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Supersymmetry, naturalness and environmental selection

Supersymmetry, naturalness and environmental selection. G.F. Giudice. G.F.G., R. Rattazzi, hep-ph/0606105 [& N. Arkani-Hamed, A. Delgado, G.F.G., NPB 741, 108 (2006) ]. Guiding principle for physics BSM One of the main motivations for LHC. Hierarchy problem. SM. Broken EW. Unbroken EW.

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Supersymmetry, naturalness and environmental selection

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  1. Supersymmetry, naturalness and environmental selection G.F. Giudice G.F.G., R. Rattazzi, hep-ph/0606105 [& N. Arkani-Hamed, A. Delgado, G.F.G., NPB 741, 108 (2006)]

  2. Guiding principle for physics BSM • One of the main motivations for LHC Hierarchy problem SM Broken EW Unbroken EW 0 Why is nature so close to the critical line? Formulation in terms of criticality:

  3. Exact susy (and =0)  critical line • Dynamical susy breaking MS~MP e1/  • For “generic” parameters  mH2 ~ MS2 small departure from critical line stabilization of flat direction |H1|=|H2| Supersymmetry: Expectations for discovery at LEP: unfulfilled!

  4. unrelated to MS (depends on ci, a) • much smaller than UV scale QC ~ e1/MP Why supersymmetry should prefer to be near critical? “generic” supersymmetry: MS << QC << MP MS and QC equal to few % “tuned” supersymmetry: MS ~ QC << MP MS < QC broken EW; MS > QC unbroken EW

  5. Phase diagram of supersymmetric SM • A measure of the fine tuning • A characterization of the tuning

  6. Need large stop corrections  close to criticality

  7. STATISTICAL CRITICALITY Assume soft terms are environmental parameters Simplest case: mi=ci MS and MS scans in multiverse QC = MP F(ci,a,t) is fixed Two possibilities: MS > QC: unbroken EW 2) MS < QC: broken EW Impose prior that EW is broken (analogy with Weinberg)

  8. In “field-theoretical landscapes” we expect Probability distributiondP= • Susy prefers to be broken at high scale • Prior sets an upper bound on MS Susy near-critical Little hierarchy: Supersymmetry visible at LHC, but not at LEP (post-diction)

  9. CRITICALITY Distribution of vacua Prior of EW breaking Supersymmetry looks tuned because there many more vacua with <H> = 0 than with <H>  0 The level of tuning is dictated by RG running, and it is of the order of a one-loop factor

  10. TESTING STATISTICAL CRITICALITY:

  11. MZ Weak Principle MS QC Atomic Principle MZ Weak Principle “untuned” susy “split” susy MS QC STABILITY UNDER DIFFERENT PRIORS “tuned” susy If we require vF < 103QCD (to form chemical structures) If alsoQCD scans, we go back to “tuned” supersymmetry “Tuned” susy is obtained if enough parameters scan

  12. solution to  problem • prediction for  and tan • compatible with well-tempered bino-higgsino Statistical solution to  problem If  and MS scan independently: Critical line: Assume

  13. Susy-breaking vacua V(X) Susy vacuum X Denef, Douglas Dine, O’Neil, Sun Distribution of susy scale 3 conditions on complex parameters to have a local minimum (k1=0), stable (|k3|>2|k2|) with susy breaking at MS (|a1|=MS) If susy vacua dominate and strong dynamics occur:

  14. dynamics? chance ? statistics ? Problem of criticality: Quantitative difference after LEP & WMAP: DMh2=0.127 For MS>MZ :  is almost pure state +0.0070.013 B-ino: annihilation through sleptons (too slow without coannihilation): me < 115 GeV at 95% CL (LEP: me > 100 GeV) H-ino, W-ino: annihilation through gauge bosons (too fast) ~ ~ RECAP: Supersymmetry & Naturalness EW BREAKING Talks by Nomura, Dermisek, Toro, Okumura, Kitano, Falkowski, Shirman, Maekawa After LEP: a % tuning on soft terms DARK MATTER

  15. DM is possible in “special” regions: • coannihilation • Higgs resonance • “Well-tempered” • or non-thermal Both MZ and DM can be reproduced by low-energy supersymmetry, but with “atypical” parameter choices. Unlucky circumstances or dynamical explanation? Statistics? (always assumed when tuning is discussed?)

  16. RECAP: Supersymmetry & Environmental Selection • Use of anthropic principle controversial • Symmetry principles have been very successful • Lack of predictive power • However: • Failure of dynamical explanation for CC • Landscape in string theory • Predictions are possible: probabilistic (CC, axion) • change of perspective (Split Susy) • Near-criticality of susy?

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