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Meta-stable vacuum in supersymmetric gauge theory

Meta-stable vacuum in supersymmetric gauge theory. M. Arai, M. Claus, N. Okada, S. Sasaki Talk based on arXiv:0708.0668  [hep-th] (to appear in Phys. Rev. D). Introduction . Naturalness problem (fine-tuning problem) The Standard Model (SM) is quite successful theory in particle physics.

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Meta-stable vacuum in supersymmetric gauge theory

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  1. Meta-stable vacuum in supersymmetric gauge theory M. Arai, M. Claus, N. Okada, S. Sasaki Talk based on arXiv:0708.0668 [hep-th] (to appear in Phys. Rev. D)

  2. Introduction • Naturalness problem (fine-tuning problem) • The Standard Model (SM) is quite successful theory in particle physics. • Quarks, leptons, gauge bosons, Higgs • Non-zero Higgs VEV determines the vacuum. W, Z bosons get masses of O(100) GeV • Serious problem : SM vacuum is not stable under quantum corrections. is cut-off.

  3. New physics scale >> electroweak scale • What is a solution? • New physics without quadratic divergence in quantum corrections Supersymmetry

  4. Supersymmetry • Supersymmetry (SUSY) • Symmetry that a boson and a fermion have the same mass spectra: • Ex: electron superpartner of electron (fermion) (sfermion) • Fine tuning problem can be solved. : fermion : sfermion +

  5. SUSY and unification • SUSY favors unification of couplings SM Minimal SUSY SM couplings Energy scale Unify exactly!

  6. SUSY in future collider • SUSY is expected to be observed at near future colliders • the Large Hadron Collider (LHC) • International Linear Collider (ILC) • A possible observation • Minimal SUSY SM and a superpartner in this model • SUSY Grand Unified Theory (SU(5) and SO(10)) • … However…

  7. SUSY breaking • SUSY must be broken. • No observation of superpartners of the SM particles yet (ex: superpartner of the electron) • How to break SUSY? • SUSY is broken by a scalar potential (as like gauge symmetry breaking by Higgs potential in the SM)

  8. SUSY breaking and scalar potential • An order parameter of SUSY breaking • SUSY Potential energy at vacuum is zero. • Breaking of SUSY Potential energy is non-zero. SUSY vacuum SUSY breaking vacuum

  9. A meta-stable vacuum • Global or local? Global SUSY breaking vacuum SUSY vacuum Local SUSY breaking vacuum If decay time is larger than age of universe, this vacuum is called a meta-stable vacuum. A new possibility! (Seiberg-Intriligator-Shih)

  10. How to realize? • How to realize SUSY breaking? • Like Higgs potential Theory has symmetry Symmetry is spontaneously broken

  11. Spontaneous SUSY breaking • O’Raifeartaigh model SUSY is spontaneously broken.

  12. Problems in O’Raifeartai model • SUSY is broken but vacuum is degenerate. • Any vacuum can be chosen. • Mass scale cannot be fixed. • E.g. Yukawa coupling: • If is the SM Higgs, it should be O(100) GeV

  13. Removing degeneracy? • Taking quantum corrections into account • Suppose that is charged under gauge symmetry • Gauge quantum corrections would remove degeneracy SUSY breaking minimum

  14. Calculable? • Estimation of quantum corrections is quite difficult • We need to estimate • pertubative corrections • non-pertubative corrections (gauge coupling strength is strong) g + +… g g g g It is non-trivial!

  15. What we did • Construction of specific SUSY model with spontaneous SUSY breaking • Removing degeneracy by taking into account all the quantum corrections • Such a estimation is possible in certain class of SUSY models • An phenomenological application of our model

  16. Potential plots • Classical potential V X Y Y Degeneracy of vacuum SUSY vacuum vacuum X Y

  17. Quantum potential • Taking quantum corrections into account V X SUSY breaking minimum It goes to infinity and to SUSY vaccum.

  18. Decay rate of vacuum • This theory has several parameters. • Decay rate of a local vacuum can be very small. V Realization of a meta-stable vacuum!

  19. A phenomenological application • SUSY breaking and Minimal SUSY SM(MSSM) • SUSY is broken by above mentioned mechanism. • Fields in SUSY breaking sector cannot couple to MSSM sector • Flavor changing neutral current • A new field couples to both sector • Messenger field MSSM sector SUSY breaking Sector (meta-stable) Messenger field Messenger scenario

  20. Conclusion • We considered a possibility that our universe is a metastable vacuum. • Such a situation is realized in SUSY gauge theory. • Classical model: Degenerate vacua • Quantum model: Degeneracy is removed. • Nontrivial task! Estimation of quantum corrections. • An application to phenomenology • Messenger scenario • Conforming in cosmology

  21. A meta-stable vacuum & finite temperature • A SUSY breaking scenario including finite temperature (Abel et al. JHEP 0701:089,2007) At low temperature Meta-stable vacuum realizes (black line-zero temp.) At high temperature only global minimum is at the origin.

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