Assessment of Naturalness in German Forest Nature Conservation
Landscape Naturalness
description
Transcript of Landscape Naturalness
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Landscape Naturalness
M. Dine, E. Gorbatov, S. Thomas
P. Graham, S. Thomas
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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 ?
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(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 ?
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Fundamental Theory with a Multiverse
Landscape Naturalness :
Most Common on Landscape is Most Natural(Subject to some Constraints)
(Landscape of Vacua + Mechanism for Populating)
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Fundamental Theory with a Multiverse
Landscape Naturalness :
Most Common on Landscape is Most Natural(Subject to some Constraints)
(Landscape of Vacua + Mechanism for Populating)
Multiverse Wavefunctional () = Cosmological Trajectory on the Landscape
Correlations Among Observables : Necessarily Probabilistic
Observables Multiverse ExternalMeasure Measure / Restrictions
Note: No Predictions Without (Some Assumptions For) . Correlations from Underlying Theory
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• Experimental Priors yj à Versus ! External Restrictions ()
Give up Explaining Relations Among
. Known Observables
Give up Practical Utility of Program
Selection Effects are Not Physical Principles
But Must Admit that in a Multiverse there are in Fact Selection EffectsMay not be clear when to Stop
Note: No Predictions Without (Some Assumptions For) . Correlations from Underlying Theory
• Here yj = { Current Data }
No Weighting by “Observers”
Conditional
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Vacuum Energy (Banks ; Linde ; Weinberg)
0
Rapid Collapse
of Universe
Galaxy Formation
Suppressed
Any Galaxy Forms
Weight by Fraction of Collapsed Baryon
Acceleration Terminates
Galaxy Formation
few
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Vacuum Energy (Banks ; Linde ; Weinberg)
0
Rapid Collapse
of Universe
Galaxy Formation
Suppressed
Any Galaxy Forms
Weight by Fraction of Collapsed Baryon
Acceleration Terminates
Galaxy Formation
few
i) Hold Everything Fixed but (No Correlations)
ii) P() smooth near ' 0 (mild)
Assumptions :
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V = 0
V = 0
If Vacuum Energy Uncorrelated and Random Local Minima
All the Ingredients
Take Landscape Seriously ….
Discretuum Vacuum Energy on the Landscape
Nus À 10120
Nvac > 101010+?
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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 ?
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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, ….
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Importance of Symmetries on the Landscape
0
x Unprotected by Symmetry
P(x)
x
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Importance of Symmetries on the Landscape
0
x Unprotected by Symmetry
x Protected by Unbroken Symmetry
P(x)
x
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Importance of Symmetries on the Landscape
0
x Unprotected by Symmetry
x Protected by Unbroken Symmetry
x Protected by Symmetry -- Power Law (Froggatt-Nielsen)
P(x)
x
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Importance of Symmetries on the Landscape
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)
P(x)
x
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Importance of Symmetries on the Landscape
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
Note: Possible that
. P() >> P() . s P(x) dx << s P(x) dx
P(x)
x
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Landscape Naturalness for Hierarchies
• Symmetries which Protect Hierarchy ?
• Mechanisms for (Hierarchical) Symmetry
• Compare Classes of Mechanisms
• Ask Correct Conditional Questions
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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
Classical
Non-Perturbative
Non-Perturbative :
Assumptions :
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SUSY U(1)R V ' 0 mZ2
High Classical Classical 10-120 1-10-32
Intermediate NP Classical 10-120 1-10-32
Low NP NP 10-60 1
10-120
10-120
10-60
The Branches of the Landscape
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SUSY U(1)R V ' 0 mZ2
High Classical Classical 10-120 1-10-32
Intermediate NP Classical 10-120 1-10-32
Low NP NP 10-60 1
10-120
10-120
10-60
Statistics Overwhelms Tuning
Tuning Overwhelms Statistics
The Branches of the Landscape
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SUSY U(1)R V ' 0 mZ2 n
High Classical Classical 10-120 1-10-32 0-1/2
Intermediate NP Classical 10-120 1-10-32 0-1/2
Low NP NP 10-60 1 0
10-120
10-120
10-60
• Relative Occurrence Each Branch
The Branches of the Landscape
• Robust Feature of Local Supersymmetry
Statistics Overwhelms Tuning
Tuning Overwhelms Statistics
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SUSY U(1)R V ' 0 mZ2 n
High Classical Classical 10-120 1-10-32 0-1/2
Intermediate NP Classical 10-120 1-10-32 0-1/2
Low NP NP 10-60 1 0
10-120
10-120
10-60
• Relative Occurrence Each Branch
• Sub-Branches …..
The Branches of the Landscape
• Robust Feature of Local Supersymmetry
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• 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
• ……….
The Structure of the Landscape
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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
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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
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mt = 173 GeV
Quasi-fixed Point
mh2 = 4 / (23/2 GF)
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= 63
1
0.4
0.2
0.1
0.05
0
-0.05
M = 1016 GeV
Correlation Between mh and mt
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Higgs Self Coupling
• MSUSY » M
• MSUSY < M (Cutoff in Distribution)
SUSY Boundary Condition for at Matching Scale
VD Potential
VD (cos2 2 = 0) = 0
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cos2 2 = 1
0
M = 1016 GeV
Correlation Between mh and mt – SUSY Boundary Condition
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Higgs Self Coupling on the Landscape - SUSY Boundary Condition
Assumption : Random, . Uncorrelated
Step Function
Gaussian
h i ' 0.01 +- 0.01
(1/8)((3/5)g12+g2
2) ' 0.06
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Universality Class of P(mh:mt) Correlation – SUSY Boundary Condition
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LHC : > 30 fb-1
mh ' 0.2 GeV
mt ' 1 GeV
h0 ! ZZ* ,
Universality Class of P(mh:mt) Correlation – SUSY Boundary Condition
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Corrections and Uncertainties in mh Correlation
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 %
Corrections : mh / mh
Uncertainties :
s(mz) +- 1 %
2-Loop Running +- 1-2 % (estimate)
Landscape Statistical +- 1.3 %
Boundary Scale 1015 – 1018 GeV +- 0.4 % (Near ' 0)
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Corrections and Uncertainties in mh Correlation
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 %
Corrections : mh / mh
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
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Robustness of Universality Class to UV Completion
' 0 Delicate Boundary Condition
High Scale Thresholds ht ' 0.5
Hard SUSY mSUSY < 10-(1-2) M
Slepton Flavor Violation Hu , Hd , Li
R-Parity Violation
X Additional Vector Rep States Coupled to Higgs/Sleptons
Robust Universality Class of mh ' f(mt) Correlation . Rather Insensitive to UV Physics + (mh;mt | )
Slightly small Parameter mSUSY / M
W = S Hu Li +
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SUSY Gauge Coupling Unification Landscape 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)
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Gauge Coupling (Non)-Unification
1-1
(GeV)
2-1
3-1
sin2 W ' 3/7 1017 GeV
U(1)Y Normalization
Brane Realizations : g4,i-2 = VD-4 gD,i
-2
Gauge Coupling Unification May Not be Landscape Natural
SU(3)
SU(2)
Quark
W-Boson
Gluon
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Living Dangerously
P(x)
x
Selection Effect
In-Hospitable Hospitable
Most Likely Value Near Boundary of In-Hospitable Region
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-1 < H0-1
Living Dangerously Versus Comfortably
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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 ………