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Basic Supersymmetry

Basic Supersymmetry. Aldo F. Saavedra LBL. Outline:. Motivation A bit of algebra Signals. Some Shortcomings of the Standard Model. Hierarchy problem:. For spontaneous symmetry breaking one needs:. Where H and  are higgs field responsible for symmetry breaking of SU(2) and GUT groups.

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Basic Supersymmetry

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  1. Basic Supersymmetry Aldo F. Saavedra LBL

  2. Outline: • Motivation • A bit of algebra • Signals

  3. Some Shortcomings of the Standard Model Hierarchy problem: For spontaneous symmetry breaking one needs: Where H and  are higgs field responsible for symmetry breaking of SU(2) and GUT groups. The first question is how to get such a small number. The only way is to tune coupling constants. A radiative correction will certainly disrupt the fore metioned hierarchy.

  4. The feynman diagram for a the radiative correction to a ligh higgs mass is shown and is proportional to the squared mass of the particle Not cancelled will disrupt the hierachy In supersymmetry the contribution of the superpartners of the higgs particle perform the cancellation:

  5. Unification of the Couplings of Electromagnetic, Weak and Strong Forces D.I. Kazakov Phys. Rept. 344, 309, (2001)

  6. Muon Anomalous Magnetic Moment: Collaboration E821 at Brookhaven measured a value for a = (g -2) /2 which deviates by 2.6 from the Standard Model.

  7. The collaboration claims that the difference can be accounted for in a number particle physics models employing weak scale supersymmetry. In hep-ph/0103280 different SUSY models are compared. Some are favoured and some are not.

  8. The only possible extension of symmetry beyond Lie symmetries. Coleman- Mandula Theorem.(1967). This came from an attempt to combine internal and Lorentz symmetries and it states that: The only conserved quantities that transform as tensors under Lorentz transformation in a theory with non-zero scattering amplitudes in 4 dimensions are the generators of Poincare group and Lorentz invariant quantum numbers(scalar charges)

  9. But it does not forbid conserved of spinor charges, Q. (Graded Lie algebra) Q| Boson = | Fermion  Q| Fermion = | Boson  [Q,H] = 0 [{Q, Q*},H] = 0 {Q, Q*} = 2*P {Q, Q} = 0 {Q*, Q*} = 0 Translation Supersymmetry relates particles of different spin with equal quantum numbers of identical masses 1 1/2 g (gluon) q (quark)   1/2 0 g (gluino) q (squark) Chiral supermultiplet Gauge supermultiplet

  10. R-parity • Consequences: • SUSY particles produced in pairs. • Lightest SUSY particle (LSP) must be neutral • and colourless (from cosmological constraints). • LSP is stable. • No theoretical argument requires R-parity. • Some models conserve, others violate R-parity.

  11. References: • Jose Miguel Figueroa-O’Farrill , • BUSSTEPP Lectures on supersymmetry, hep-th/0109172 21 sep 2001. • Stephen P. Martin, A Supersymmetry Primer, hep-ph/9709356. • Marco Battaglia, Ian Hinchliffe, Daniel Tovey, • Cold Dark Matter and the LHC, hep-ph/0406147 • M. Biglietti et al , Full Supersymmetry Simulation for ATLAS in DC1, • ATL-PHYS-2004-011.

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