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Landscape of Little Hierarchy

Landscape of Little Hierarchy. Yukihiro Mimura (Texas A&M University). based on PLB 648 (2007) 357 with Bhaskar Dutta and a paper in preparation with B. Dutta and D.V. Nanopoulos. Little Hierarchy and Naturalness Landscape of EWSB vacua ~Statistical approach to Little Hierarchy

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Landscape of Little Hierarchy

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  1. Landscape of Little Hierarchy Yukihiro Mimura (Texas A&M University) based on PLB648 (2007) 357 with Bhaskar Duttaand a paper in preparation with B. Dutta and D.V. Nanopoulos Little Hierarchy and Naturalness Landscape of EWSB vacua ~Statistical approach to Little Hierarchy EWSB vacua in No-scale model~Dynamical approach to Little Hierarchy Talk at PHENO 2007 conference, on 5.8.2007

  2. Little Hierarchy and Naturalness Non-observation of uncolored particles in LEP2Lightest Higgs mass bound Simple unified boundary condition of SUSY breaking Little hierarchy between Z boson and SUSY breaking masses

  3. Naturalness demands less fine-tuning. Sensitivity function : What should we learn before LHC?

  4. Question : • What is unnatural in EWSB vacua ? • Is there any physics to select EWSB vacua with little hierarchy? In this talk : • Landscape of EWSB vacua ~Statistical approach to Little Hierarchy • EWSB vacua in No-scale model~Dynamical approach to Little Hierarchy

  5. More conditions for radiative EWSB vacua : tree : averaged stop mass

  6. EWSB Window are independent of overall SUSY breaking because RGEs are homogeneous differential equations.

  7. Little hierarchy

  8. Criticality (Giudice-Rattazzi)

  9. Statement : Little hierarchy is probable among EWSB vacua. Sensitive but probable

  10. Distribution function depends on measure. So use the probability function by integration. At 90% probability,

  11. Lightest Higgs mass at 90% probability

  12. 90% & 95% probability in minimal SUGRA parameter space

  13. Several landscapes No preference. Naturalness is demanded. Little hierarchy is probable. Natural vacua is probable.

  14. Little hierarchy is probable among EWSB vacuawhen SUSY breaking scale is distributed. However, EWSB vacua are not probable in multiverse. Selection of EWSB vacua in multiverse is ANTHROPIC. In any SUSY breaking models, selection of EWSB vacua is anthropic. Exception: No-scale model (Ellis-Kounnas-Lahanas-Nanopoulos-Tamvakis)

  15. No-scale model The modulus T is not determined until it feels EW potential.

  16. EWSB vacua is the minimal of the potential. Little hierarchy This formula do not depend on the universal conditionof the boundary condition.

  17. Dangerous term in the quantum correction needsto be forbidden. But there can be harmless correction : Minimization condition : ~ which gives upper bounds for SUSY breaking. ~

  18. minimal SUGRA example No-scale predictiondo not depend on the universality assumption very much. Predicted region can be tested soon.

  19. Summary • We consider little hierarchy in 1. statistical approach 2. dynamical approach (no-scale model) • Little hierarchy is probable among EWSB vacua when SUSY breaking scale is distributed. • EWSB minimal is found in no-scale potential. In such vacua, there is a little hierarchy. SUSY breaking scale has a testable upper bound.

  20. Boundary condition in no-scale model gauge kinetic function:

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