nX will be increasingly suppressed as the univer. cools, quickly becomes irrel. • To evade this fate, • Particle-aniparticle asymmetry • Hubble expansion to dilute the small annihilation rate

7. Expansion vs annihilation • The evolution of the particle density obeys the Boltzmann equation where hubble constant, describes the expansion, and is the thermally averaged annihilation cross section, multiplied by velocity. • At very high T, due to large cross section, the density is given by eq. density • At small T, eq. density can be ignored, along with the entire annihilation term, the density dilutes through hubble expansion only. (comoving density remains constant)

8. Comoving density • Temp. at which the comoving density ceases to decrease expon. is called the freezout temp. • c ~ 0.5, a, b is defined from • The relic density of the universe

9. DM density: WIMP miracle • If X has a GeV-TeV scale mass and a roughly weak-scale annihilation cross-section, xFO = 20-30, resulting relic abundance. • From the DM density, one finds that on the order to 3 x 10-26 cm3/s • This is just consistent with the DM particle has weak interaction cross section. Therefore apart from gravity, DM shall have weak interactions.

10. SM Neutrinos • The annihilation cross section and light mass leads to an overall freeze-out temp on the order of few MeV, the relic density is • Since the SM neutrino mass is well below 9 eV, only a small fraction of the dark matter could possibly be the SM neutrinos. • Even if the neutrino mass were around 9eV , at the time of freeze-out, the particle is relativistic, the large scale structure of the universe will be much smoother than what has been observed (Warm Dark Matter)

11. A heavy neutrino • The annihilation cross section becomes much larger, growing with the square of mass up to the Z-pole, , declining with 1/m^2 above this. In this case, the free-out yields a cold relic T – m/10, the abundance is given by, • Therefore, if the relic density is explained by a heavy neutrino, its mass must be either around 5GeV, or several hundred GeV. • 5GeV is ruled out by the LEP Z-width. The heavy one is already excluded by the direct DM detection exp.

12. superWIMP scenario • A scenario in which the WIMP is unstable, decay to gravitating stable particle. • This is a nightmare for DM search

13. Supersymmetry • Supersymmetry is motivated by the large scale discrepancy between the electroweak symmetry breaking (240 GeV) and Planck scale (1019 GeV). The symmetry ensures that the quantum fluctuations at high-energy scale get cancelled through symmetry. • According to the symmetry, every fermion has a bosonic partner (s-paticle) and every boson has a fermionic partner (…inos) • Supersymmetry breaking can happen at electroweak scale so that so that all super-particles have masses around weak scale. In this case, the weak scale is related to the SUSY breaking.

14. Superparticles

15. DM candidates in SUSY • The lightest SUSY particle (LSP) is stable if R-parity is a good symmetry R = 1 for SM particles and R=-1 for SUSY partners. • The identity for LSP depends on the details of SUSY breaking. • Only if it is electrically and color-neutral, LSP can be a DM candidate • Four neutralinos (super-partner of the electrical neutral SM particle): • Gauginos for neutral gauge bosons (Z, gamma), • Higgsinos for higgs bosons (h, H) • three sneutrinos (spin-0), • gravitino (spin, 3/2)

16. Ruling out sneutrinos • In many respects, sneutrino is very similar to a fourth generation neutrino. It can annihilate into SM fermions through s-channel exchange of Z boson. • It must be on the order of 500GeV to 1TeV to give rise the right DM density. • It can scatter with ordinary matter through Z exchanges. The resulting cross section is too large. Already rule out by direct direction experiment.

17. Neutralinos • The lightest neutralino is a possible DM candidate. The mass matrix is M are the bino and wino masses, mu is the higgsino mass parameter. This can be diagonalized to yield the gaugino fraction and higgsino fraction are determined by the mixing coefficients, which in term depend on SUSY breaking scenarios.

18. Constraining neutralino • Assume gaugino masses evolve to a single value at GUT scale m1/2, the neutralino has a small wino fraction but a bino like if M1 is much less than mu, a higgsino like of M1 is much bigger than mu. • To neutralino over-produce the DM density, therefore,

19. CMSSM (constrained minimal supersymmetric standard model) • All scalar masses are set to m0 at GUT scale, three gaugino masses are each set to m1/2. • Blue region is where the relic density is Consistent with data. • LEP chargino bound In the upper part, LSP is a Mixed bino-higgsino type There is also a viable region close to lightest stau LSP. There is also a muon g-2 constraint.

20. Gravitino dark matter? • Because of its weak gravity coupling, gravitino decouples from the rest of the world very early, left with a huge quantity (it must be very light to avoid over-closure). • It can be diluted through inflation • Gravitino will be regenerated through reheating process. • If gravitino decays, its life time will be around M2pl/M3, which could affect BBN.

21. Gravitino dark matter? • If gravitino is the lightest supersymmetric particle, it lives long • However, decay (to gravitino) of the next-to-the lightest supersymmetric particles can affect BBN • This problem can be solve through small R-parity breaking decays, which lead to a gravitino with lifetime much longer than that of the universe.

22. Extra Dimensional Models • Superstring theories motivate space-time with extra dimensions • Many popular scenarios • Flat large extra dimension (millimeter scale) • Randall-Sundrum scenario • Universal extra dimension (UED) in which all SM fields are free to propagate in the bulk • … • UED model assumes the extra dimension of size R ~TeV-1. The excitation in the extra dimension has TeV scale mass and can serve as a DM candidate.

23. Kaluza-Klein states • KK states arise from the excitations in the extra dimension with masses the additional mass is called xero mode mass. • KK parity ensures that the extra dimensional excitation is stable. • DM candidates include the KK excitations of photon, Z, and neutrinos, higgs boson, and graviton. The best possible candidates are the first two types.

24. Mass matrix and relic density