Symmetry between fermions and bosons. Every type of fermion has a similar type boson partner, and vice versa. Number of fundamental particles doubles.

Transkript

1 April 7, 2010 Lecture 4 of ORICL Science & Technology Group Yuri Kamyshkov University of Tennessee kamyshkov@utk.edu

2 Symmetry between fermions and bosons. Every type of fermion has a similar type boson partner, and vice versa. Number of fundamental particles doubles. For every virtual fermion loop now there is a corresponding virtual boson loop canceling the former contribution. That would resolve the hierarchy divergence problem in a principle way!

3 O ( ) ( λ, ) H = H + bare i Λ M M g O 2 M P gi ln M W Coupling strength proportional to mass fermion ( ) boson (+) g g 2 t t g t

4 Standard Model (SM) mixed mixed Spin Fermions Spin Bosons 1/2 leptons: e,ν 1/2 quarks: u, d 0 Higgs bosons: H 1 gauge bosons: 2 graviton: G γ ± 0, W, Z, g Minimal Supersymmetric Standard Model (MSSM) mixed mixed Spin Fermions Spin Bosons e, ν ud, hhah,,, ± hhah,,, ± 0 γ, W ±, Z ± 0, g γ, W, Z, g G G 1/2 leptons: e,ν 0 sleptons: 1/2 quarks: u, d 0 squarks: 1/2 higgsino: 0 Higgs bosons: 1/2 gauginos: 1 gauge bosons: 3/2 gravitino: 2 graviton: G W ± ± ±, H χ charginos; γ, Z, h, H χ neutralinos

5 = p n E = mc 2 or m = E c 2 in Standard Model the stable particles are + γ, e, e, p, p, ν, ν (gluons are confined in nuclei; gravitons are not detectable) e e in GeV/c 2 Mass γ e ν? What makes the particles stable? Bosons Fermion

6 Supersymmetry is a broken symmetry: SUSY particles are much more massive than regular SM particles. Here is one of the MSSM models of SUSY masses. Higgs Sleptons Neutralino Squarks Chargino 2010 Particle Data Group: Lightest Supersymmetric Particle (LSP) is neutralino χ (mix of photino, Zino, and higgsino) 0

7 For different models of super-symmetry breaking where SUSY masses are parameters Generic features: Colored particles heavy; non-colored light; neutralino is LSP; the overall scale is a free parameter

8 For each normal SM light particle there is a heavier Super-particleparticle By the purpose of their introduction the Super-particles should have the same interaction strength as SM particles (virtual loops of SUSY particles should compensate virtual loops of regular particles)

9 How we can make SUSY particles? 1-st sufficient energy is required to make heavy-weighted SUSY particles Production of smuons in high-energy electron-positron collisions Decay of smuons to LSP neutralino Stable neutralino is a Dark Matter candidate

10 heavy SUSY particles should decay quickly to neutral LSP + regular particles; no atoms with SUSY all charged SUSY particles (as massive) are unstable; no SUPER-stars, galaxies, novae, black holes, etc.; (BTW: supernovae have nothing to do with Supersymmetry); no Pauli principle in action for charged SUSY bosons (sleptons and squarks); the only stable form of SUSY matter in the Universe can be LSP; LSP is #1 candidate for dark matter search; but all SUSY particles appear in the virtual radiative correction loops

11 LSP: Lightest Supersymmetric Particle are believed to be neutralinos i.e. mixture of photino SUSY partner of photon Zino SUSY partner of Z boson higgsino SUSY partner of neutral Higgs they are all neutral spin ½ fermions (similar to ν in the SM) neutralinos interact only weakly (as ν) and gravitationally (as massive) detection ti of SUSY particles (e.g. at LHC) is very difficult: non-lsp quickly decay LSP interact only weakly But is some SUSY models the Lightest Supersymmetric Particle is gravitino

12 Examples of SUSY Signatures at LHC The gluino pair production cascade decays to jets + leptons + missing transversal momentum. Gluino is a Majorana particle, like sign for dileptons The gaugino pairs cascade decay to missing transverse momentum + 3 leptons which h is a very clean signature, but with smaller cross section These signatures likely will not be unique: no peaks identifying a SUSY particle or a mechanism. Reconstruction of the whole SUSY spectrum is questionable.

13 Sparticle Cascades Use SUSY cascades to the stable LSP to sort out the new spectroscopy. Decay chain used is : o χ1 + χ χ b χ2 + b g b + b Final state is + b + b χ

14 Di, Tri-Lepton Signatures χ χ μ μ ( + ) Z + ( J + J) W At lower cross section there are more spectacular topologies, such as missing P T + 3 leptons or missing P T+ 2 jets + 2 leptons. If one will see an enhancement above the SM is it MSSM SUSY?

15 from LEP and Tevatron experiments and under MSSM model assumptions SUSY particle 0 χ 1 0 χ 2 0 χ 3 0 χ 4 Mass limit in GeV >46 >62.4 >99.9 >116 χ ± i e >94 >73 μ >94 τ >81.9 q >379 b t t g >89 >95.7 >308

16 SUSY mass scale makes running coupling constant convergent. GUT doesn t work without SUSY. And the only evidence for SUSY is that the coupling constants can be unified.

17 SUSY and GUT models So far we have no experimental facts that uniquely confirm SUSY or GUT This is an example when two theories GUT and SUSY (none of them supported by the experimental observations) are motivating each other. Experimental data

18 as SUSY LSP particle Existence of Dark Matter (DM) is established by ( ) y galactic rotation speed; by CMBR, by gravitational lensing, by large structure of universe...

19 Average density of regular matter in the universe ~ 0.3 GeV/m 3 Average density of Dark Matter in the universe ~ 1.5 GeV/m 3 Local density of Dark Matter in our galaxy ~ 300,000 GeV/m 3 Density of liquid id water (1 g/cc) ~ GeV/m 3

20 Interactions of Dark Matter If Dark Matter is SUSY neutralino with mass ~ 100 GeV then we have ~ 1 neutralino per cup of coffee It interacts with matter as weakly as neutrino, i.e. usually goes through the Earth without any interaction. It is called WIMP: Weakly Interacting Massive Particle WIMPs velocity in the galactic reference frame is ~ 300 km/s; velocity of Earth motion around the Sun ~ 30 km/s can be added or subtracted from this. WIMP interaction rate with matter will depend on the relative velocity. if WIMP collides with the atom it can transfer small kinetic energy to the atom in ~ kev range that can be detected.

21 DAMA/LIBRA experiment in Gran Sasso (Italy) claims annual variation of dark count rate in underground NaI scintillation detectors

22 Cryogenic CDMS-II experiment in Soudan mine in northern Minnesota

23 SUSY MSSM

24 graviton is the boson with spin 2 mediating gravitational interactions gravitino is the fermion spin 3/2 mediating supergravity interactions Due to broken Super-Symmetry gravitino has mass ~ TeV scale, ie i.e. <M Plank another mass hierarchy problem If gravitino is LSP i.e. stable it can be a candidate for Dark Matter. Then its calculated density of gravitinos is much higher than the observed density of Dark Matter. If gravitino is not-lsp and not stable but decays gravitationally i.e. very weakly, its life time should be rather long ~ 1day. In this case its decay products will prevent nucleosynthesis in the universe. With more parameters added to the SUSY models these problems can be fixed

25 Parameters of Standard Model and SUSY models Since it was discovered that neutrinos have masses, they can oscillate, and likely l are Majorana particles, this should add 7-9 ad hoc parameters to the es SM. (19 28). Supersymmetry (in its minimal configuration called MSSM) adds additional ~ parameters to the theory. Are we on the way to the ultimate theory?

26 Supersymmetry... has generated so many thousands of papers it must be correct Sheldon Glashow at the Workshop on Grand Unification

27 Conclusions SUSY, GUT are theoretically inspired models not confirmed by experiments ~90% of theoreticians and ~10% of experimentalists think that SUSY exists LHC and DM search are fields where SUSY indications might appear soon If SUSY will be experimentally confirmed its impact on the cosmology and unification will be revolutionary It will be interesting to see whether we can guess the intentions of Nature in the case of SUSY and GUT theories If not, is it a social mechanism or a kind of religion that makes people follow enthusiastically the ideas that have no realities in the life?