1. Determining SUSY particle mixing with polarized hadron beams Michael Klasen (LPSC Grenoble) in collaboration with G. Bozzi, J. Debove, and B. Fuks April 22, 2010 Phys. Lett. B 609 (2005) 339 & Phys. Rev. D 80 (2009) 074006

2. April 22, 2010Michael Klasen, LPSC Grenoble2 Open questions in the Standard Model Where is the Higgs boson? Can we unify the electroweak and strong forces of nature? Is it possible to include gravity? Why is m h « m Pl. ? Why is there so little anti-matter? Why is CP-symmetry broken? What is dark matter made of?

3. April 22, 2010Michael Klasen, LPSC Grenoble3 Supersymmetric answers Where is the Higgs boson? SUSY-relation: m h < m Z (at 2-loop level < 135 GeV) Can we unify the electroweak and strong forces of nature? Standard Model:SUSY: Is it possible to include gravity? Local symmetry  Supergravity  Graviton, Gravitino Why is m h « m Pl. ? No quadratic divergences, cancellation of Why is there so little anti-matter? Why is CP-symmetry broken? SUSY contains numerous complex phases  Phase in CKM matrix What is dark matter made of? Stable LSP: Neutralino (SUGRA, AMSB), Gravitino (GMSB)

4. April 22, 2010Michael Klasen, LPSC Grenoble4 Supersymmetric answers Where is the Higgs boson? SUSY-relation: m h < m Z (at 2-loop level < 135 GeV) Can we unify the electroweak and strong forces of nature? Standard Model:SUSY: Is it possible to include gravity? Local symmetry  Supergravity  Graviton, Gravitino Why is m h « m Pl. ? No quadratic divergences, cancellation of Why is there so little anti-matter? Why is CP-symmetry broken? SUSY contains numerous complex phases  Phase in CKM matrix What is dark matter made of? Stable LSP: Neutralino (SUGRA, AMSB), Gravitino (GMSB)

5. April 25, 2006Michael Klasen, LPSC Grenoble5 Minimal Supersymmetric Standard Model

6. April 25, 2006Michael Klasen, LPSC Grenoble6 Minimal Supersymmetric Standard Model

7. April 25, 2006Michael Klasen, LPSC Grenoble7 Minimal Supersymmetric Standard Model

8. April 25, 2006Michael Klasen, LPSC Grenoble8 Current SUSY particle mass limits

9. April 25, 2006Michael Klasen, LPSC Grenoble9 Current SUSY particle mass limits

10. Slepton mixing 2-dimensional slepton mass matrix: with Diagonalized by: Mass eigenvalues: Mixing angle: April 22, 2010Michael Klasen, LPSC Grenoble10

11. Chargino mixing 2-dimensional chargino mass matrix: Diagonalized by: with Mass eigenvalues: Mixing angle: April 22, 2010Michael Klasen, LPSC Grenoble11

12. Chargino mixing 2-dimensional chargino mass matrix: with Diagonalized by: with Mass eigenvalues: Mixing angle: April 22, 2010Michael Klasen, LPSC Grenoble12

13. Chargino mixing RHIC:Tevatron, LHC: April 22, 2010Michael Klasen, LPSC Grenoble13

14. Neutralino mixing 4-dimensional neutralino mass matrix: Diagonalized by: Real, non-negative eigenvalues  N is generally complex Mass eigenvalues: Analytically calculable using projection operators Gounaris, Le Mouel, Porfyriadis, PRD 65 (2002) 035002 April 22, 2010Michael Klasen, LPSC Grenoble14

15. Neutralino mixing 4-dimensional neutralino mass matrix: with Diagonalized by: Real, non-negative eigenvalues  N is generally complex Mass eigenvalues: Analytically calculable using projection operators Gounaris, Le Mouel, Porfyriadis, PRD 65 (2002) 035002 April 22, 2010Michael Klasen, LPSC Grenoble15

16. Neutralino mixing RHIC:Tevatron, LHC: April 22, 2010Michael Klasen, LPSC Grenoble16

17. Neutralino Feynman rules Couplings to gauge bosons: Higgsino component Couplings to (s)quarks: Gaugino component April 22, 2010Michael Klasen, LPSC Grenoble17

18. Hadroproduction of SUSY particles April 22, 2010Michael Klasen, LPSC Grenoble18

19. Polarized hadron colliders Polarized protons: Atomic or optically pumped ion source, P = 87 % (1 mA H  ) Polarization loss from resonance crossing during acceleration Can be avoided with Siberian snakes RHIC @ BNL:  S = 500 GeV and P = 65  70 % 10-week physics runs from 2009 to 2012, L  266 pb -1 Tevatron @ FNAL:  S = 1.96 TeV and L > 4 fb -1 Baiod, Martin, Russell, SPIN Collaboration, FNAL (1995) Must replace some dipoles to install 6 Siberian snakes P = 65  70 % for protons, but not for anti-protons LHC @ CERN:  S = 7  14 TeV and L  1  100 fb -1 Upgrades under discussion (SSC reserved space for snakes) April 22, 2010Michael Klasen, LPSC Grenoble19

20. Expected RHIC performance April 22, 2010Michael Klasen, LPSC Grenoble20

21. April 22, 2010Michael Klasen, LPSC Grenoble21 Slepton cross section Polarized cross section: No polarized beam : One polarized beam : Two polarized beams: Asymmetries: 

22. Gaugino cross section Polarized cross section: Generalized charges: Single-spin asymmetry: April 22, 2010Michael Klasen, LPSC Grenoble22

23. April 22, 2010Michael Klasen, LPSC Grenoble23 Slepton cross sections and asymmetries [Bozzi, Fuks, MK, Phys. Lett. B 609 (2005) 339]

24. April 22, 2010Michael Klasen, LPSC Grenoble24 Gaugino cross sections and asymmetries [Debove, Fuks, MK, Phys. Rev. D 78 (2008) 074020]

25. April 22, 2010Michael Klasen, LPSC Grenoble25 Gaugino cross sections and asymmetries [Debove, Fuks, MK, Phys. Rev. D 78 (2008) 074020]

26. April 22, 2010Michael Klasen, LPSC Grenoble26 Gaugino cross sections and asymmetries [Debove, Fuks, MK, Phys. Rev. D 78 (2008) 074020]

27. Conclusion SUSY-particle mixing: Left/right chiral fermions  sfermion mass eigenstates  Strong correlation with beam, A L (cos   ) < 0.6 @ RHIC  Direct access to trilinear scalar coupling A 0 Gauge/Higgs bosons  gaugino mass eigenstates  Decomposition has important implications for dark matter   2 0  2 0 best, A L =  0.2…0.1 @ LHC (  0.5…0.3 @ Tevatron) High-energy polarized hadron collisions: RHIC now operating at  s = 500 GeV Would be an interesting option for Tevatron & LHC upgrades Accelerator studies existed (for Tevatron & SSC, mid-1990s) QCD physics program largely unexplored! ~