Is SUSY still alive? Dmitri Kazakov JINR

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1 The l o o h c S n a e p o r Eu y g r e n E h g i of H s c i s y PAnhjou, France e n 6 19 Ju Is SUSY still alive? Dmitri Kazakov JINR 1 1

2 Why do we love SUSY? Unifying various spins SUSY opens the road toward unification with gravity Local SUSY = Theory of (super)gravity GUT 2 2

3 Why do we love SUSY? Unifying various spins SUSY opens the road toward unification with gravity Local SUSY = Theory of (super)gravity Unifyes the gauge couplings of the SM towards Grand Unified Theory (GUT) 3 3

4 Why do we love SUSY? Unifying various spins SUSY opens the road toward unification with gravity Local SUSY = Theory of (super)gravity Unifyes the gauge couplings of the SM towards Grand Unified Theory (GUT) Stabilizes the GUT theory (hierarchy problem) Cancellation of quadratic terms (divergences) m 2 H g 2 M 2 SUSY 4 4

5 Why do we love SUSY? Unifying various spins SUSY opens the road toward unification with gravity Local SUSY = Theory of (super)gravity Unifyes the gauge couplings of the SM towards Grand Unified Theory (GUT) Stabilizes the GUT theory (hierarchy problem) Provides the Dark Matter particle (WIMP) Dark Matter in the Universe: Hot DM (not favoured by galaxy formation) Cold DM (rotation curves of Galaxies) SUSY 5 5

6 Why do we love SUSY? Unifying various spins SUSY opens the road toward unification with gravity Local SUSY = Theory of (super)gravity Unifyes the gauge couplings of the SM towards Grand Unified Theory (GUT) Stabilizes the GUT theory (hierarchy problem) Provides the dark Matter particle (WIMP) Provides the first integrable 4-dim quantum theory (N=4 SYM) N=4 maximally Supersymmetric Yang-Mills theory shows all the features and seems to provide the first integrable model in 4 space-time dimensions 6 6

7 Why do we love SUSY? Unifying various spins SUSY opens the road toward unification with gravity Local SUSY = Theory of (super)gravity Unifyes the gauge couplings of the SM towards Grand Unified Theory (GUT) Stabilizes the GUT theory (hierarchy problem) Provides the dark Matter particle (WIMP) Provides the first integrable 4-dim quantum theory (N=4 SYM) Stabilizes the string as an origin of a unified superstring theory No tachions 7 7

8 Where is SUSY? Accelerators Susy Telescopes Underground facilities 8 8

9 New Dimensions x µ Superspace, Grassmannian numbers 4D space time Grassmannian extra dim µ =0, 1, 2, 3, =1, = 2 2 =0 1 2 = 2 1 6=0 9 9

10 Superalgebra Superspace x µ! x µ,, Grassmannian parameters SUSY Generators Supertranslation x µ! x µ + i µ! +, 10! + i µ, 10

11 Superfield in Superspace N=1 SUSY Chiral supermultiplet: superfield spin=0 Gauge supermultiplet: (y, ) spin=1/2 Expansion over grassmannian parameter Auxiliary field (unphysical d.o.f. needed to close SYSY algebra ) component fields spin=1 Auxiliary fields 11 spin=1/2 11

12 SUSY Multiplets helicity Chiral multiplet # of states -1/2 0 1/ scalar spinor Vector multiplet helicity # of states -1-1/2 1/ Members of a supermultiplet are called superpartners spinor vector N=4 SUSY YM helicity -1 1/2 0 1/2 1 λ = -1 # of states N=8 SUGRA helicity -2 3/2 1 1/2 0 1/2 1 3/2 2 λ = -2 # of states spin For renormalizable theories (YM) For (super)gravity 12 12

13 Simplest (N=1) SUSY Multiplets Bosons and Fermions come in pairs (g, g) Spin 0 Spin 1/2 Spin 1/2 Spin 1 Spin 3/2 Spin 2 scalar chiral fermion majorana fermion vector gravitino graviton 13 13

14 Minimal Supersymmetric Standard Model (MSSM) SUSY: # of fermions = # of bosons N=1 SUSY: SM: 28 bosonic d.o.f. & 90 (96) fermionic d.o.f. There are no particles in the SM that can be superpartners SUSY associates known bosons with new fermions and known fermions with new bosons Even number of the Higgs doublets min = 2 Cancellation of axial anomalies (in each generation) Higgsinos -1+1=

15 Particle Content of the MSSM sleptons leptons squarks quarks Higgses { higgsinos { 15 15

16 1 st step How to write SUSY Lagrangians Take your favorite Lagrangian written in terms of fields 2 nd step Replace 3 rd step Replace Grassmannian integration in superspace 16 16

17 The MSSM Lagrangian The Yukawa Superpotential Superfields Yukawa couplings Higgs mixing term Violate: Lepton number Baryon number These terms are forbidden in the SM 17 17

18 The consequences: R-parity The Usual Particle : R = + 1 SUSY Particle : R = - 1 The superpartners are created in pairs The lightest superparticle is stable B - Baryon Number L - Lepton Number S - Spin p The lightest superparticle (LSP) should be neutral - the best candidate is neutralino (photino or higgsino) It can survive from the Big Bang and form the Dark matter in the Universe p 18 18

19 Interactions in the MSSM SM MSSM Vertices 19 19

20 Superpartners Production at LHC Annihilation Quark- gluon Fusion 20 20

21 Decay of Superpartners squarks q L,R q + χ i 0 q L q'+ χ i ± q L,R q + g sleptons l l + χ 0 i chargino l L ν l + ± χ i ± χ i e + νe + χ i 0 neutralino 0 0 χ + l + + l Final states gluino ± χ i q + q'+ χ g q + q + γ g g + γ 0 i χ i χ i χ 1 + q + q' 0 ± χ i χ 1 + l ± + ν l 0 0 χ i χ 1 + νl + ν l l + l + E T 2 jets + E T γ + E T E T 21 21

Lecture 18 - Beyond the Standard Model

Lecture 18 - Beyond the Standard Model Why is the Standard Model incomplete? Grand Unification Baryon and Lepton Number Violation More Higgs Bosons? Supersymmetry (SUSY) Experimental signatures for SUSY