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Landscape Naturalness

Landscape Naturalness. P. Graham, S. Thomas. M. Dine, E. Gorbatov, S. Thomas. What is String Theory ?. Toy Theory of Quantum Gravity …. Theory of Nature Landscape of Solutions ….

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Landscape Naturalness

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  1. Landscape Naturalness P. Graham, S. Thomas M. Dine, E. Gorbatov, S. Thomas

  2. What is String Theory ? • Toy Theory of Quantum Gravity • …. • Theory of Nature • Landscape of Solutions … How in Principle and in Practice Can Predictions be Extracted from a Fundamental Theory with a Landscape of Solutions ?

  3. (Technical) Naturalness • Electroweak Symmetry Breaking Stabilizing Physics < TeV  Most General Form in Conflict with …. Precision EW Higgs Mass Quark and Lepton FCNC E and M Dipole Moments Four-Fermi Contact Interactions Small Neutrino Masses Proton Stability Direct Bounds on New States Mechanisms to Avoid ….. Could Standard Model be a Good Theory >> TeV ? • Vacuum Energy UV-IR / Holographic Properties of (Virtual) States . Q-Gravity  » » 10-120 Mp4 ?

  4. Fundamental Theory with a Multiverse (Landscape of Vacua + Mechanism for Populating) Landscape Naturalness : Most Common on Landscape is Most Natural (Subject to some Constraints)

  5. Fundamental Theory with a Multiverse (Landscape of Vacua + Mechanism for Populating) Landscape Naturalness : Most Common on Landscape is Most Natural (Subject to some Constraints) Multiverse Wavefunctional ()  = Cosmological Trajectory on the Landscape CorrelationsAmong Observables : Necessarily Probabilistic Observables Multiverse External Measure / Restrictions Measure Note: No Predictions Without (Some Assumptions For) . Correlations from Underlying Theory

  6. Conditional • Experimental Priors yjÃVersus ! External Restrictions () Give up Explaining Relations Among . Known Observables Selection Effects are Not Physical Principles But Must Admit that in a Multiverse there are in Fact Selection Effects May not be clear when to Stop Give up Practical Utility of Program • Here yj = { Current Data }  No Weighting by “Observers” Note: No Predictions Without (Some Assumptions For) . Correlations from Underlying Theory

  7. Vacuum Energy(Banks ; Linde ; Weinberg) Acceleration Terminates Galaxy Formation Any Galaxy Forms Rapid Collapse of Universe Galaxy Formation Suppressed Weight by Fraction of Collapsed Baryon few 0

  8. Vacuum Energy(Banks ; Linde ; Weinberg) Acceleration Terminates Galaxy Formation Any Galaxy Forms Rapid Collapse of Universe Galaxy Formation Suppressed Weight by Fraction of Collapsed Baryon few 0 Assumptions : i) Hold Everything Fixed but  (No Correlations) ii) P() smooth near ' 0 (mild)

  9. Discretuum Vacuum Energy on the Landscape If Vacuum Energy Uncorrelated and Random Local Minima NusÀ 10120 Nvac > 101010+? V = 0 V = 0 V = 0 All the Ingredients Take Landscape Seriously ….

  10. Problems with Implementing Landscape Naturalness for . Other Observables • Full Landscape and {  } Unknown • Full () Unknown • Much of Landscape may be Incalculable . (Restrict to Representative ? Samples) • Measure D Unknown • Restrict to Local Minima – Unlikely Uniformly Populated • Can’t Calculate Many Observables of Interest Even in a Single Vacuum . (Limited to Discrete Quantities) Possible to Make Analogous Predictions ?

  11. Problems with Implementing Landscape Naturalness for . Other Observables • Full Landscape and {  } Unknown • Full () Unknown • Much of Landscape may be Incalculable . (Restrict to Representative ? Samples) • Measure D Unknown • Restrict to Local Minima – Unlikely Uniformly Populated • Can’t Calculate Many Observables of Interest Even in a Single Vacuum . (Limited to Discrete Quantities) Identify Robust Quantities  Classify Distributions of Vacua • Origin of Small Parameters (Associated with Large Hierarchies) . on the Landscape - EW Hierarchy, Vacuum Energy, Inflation, Yukawas, ….

  12. Importance of Symmetries on the Landscape P(x) x 0 x Unprotected by Symmetry

  13. Importance of Symmetries on the Landscape P(x) x 0 x Unprotected by Symmetry x Protected by Unbroken Symmetry

  14. Importance of Symmetries on the Landscape P(x) x 0 x Unprotected by Symmetry x Protected by Unbroken Symmetry x Protected by Symmetry -- Power Law (Froggatt-Nielsen)

  15. Importance of Symmetries on the Landscape P(x) x 0 x Unprotected by Symmetry x Protected by Unbroken Symmetry x Protected by Symmetry -- Power Law (Froggatt-Nielsen) x Protected by Symmetry – Exponential (Non-Perturbative)

  16. Importance of Symmetries on the Landscape P(x) Note: Possible that . P() >> P() . s P(x) dx << s P(x) dx x 0 x Unprotected by Symmetry x Protected by Unbroken Symmetry x Protected by Symmetry -- Power Law (Froggatt-Nielsen) x Protected by Symmetry – Exponential (Non-Perturbative) • (Technical) Naturalness - Important Organizing Principles on Landscape • Conditional Nature of Correlations Important

  17. Landscape Naturalness for Hierarchies • Symmetries which Protect Hierarchy ? • Mechanisms for (Hierarchical) Symmetry • Compare Classes of Mechanisms • Ask Correct Conditional Questions

  18. The Scale of SUSY on the Landscape V ' 0(M. Dine, E. Gorbatov, S.T.) SUSY U(1)R SUSY . Classical Classical Non-Perturbative Classical Non-Perturbative Non-Perturbative Non-Renormalization Thms Classical Non-Perturbative Assumptions : Classical Non-Perturbative Non-Perturbative :

  19. The Branches of the Landscape 10-60 10-120 10-120

  20. The Branches of the Landscape Statistics Overwhelms Tuning Tuning Overwhelms Statistics 10-60 10-120 10-120

  21. The Branches of the Landscape Statistics Overwhelms Tuning Tuning Overwhelms Statistics 10-60 10-120 10-120 • Robust Feature of Local Supersymmetry • Relative Occurrence Each Branch

  22. The Branches of the Landscape 10-60 10-120 10-120 • Robust Feature of Local Supersymmetry • Relative Occurrence Each Branch • Sub-Branches …..

  23. The Structure of the Landscape • Realization and Breaking of Symmetries • (Technical) Naturalness Enforced by (Approximate) Symmetries • Distributions can (Dramatically) Peak • Careful About Landscape Genericity – Conditional Correlations • Statistics versus Tuning • SUSY Branches . Feature of Any Theory with Local Supersymmetry – Robust . Step Towards a Priori (Probabilistic) Prediction of SUSY Scale • Realizations of Branches • Sub-Branches • Experimental Signatures • ……….

  24. Universality Classes of Landscape Correlations Correlations P(xi;yj) which are Insensitive to . Details of (xi;yj|) Within Some Wide Class of Vacua Predictive if 8 {} ¾ Class Vacua 9 P(x_i ; y_j) So Narrow ) xi' f(yj) Universality Class of Predictions from Landscape Naturalness Opportunity to Extract Real Predictions from Landscape Naturalness . Within Classes of Vacua – Possible with Current Technology

  25. Realizations of EWSB on High Scale SUSY Branch Technicolor Warped Throat Elementary Higgs ………….. Conjecture: (Statistics Overwhelm Tuning) The Higgs Sector Responsible for EWSB is a Single Elementary Scalar Higgs Doublet at or not too Far Below the Fundamental Scale The Landscape Standard Model(P. Graham, S.T.) The Entire Visible Sector is the Three Generation Standard Model at or not too Far Below the Fundamental Scale The Only Remaining Observable of EW Scale Physics is the . Higgs Mass

  26. Quasi-fixed Point mt = 173 GeV mh2 = 4  / (23/2 GF)

  27. Correlation Between mh and mt = 6 3 1 0.4 0.2 0.1 0.05 0 -0.05 M = 1016 GeV

  28. Higgs Self Coupling • MSUSY» M • MSUSY < M(Cutoff in Distribution) SUSY Boundary Condition for  at Matching Scale VD Potential VD (cos2 2  = 0) = 0

  29. Correlation Between mh and mt – SUSY Boundary Condition cos2 2  = 1 0 M = 1016 GeV

  30. Higgs Self Coupling on the Landscape - SUSY Boundary Condition Assumption : Random, . Uncorrelated (1/8)((3/5)g12+g22) ' 0.06 h i' 0.01 +- 0.01 Step Function Gaussian

  31. Universality Class of P(mh:mt) Correlation – SUSY Boundary Condition

  32. Universality Class of P(mh:mt) Correlation – SUSY Boundary Condition LHC : > 30 fb-1 h0! ZZ* ,  mh' 0.2 GeV mt' 1 GeV

  33. Corrections and Uncertainties in mh Correlation Corrections :  mh / mh Renormalization Group Running + 100 % Finite mtpole Corrections QCD 1-Loop -10.8 % QCD 2-Loop - 3.3 % GF mt2 1-Loop + 3.7 % GF mh2 1-Loop - 3.5 % Finite mhpole Corrections (GF mt2)1,2 1-Loop + 2.9 % GF mh2 1-Loop + 1.4 % Uncertainties : s(mz) +- 1 % 2-Loop Running +- 1-2 % (estimate) Landscape Statistical +- 1.3 % Boundary Scale 1015 – 1018 GeV +- 0.4 % (Near ' 0)

  34. Corrections and Uncertainties in mh Correlation Corrections :  mh / mh Renormalization Group Running + 100 % Finite mtpole Corrections QCD 1-Loop -10.8 % QCD 2-Loop - 3.3 % GF mt2 1-Loop + 3.7 % GF mh2 1-Loop - 3.5 % Finite mhpole Corrections (GF mt2)1,2 1-Loop + 2.9 % GF mh2 1-Loop + 1.4 % Uncertainties : s(mz) +- 1 % 2-Loop Running +- 1-2 % (estimate) Landscape Statistical +- 1.3 % Boundary Scale 1015 – 1018 GeV +- 0.4 % (Near ' 0) Level of Irreducible Uncertainties

  35. Robustness of Universality Class to UV Completion ' 0 Delicate Boundary Condition • High Scale Thresholdsht' 0.5 • Hard SUSY mSUSY < 10-(1-2) M • Slepton Flavor Violation Hu , Hd , Li • R-Parity Violation • XAdditional Vector Rep States Coupled to Higgs/Sleptons W = S Hu Li +  Slightly small Parameter mSUSY / M  Robust Universality Class of mh' f(mt) Correlation . Rather Insensitive to UV Physics + (mh;mt | )

  36. SUSY Gauge Coupling UnificationLandscape SM Higgs Mass Desert Desert . (No split GUT multiplets) (No significant coupling to Higgs) One Relation One Relation . Among Two Ratios Among Two Masses % Level Prediction % Level Prediction High Scale Thresholds High Scale Thresholds . Can Modify Can Modify Requires (Slightly) Requires (Slightly) . Small Parameter - MU/M Small Parameter MSUSY/M Successful Prediction ?? (As yet No Other Evidence for SUSY) (Easily Disproven)

  37. Gauge Coupling (Non)-Unification 1-1 2-1 3-1 (GeV) sin2W' 3/7 1017 GeV U(1)Y Normalization SU(2) Gluon Quark Brane Realizations : g4,i-2 = VD-4 gD,i-2 SU(3) W-Boson Gauge Coupling Unification May Not be Landscape Natural

  38. Living Dangerously Selection Effect In-Hospitable Hospitable P(x) x Most Likely Value Near Boundary ofIn-Hospitable Region

  39. Living Dangerously Versus Comfortably -1 < H0-1

  40. Conclusions • Fundamental Theory with Many Vacua  . Landscape Naturalness • (Conditional) Correlations Among Observables from () • Symmetries Organize Structure of Landscape • Supersymmetry: Non-Renormalization Thms + V ' 0  . Low, Intermediate, High Scale SUSY Branches • Additional Symmetries: Sub-Branches ….. • Universality Classes of Correlations  Path to Predictions • Landscape Standard Model + SUSY B.C.  . mh' f(mt) Correlation Wide Class of Vacua . Landscape Uncertainties » Irreducible Uncertainties in Calculation . Well Tested by LHC • Other Universality Classes ………

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