How and Why to go Beyond the Discovery of the Higgs Boson

How and Why to go Beyond the Discovery of the Higgs Boson John Alison University of Chicago http://hep.uchicago.edu/~johnda/comptonlectures.html

Lecture Outline April 1st: Newton s dream & 20th Century Revolution April 8th: Mission Barely Possible: QM + SR April 15th: The Standard Model April 22nd: Importance of the Higgs April 29th: Guest Lecture May 6th: The Cannon and the Camera May 13th: The Discovery of the Higgs Boson May 20th: May 27th: Problems with the Standard Model Memorial Day: No Lecture June 3rd: Going beyond the Higgs: What comes next? 2

Reminder: Last Week 2012: Discovered new particle consistent with expectations Fig. 12 Confidence intervals in the (µ,m H ) plan n 3

Reminder: Last Week 2012: Discovered new particle consistent with expectations κ F v F m or κ V v V m 10 1-1 ATLAS s = 7 TeV, 4.5-4.7 fb s = 8 TeV, 20.3 fb Observed SM Expected -1-1 W Z t 10-2 10-3 µ τ b Fig. 12 Confidence intervals in the (µ,m H ) plan n 10 1 10 10 Particle mass [GeV] Since then: Significant improvement in sensitivity ults for the reduce Agreement with Higgs interpretation ~20% level No sign of any deviations -1 q 2 4

What it Took: In Numbers - >10,000 scientists and engineers from 85 countries - 27 kilometer particle accelerator - Protons moving at 99.9999993% the speed of light - ~1 billion proton collisions / second (for 2 years) - Total budget: ~10 billions dollars - Detectors - size of apartment buildings - operating at 40 MHz - Generate 80 TB/s (~10 size of library of congress ) - (Salary of physicist) << (Salary of banker or engineer) What is the Higgs boson?!? Why did we need such extremes to find it? Why look for the Higgs boson in the first place? Are we done now that we have found it? 5

What it Took: In Numbers - >10,000 scientists and engineers from 85 countries - 27 kilometer particle accelerator - Protons moving at 99.9999993% the speed of light - ~1 billion proton collisions / second (for 2 years) - Total budget: ~10 billions dollars - Detectors - size of apartment buildings - operating at 40 MHz - Generate 80 TB/s (~10 size of library of congress ) - (Salary of physicist) << (Salary of banker or engineer) What is the Higgs boson?!? Why did we need such extremes to find it? Why look for the Higgs boson in the first place? Are we done now that we have found it? 6

What it Took: In Numbers - >10,000 scientists and engineers from 85 countries - 27 kilometer particle accelerator - Protons moving at 99.9999993% the speed of light - ~1 billion proton collisions / second (for 2 years) - Total budget: ~10 billions dollars - Detectors - size of apartment buildings - operating at 40 MHz - Generate 80 TB/s (~10 size of library of congress ) - (Salary of physicist) << (Salary of banker or engineer) What is the Higgs boson?!? Why did we need such extremes to find it? Why look for the Higgs boson in the first place? Are we done now that we have found it? 7

What it Took: In Numbers - >10,000 scientists and engineers from 85 countries - 27 kilometer particle accelerator - Protons moving at 99.9999993% the speed of light - ~1 billion proton collisions / second (for 2 years) - Total budget: ~10 billions dollars - Detectors - size of apartment buildings - operating at 40 MHz - Generate 80 TB/s (~10 size of library of congress ) - (Salary of physicist) << (Salary of banker or engineer) What is the Higgs boson?!? Why did we need such extremes to find it? Why look for the Higgs boson in the first place? Are we done now that we have found it? 8

What it Took: In Numbers - >10,000 scientists and engineers from 85 countries - 27 kilometer particle accelerator - Protons moving at 99.9999993% the speed of light - ~1 billion proton collisions / second (for 2 years) - Total budget: ~10 billions dollars - Detectors - size of apartment buildings - operating at 40 MHz - Generate 80 TB/s (~10 size of library of congress ) - (Salary of physicist) << (Salary of banker or engineer) What is the Higgs boson?!? Why did we need such extremes to find it? Why look for the Higgs boson in the first place? Are we done now that we have found it? Focus of last two lectures 9

Today s Lecture Problems with the Standard Model 10

Length Scales 10 20 GeV 1 (10 36 m) weak-scale nuclei Planck scale ( p G N ) atoms cells animals planets 10 41 GeV 1 (10 25 m) stars solar systems galaxies observable universe 11

Length Scales 10 20 GeV 1 (10 36 m) weak-scale nuclei Planck ( p scale G N ) 10 11 m atoms cells animals planets 10 41 GeV 1 (10 25 m) stars solar systems galaxies observable universe 12

Length Scales 10 20 GeV 1 (10 36 m) weak-scale nuclei Planck ( p scale G N ) 10 11 m atoms cells animals 10 1 m planets stars q 10 7 m1 10 41 GeV 1 (10 25 m) solar systems galaxies observable universe 13

Length Scales 10 20 GeV 1 (10 36 m) weak-scale nuclei Planck ( p scale G N ) atoms cells animals planets 10 41 GeV 1 (10 25 m) stars solar systems galaxies observable universe 14

Length Scales ~unexplored LHC Directly Probed Experimentally 10 20 GeV 1 (10 36 m) weak-scale nuclei Planck ( p scale G N ) atoms cells animals planets 10 41 GeV 1 (10 25 m) stars solar systems galaxies observable universe 15

Length Scales Failure WW scattering ~unexplored LHC Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) weak-scale nuclei Planck ( p scale G N ) atoms cells animals planets 10 41 GeV 1 (10 25 m) stars solar systems galaxies observable universe 16

(In principle) Failure WW scattering ~unexplored LHC Length Scales Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) weak-scale nuclei Planck ( p scale G N ) atoms cells animals planets 10 41 GeV 1 (10 25 m) stars solar systems galaxies observable universe 17

(In principle) Failure WW scattering ~unexplored LHC Length Scales Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) weak-scale nuclei Planck ( p scale G N ) atoms cells 10 41 GeV 1 (10 25 m) animals planets stars Now (first time ever?) have theory can be extrapolated to exponentially higher energies. solar systems galaxies observable universe Another reason why the Higgs was such a big deal! 18

(In principle) Failure WW scattering ~unexplored LHC Length Scales Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) weak-scale nuclei Planck ( p scale G N ) atoms cells animals planets 10 41 GeV 1 (10 25 m) stars solar systems galaxies observable universe 19

(In principle) Failure WW scattering ~unexplored LHC Length Scales Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) weak-scale nuclei Planck ( p scale G N ) atoms cells animals planets 10 41 GeV 1 (10 25 m) stars All intermediate scales directly set by basic fundamental physical parameters (Seen explicit examples of some of these) solar systems galaxies observable universe 20

(In principle) Failure WW scattering ~unexplored Fundamental Length Scales LHC Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) Planck scale ( p G N ) 10 3 GeV 1 (10 19 m) weak scale 10 41 GeV 1 (10 25 m) observable universe observable universe 21

(In principle) Failure WW scattering ~unexplored Fundamental Length Scales LHC Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) 10 3 GeV 1 (10 19 m) 10 41 GeV 1 (10 25 m) Planck ( p scale weak scale observable universe G N ) Weak scale: Fundamental scale in physics - Scale associated with fundamental particle masses - Typical at which massive particles interact with Higgs field - The first time start seeing the forces have same underlying structure v v v v weak-scale observable universe 22

(In principle) Failure WW scattering ~unexplored 10 20 GeV 1 (10 36 m) Fundamental Length Scales LHC 10 3 GeV 1 (10 19 m) Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 41 GeV 1 (10 25 m) LHC exciting both because: - it is the frontier but also - exploring fundamental scale of nature Planck ( p scale weak scale observable universe G N ) Weak scale: Fundamental scale in physics - Scale associated with fundamental particle masses - Typical at which massive particles interact with Higgs field - The first time start seeing the forces have same underlying structure v v v v weak-scale observable universe 23

(In principle) Failure WW scattering ~unexplored Fundamental Length Scales LHC Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) Planck ( p scale G N ) 10 3 GeV 1 (10 19 m) weak scale 10 41 GeV 1 (10 25 m) Hubble scale observable universe 24

(In principle) Failure WW scattering ~unexplored Fundamental Length Scales LHC Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) Planck ( p scale G N ) 10 3 GeV 1 (10 19 m) weak scale 10 41 GeV 1 (10 25 m) Hubble scale - Large range, but not infinite. - Claim: Everything we know, and can possibly know, within this range - Upper bound set by finite upper speed limit (finite age of universe) - Talk about lower bound, next. Believed to really be hard lower bound - Deep mysteries/problems with SM, directly associated with each of these fundamental scales. observable universe 25

(In principle) Failure WW scattering ~unexplored Fundamental Length Scales LHC Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) Planck ( p scale G N ) 10 3 GeV 1 (10 19 m) weak scale 10 41 GeV 1 (10 25 m) Hubble scale - Large range, but not infinite. - Claim: Everything we know, and can possibly know, within this range - Upper bound set by finite upper speed limit (finite age of universe) - Talk about lower bound, next. Believed to really be hard lower bound - Deep mysteries/problems with SM, directly associated with each of these fundamental scales. observable universe 26

(In principle) Failure WW scattering ~unexplored Fundamental Length Scales LHC Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) Planck ( p scale G N ) 10 3 GeV 1 (10 19 m) weak scale 10 41 GeV 1 (10 25 m) Hubble scale - Large range, but not infinite. - Claim: Everything we know, and can possibly know, within this range - Upper bound set by finite upper speed limit (finite age of universe) - Talk about lower bound, next. Believed to really be hard lower bound - Deep mysteries/problems with SM, directly associated with each of these fundamental scales. observable universe 27

(In principle) Failure WW scattering ~unexplored Fundamental Length Scales LHC Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) Planck ( p scale G N ) 10 3 GeV 1 (10 19 m) weak scale 10 41 GeV 1 (10 25 m) Hubble scale - Large range, but not infinite. - Claim: Everything we know, and can possibly know, within this range - Upper bound set by finite upper speed limit (finite age of universe) - Talk about lower bound, next. Believed to really be hard lower bound - Deep mysteries/problems with SM, directly associated with each of these fundamental scales. observable universe 28

(In principle) Failure WW scattering ~unexplored Fundamental Length Scales LHC Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally 10 20 GeV 1 (10 36 m) Planck ( p scale G N ) 10 3 GeV 1 (10 19 m) weak scale 10 41 GeV 1 (10 25 m) Hubble scale - Large range, but not infinite. - Claim: Everything we know, and can possibly know, within this range - Upper bound set by finite upper speed limit (finite age of universe) - Talk about lower bound, next. Believed to really be hard lower bound - Deep mysteries/problems with SM directly associated with each fundamental scale observable universe 29

Problem with the Planck Scale 30

Relative Strength of Gravity Electromagnetic Interaction F EM = e2 4 1 r 2 mp r mp } Pure number: α 31

Relative Strength of Gravity Electromagnetic Interaction F EM = e2 4 1 r 2 mp r mp } Pure number: α Gravitational Interaction F G =G N m 2 p r 2 } Dimensionful number G N (l Pl ) 2 (10 20 GeV 1 ) 2 32

Relative Strength of Gravity Electromagnetic Interaction F EM = e2 4 1 r 2 mp r mp } Pure number: α F G F EM Gravitational Interaction F G =G N m 2 p r 2 } Dimensionful number 10 37 G N (l Pl ) 2 (10 20 GeV 1 ) 2 1 Distance GeV 1 m p 33

Relative Strength of Gravity Electromagnetic Interaction F EM = e2 4 1 r 2 } Pure number: α Gravitational Interaction F G F EM mp r mp Uncertainty principle kicks in. Takes E (=m) to keep together F G =G N m 2 p r 2 } Dimensionful number 10 37 G N (l Pl ) 2 (10 20 GeV 1 ) 2 1 Distance GeV 1 m p 34

Electromagnetic Interaction F EM = e2 At short distances, (comparable to lpl) gravitational mp interaction dominates - lpl the scale at which gravity is becoming strong Gravitational Relative Strength of Gravity 4 } 1 r 2 Pure number: α Gravitational Interaction F G F EM r mp Uncertainty principle kicks in. Takes E (=m) to keep together F G =G N m 2 p r 2 } Dimensionful number 10 37 G N (l Pl ) 2 (10 20 GeV 1 ) 2 1 Distance GeV 1 m p 35

36 Probing Smaller Distance Scales 10 20 GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 10 41 GeV 1 (10 25 m) Hubble ~unexplored LHC Directly Probed Experimentally

37 Probing Smaller Distance Scales 10 20 GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 10 41 GeV 1 (10 25 m) Hubble ~unexplored LHC Directly Probed Experimentally - Say we decided to probe smaller and smaller distance scales - Build collider, go to higher and higher energies - Eventually reach point where gravitational interaction dominates - Continue to smaller distance then something new happens

38 Probing Smaller Distance Scales 10 20 GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 10 41 GeV 1 (10 25 m) Hubble ~unexplored LHC Directly Probed Experimentally - Say we decided to probe smaller and smaller distance scales - Build collider, go to higher and higher energies - Eventually reach point where gravitational interaction dominates - Continue to smaller distance then something new happens

39 Probing Smaller Distance Scales 10 20 GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 10 41 GeV 1 (10 25 m) Hubble ~unexplored LHC Directly Probed Experimentally - Say we decided to probe smaller and smaller distance scales - Build collider, go to higher and higher energies - Eventually reach point where gravitational interaction dominates - Continue to smaller distance then something new happens

40 Probing Smaller Distance Scales 10 20 GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 10 41 GeV 1 (10 25 m) Hubble ~unexplored LHC Directly Probed Experimentally - Say we decided to probe smaller and smaller distance scales - Build collider, go to higher and higher energies - Eventually reach point where gravitational interaction dominates - Continue to smaller distance then something new happens

Create Black Holes! Some point put so much energy into collisions that you create black hole Estimate scale when this happens: G N m 2 r mc 2 G N 1 r 3 1 r At high energies, mass dominated by E associated w/ m 1 r r p G N l Pl 41

Create Black Holes! Some point put so much energy into collisions that you create black hole Estimate scale when this happens: G N m 2 r mc 2 G N 1 r 3 1 r At high energies, mass dominated by E associated w/ m 1 r r p G N l Pl 42

Create Black Holes! Some point put so much energy into collisions that you create black hole Estimate scale when this happens: G N m 2 r mc 2 G N 1 r 3 1 r At high energies, mass dominated by E associated w/ m 1 r r p G N l Pl 43

Create Black Holes! Some point put so much energy into collisions that you create black hole Estimate scale when this happens: G N m 2 r mc 2 At high energies, mass dominated by E associated w/uncertainty principle m 1 r r p G N l Pl 44

Create Black Holes! Some point put so much energy into collisions that you create black hole Estimate scale when this happens: G N m 2 r mc 2 At high energies, mass dominated by E associated w/uncertainty principle G N 1 r 3 1 r m 1 r r p G N l Pl 45

Create Black Holes! Some point put so much energy into collisions that you create black hole Estimate scale when this happens: G N m 2 r mc 2 At high energies, mass dominated by E associated w/uncertainty principle G N 1 r 3 1 r m 1 r r p G N l Pl 46

Probing Smaller Distance Scales 10 20 GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 10 41 GeV 1 (10 25 m) Hubble ~unexplored LHC Directly Probed Experimentally - Go to higher-higher energies Gravity begins to dominate - At lpl make blackhole / Cant tell whats happening in blackhole - Even higher energies gives bigger blackhole - Nothing can do (in principle) to get information about smaller scales - Physics telling us that smaller scales dont exist (Seen kind of thing before in QM and Relativity) 47

Probing Smaller Distance Scales 10 20 GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 10 41 GeV 1 (10 25 m) Hubble ~unexplored LHC Directly Probed Experimentally - Go to higher-higher energies Gravity begins to dominate - At lpl make blackhole / Cant tell whats happening in blackhole - Even higher energies gives bigger blackhole - Nothing can do (in principle) to get information about smaller scales - Physics telling us that smaller scales dont exist (Seen kind of thing before in QM and Relativity) 48

Probing Smaller Distance Scales 10 20 GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 10 41 GeV 1 (10 25 m) Hubble ~unexplored LHC Directly Probed Experimentally - Go to higher-higher energies Gravity begins to dominate - At lpl make blackhole / Cant tell whats happening in blackhole - Even higher energies gives bigger blackhole - Nothing can do (in principle) to get information about smaller scales - Physics telling us that smaller scales dont exist (Seen kind of thing before in QM and Relativity) 49

Probing Smaller Distance Scales 10 20 GeV 1 (10 36 m) 10 3 GeV 1 (10 19 m) Lower Limit to Spacetime 10 41 GeV 1 (10 25 m) Plank Notion of space-time Weakbreaking down lpl /Not clear what replaces Universe it. Major issue: - Understanding of these short scales needed for: - Early universe: What happened when universe curvature lpl ~unexplored - Details of blackholes LHC Directly Probed Experimentally - Physics is about what happens in space-time - Other Go to hints higher-higher that some energies dramatic need Gravity ( Holographic begins to dominate Principle ) - At - Black lpl make hole blackhole information / Cant scales tell like whats area happening in blackhole - Even - Observables higher energies with QM gives can bigger in principle blackhole perfectly predict - Nothing - Toy models can do where (in principle) see space to emerging get information about smaller scales -- Physics telling us that smaller scales dont exist (Seen kind of thing before in QM and Relativity) 50

Problems with Weak and Hubble Scales 51

Problems with Weak and Hubble Scales Problems associated with other two scales close related to one another - Both come down to vacuum fluctuations 52

Problems with Weak and Hubble Scales Lecture 2 Problems associated with other two scales close related to one another Combining - Both come Relativity down to vacuum and Quantum fluctuationsmechanics - To preserve causality needed to Anti-particle must exist - In turn, major implications on the vacuum: E > 2m e c 2 e x 1 m e E > 2m µ c 2 µ x 1 m µ e + µ + 53

Vacuum Fluctuations ARE REAL! e e e + Precisely predict magnetic properties g/2 = 1.0011596521809(8), (Agree to better than one part in a trillion.) 54

Vacuum Fluctuations ARE REAL! e e e + Z t Z t Precisely predict magnetic properties g/2 = 1.0011596521809(8), (Agree to better than one part in a trillion.) 55

Vacuum Fluctuations ARE REAL! e e e + Precisely predict magnetic properties g/2 = 1.0011596521809(8), (Agree to better than one part in a trillion.) Z W mh t H Z t 50 150 GeV 115 GeV (Predicted) (Discovered) 56

Classically (w/o QM) Vacuum Has Energy Lowest possible energy is 0 57

Vacuum Has Energy Classically (w/o QM) Quantum World Minimum non-zero energy: E~hω Lowest possible energy is 0 Δp Δx 58

Vacuum Has Energy Classically (w/o QM) Quantum World Minimum non-zero energy: E~hω Lowest possible energy is 0 Δp Δx Estimate energy density in region of empty space: Dimensional Analysis L Λ ~ E/V ~ 1/L^4 (V ~ L³) (E ~ 1/L) 59

Vacuum Has Energy Classically (w/o QM) Quantum World Minimum non-zero energy: E~hω Lowest possible energy is 0 Δp Δx Estimate energy density in region of empty space: Dimensional Analysis L E V 1 L 4 60

Vacuum Has Energy Classically (w/o QM) Quantum World Minimum non-zero energy: E~hω Δp Lowest possible energy is 0 Δx Estimate energy density in region of empty space: Dimensional Analysis L E V 1 L 4 (V L 3 ) (E 1 L ) 61

Vacuum Has Energy Classically (w/o QM) Quantum World Minimum non-zero energy: E~hω Δp Lowest possible energy is 0 Δx Estimate energy density in region of empty space: Dimensional Analysis L E V 1 L 4 (V L 3 ) (E 1 L ) 62

Vacuum Has Energy Classically (w/o QM) Quantum World Minimum non-zero energy: E~hω Lowest possible energy is 0 Δp Δx Estimate energy density in region of empty space: Dimensional Analysis Smaller Box L L E V 1 L 4 (V L 3 ) (E 1 L ) Λ much bigger 63

Vacuum Has Energy Classically (w/o QM) Quantum World Minimum non-zero energy: E~hω Lowest possible energy is 0 Δp Δx Estimate energy density in region of empty space: Dimensional Analysis Smaller Box Reach: Cut-off L L lpl E Λ much bigger V 1 1 L 4 (V L 3 ) (E 1 L ) `Pl 4 64

Vacuum Has Energy Classically (w/o QM) Quantum World Minimum non-zero energy: E~hω Lowest possible energy is 0 Δp Δx Estimate energy density in region of empty space: Dimensional Analysis Smaller Box Reach: Cut-off L L lpl E V 1 L 4 (V L 3 ) (E 1 L ) Λ much bigger 1 `Pl 4 this is a problem 65

Cosmological Constant Problem Without gravity constant energies (Λ) can be ignored (overall offset) With gravity, constant energy warps space-time, interacts gravitationally Uniform matter/energy controls size/expansion of overall Universe Doubling time ~ 1/ (GN Λ) ~1 (lpl² Λ) 66

Cosmological Constant Problem Without gravity constant energies (Λ) can be ignored (overall offset) With gravity, constant energy warps space-time, interacts gravitationally Uniform matter/energy controls size/expansion of overall Universe Doubling time ~ 1/ (GN Λ) ~1 (lpl² Λ) 67

Cosmological Constant Problem Without gravity constant energies (Λ) can be ignored (overall offset) With gravity, constant energy warps space-time, interacts gravitationally Uniform matter/energy controls size/expansion of overall Universe t Double 1 p GN 1 p `Pl 2 68

Cosmological Constant Problem Without gravity constant energies (Λ) can be ignored (overall offset) With gravity, constant energy warps space-time, interacts gravitationally Uniform matter/energy controls size/expansion of overall Universe t Double p 1 GN p 1 `Pl 2 - Naive cut off at lpl: t Double 10 43 s 69

Cosmological Constant Problem Without gravity constant energies (Λ) can be ignored (overall offset) With gravity, constant energy warps space-time, interacts gravitationally Uniform matter/energy controls size/expansion of overall Universe t Double p 1 GN p 1 `Pl 2 - Naive cut off at lpl: t Double 10 43 s (would be bad for atoms/planets/people ) 70

Cosmological Constant Problem Without gravity constant energies (Λ) can be ignored (overall offset) With gravity, constant energy warps space-time, interacts gravitationally Uniform matter/energy controls size/expansion of overall Universe t Double p 1 GN p 1 `Pl 2 - Naive cut off at lpl: t Double 10 43 s (would be bad for atoms/planets/people ) - Conservative cut-off at 100 GeV: t Double 10 ns 71

Cosmological Constant Problem Without gravity constant energies (Λ) can be ignored (overall offset) With gravity, constant energy warps space-time, interacts gravitationally Uniform matter/energy controls size/expansion of overall Universe t Double p 1 GN p 1 `Pl 2 - Naive cut off at lpl: t Double 10 43 s (would be bad for atoms/planets/people ) - Conservative cut-off at 100 GeV: t Double 10 ns (would be bad for atoms(?)/planets/people ) 72

Cosmological Constant Problem Without gravity constant energies (Λ) can be ignored (overall offset) With gravity, constant energy warps space-time, interacts gravitationally Uniform matter/energy controls size/expansion of overall Universe t Double p 1 GN p 1 `Pl 2 - Naive cut off at lpl: t Double 10 43 s (would be bad for atoms/planets/people ) - Conservative cut-off at 100 GeV: t Double 10 ns (would be bad for atoms(?)/planets/people ) Measured: t Double 10 10 years cut off of 10µm! 73

Cosmological Constant Problem Without gravity constant energies (Λ) can be ignored (overall offset) With gravity, constant energy warps space-time, interacts gravitationally Uniform matter/energy controls size/expansion of overall Universe t Double p 1 GN p 1 Clearly something wrong! `Pl 2 - Naive cut off at lpl: t Double 10 43 s (would be bad for atoms/planets/people ) - Conservative cut-off at 100 GeV: t Double 10 ns (would be bad for atoms(?)/planets/people ) Measured: t Double 10 10 years cut off of 10µm! 74

Cosmological Constant Problem How do we deal with this in the current theory? 75

Cosmological Constant Problem How do we deal with this in the current theory? Λ = ΛQM + ΛClassical 76

Cosmological Constant Problem How do we deal with this in the current theory? from the vacuum fluctuations Λ = ΛQM + ΛClassical 77

Cosmological Constant Problem How do we deal with this in the current theory? from the vacuum fluctuations Λ = ΛQM + ΛClassical Constant. Input parameter to theory 78

Cosmological Constant Problem How do we deal with this in the current theory? from the vacuum fluctuations Λ = ΛQM + ΛClassical Constant. Input parameter to theory = 3. 342 862 210 554 `Pl 4 120 digits ΛQM 79

Cosmological Constant Problem How do we deal with this in the current theory? from the vacuum fluctuations Λ = ΛQM + ΛClassical Constant. Input parameter to theory = 3. 342 862 210 554 `Pl 4 + 120 digits ΛQM - 3. 342 862 210 541 `Pl 4 120 digits ΛClassical 80

Cosmological Constant Problem How do we deal with this in the current theory? Λ = ΛQM + ΛClassical Fine Tuning from the vacuum fluctuations = 3. 342 862 210 554 Constant. Input parameter to theory `Pl 4 + 120 digits ΛQM - 3. 342 862 210 541 `Pl 4 120 digits ΛClassical 81

Cosmological Constant Problem How do we deal with this in the current theory? Λ = ΛQM + ΛClassical Fine Tuning 10 20 GeV 1 (10 36 m) Planck scale from the vacuum fluctuations = 3. 342 862 210 554 + 10 3 GeV 1 (10 19 m) weak scale 120 digits? - 3. 342 862 210 541 Constant. Input parameter to theory 4 `Pl 10 41 GeV 1 ΛQM(10 25 m) ΛQM Hubble scale `Pl 4 120 digits Why is the universe so big? ΛClassical ΛClassical 82

Vacuum Fluctuations: Higgs Particle Closely related problem 83

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) h Top h ~ Λ² mh 10 20 GeV 84

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) h Top h ~ Λ² mh 10 20 GeV 85

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) mh² = 2.569678321 554 60 digits `Pl 2 Top h h ~ Λ² mh 10 20 GeV 86

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) mh² = 2.569678321 554 + 60 digits - 2.569678321 453 60 digits `Pl 2 `Pl 2 Top h h ~ Λ² mh 10 20 GeV 87

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) mh² = 2.569678321 554 + 60 digits - 2.569678321 453 60 digits `Pl 2 `Pl 2 - Estimated mass corrections unreasonably large - Instability of the Higgs mass Top h h ~ Λ² mh 10 20 GeV 88

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) mh² = 2.569678321 554 + 60 digits - 2.569678321 453 60 digits `Pl 2 `Pl 2 - Estimated mass corrections unreasonably large - Instability of the Higgs mass h new heavy particle h Top ~ Λ² mh 10 20 GeV h mh ~ m h 89

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) mh² = 2.569678321 554 + 60 digits - 2.569678321 453 60 digits `Pl 2 `Pl 2 - Estimated mass corrections unreasonably large - Instability of the Higgs mass h Top ~ Λ² mh 10 20 GeV new heavy particle h h mh ~ m h 90

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) Without small scale physics (only gravity + pencil DoF) - Bizarre, but stable + - Suggests fine 60 tuning digits mh² = 2.569678321 554-2.569678321 453 60 digits `Pl 2 `Pl 2 - Estimated mass corrections unreasonably large - Instability of the Higgs mass h Top ~ Λ² mh 10 20 GeV new heavy particle h h mh ~ m h 91

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) Without small scale physics (only gravity + pencil DoF) - Bizarre, but stable + - Suggests fine 60 tuning digits mh² = 2.569678321 554-2.569678321 453 60 digits Top Including 2 physics h at smaller scales h (vibrations/ `Pl air molecules / atoms) - Quickly lead to instability ~ Λ² mh 10 20 GeV - Suggests active mechanism (eg: glue / string) `Pl 2 - Estimated mass corrections unreasonably large - Instability of the Higgs mass new heavy particle h mh ~ m h 92

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) Without small scale physics (only gravity + pencil DoF) - Bizarre, but stable + - Suggests fine 60 tuning digits mh² = 2.569678321 554-2.569678321 453 Top Including 2 physics h at smaller scales h (vibrations/ `Pl air molecules / atoms) - Quickly lead to instability ~ Λ² mh 10 20 GeV - Suggests active mechanism (eg: glue / string) `Pl 2 Higgs mass in SM Higgs mass including new, 60 digits high new mass heavy scale physics particle mh ~ m - Estimated mass corrections unreasonably large - Instability of the Higgs mass h h 93

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) mh² = 2.569678321 554 + 60 digits - 2.569678321 453 60 digits `Pl 2 `Pl 2 - Estimated mass corrections unreasonably large - Instability of the Higgs mass h new heavy particle h Top ~ Λ² mh 10 20 GeV h mh ~ m h 94

Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) mh² = 2.569678321 554 + 60 digits - 2.569678321 453 60 digits `Pl 2 `Pl 2 - Estimated mass corrections unreasonably large - Instability of the Higgs mass h Particular to Spin-0 particles - Spin 1/2 Protected by charge conservation. Need interactions with v to get their mass - Spin 1, 3/2, 2: need needed the extra particles ω/ω-from h Top ~ Λ² mh 10 20 GeV new heavy particle h mh ~ m h 95

Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can perform similar estimate for scale of interaction with condensate v Same logic Scale should be set by the cut-off in the theory 96

Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can perform similar estimate for scale of interaction with condensate v Same logic Scale should be set by the cut-off in the theory 97

Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can perform similar estimate for scale of interaction with condensate v Same logic Scale should be set by the cut-off in the theory 1 98

Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can perform similar estimate for scale of interaction with condensate v Same logic Scale should be set by the cut-off in the theory 1 Naively, Λ ~ lpl : 1 `Pl 10 20 GeV 1 10 36 m 99

100 Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can perform similar estimate for scale of interaction with condensate v Same logic Scale should be set by the cut-off in the theory 1 Naively, Λ ~ lpl : 1 `Pl 10 20 GeV 1 10 36 m Measured scale of: 10 3 GeV 1 10 19 m

101 Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can perform similar estimate for scale of interaction with condensate v Same logic Scale should be set by the cut-off in the theory 1 Naively, Λ ~ lpl : 1 `Pl 10 20 GeV 1 10 36 m Measured scale of: 10 3 GeV 1 10 19 m Λ ~ lpl would be bad for atoms/planets/people all blackholes

102 Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can perform similar estimate for scale of interaction with condensate v Same logic Scale should be set by the cut-off in the theory 1 Naively, Λ ~ lpl : 1 `Pl 10 20 GeV 1 10 36 m Measured scale of: 10 3 GeV 1 10 19 m Λ ~ lpl would be bad for atoms/planets/people all blackholes F G F EM (`Pl 2 2 )

Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can perform similar estimate for scale of interaction with condensate v Same logic Scale should be set by the cut-off in the theory 1 Naively, Λ ~ lpl : 1 `Pl 10 20 GeV 1 10 36 m Measured scale of: 10 3 GeV 1 10 19 m Λ ~ lpl would be bad for atoms/planets/people all blackholes Expect: ~ 1 F G F EM (`Pl 2 2 ) 103

Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can perform similar estimate for scale of interaction with condensate v Same logic Scale should be set by the cut-off in the theory 1 Naively, Λ ~ lpl : 1 `Pl 10 20 GeV 1 10 36 m Measured scale of: 10 3 GeV 1 10 19 m Λ ~ lpl would be bad for atoms/planets/people all blackholes Expect: ~ 1 F G F EM (`Pl 2 2 ) Observe: 10 34 104

Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can perform similar estimate for scale of interaction with condensate v Same logic Scale should be set by the cut-off in the theory 1 Naively, Λ ~ lpl : 1 `Pl 10 20 GeV 1 10 36 m Measured scale of: 10 3 GeV 1 10 19 m Λ ~ lpl would be bad for atoms/planets/people all blackholes Expect: ~ 1 F G F EM (`Pl 2 2 ) Observe: Why is gravity so weak? 10 34 105

Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can Weakness perform similar of gravity estimate directly for scale responsible of interaction with condensate v Same logic Scale should be set by the cut-off in the theory ~ all structure around us R Planet q R Animal G r atom 1 1 4 Naively, r Λ ~ lpl : G atom 1 `Pl Measured scale of: 10 3 GeV 1 10 19 m 10 20 GeV 1 10 36 m (Stars ) Λ ~ lpl would be bad for atoms/planets/people all blackholes Expect: ~ 1 F G F EM (`Pl 2 2 ) Observe: Why is gravity so weak? 10 34 106

Vacuum Fluctuations: Higgs Field Another way of talking about same problem Can Weakness perform similar of gravity estimate directly for scale responsible of interaction with condensate v Same logic Scale should be set by the cut-off in the theory ~ all structure around us R Planet q R Animal 10 20 GeV 1 (10 36 m) Planck scale G 1 1 4 Naively, r Λ ~ lpl : G atom 10 3 GeV 1 (10 19 m) r atom 1 `Pl Measured scale of: 10 3 GeV 1 10 19 m weak scale 10 20 GeV 1 10 36 m (Stars ) Λ ~ lpl would be bad for atoms/planets/people Hierarchy Problem all blackholes F G F EM (`Pl 2 2 Expect: ~ 1? ) Why is gravity so weak? Observe: Why is gravity so weak? 10 34 10 41 GeV 1 (10 25 m) Hubble scale 107

108 Length Scales Quantum Mechanics + Space-time leads us to expect: Planck scale ~ weak scale ~ Hubble scale

109 Length Scales Quantum Mechanics + Space-time leads us to expect: Planck scale ~ weak scale ~ Hubble scale We observe: 10 17 10 44 Planck scale weak scale Hubble scale

110 Length Scales Quantum Mechanics + Space-time leads us to expect: Planck scale ~ weak scale ~ Hubble scale We observe: 10 17 10 44 Planck scale weak scale Hubble scale Current theory accounts for huge difference w/implausible cancellation Need modifications QM or Space-time to avoid fine tuning

111 Length Scales Quantum Mechanics + Space-time leads us to expect: Planck scale ~ weak scale ~ Hubble scale We observe: 10 17 10 44 Planck scale weak scale Hubble scale Current theory accounts for huge difference w/implausible cancellation Need modifications QM or Space-time to avoid fine tuning

112 What scale do we need Modification? mh = +

113 What scale do we need Modification? mh = + ~ weak-scale mhclassical ~ Λ²

114 What scale do we need Modification? mh = + ~ weak-scale mhclassical ~ Λ² Can avoid need for fine tuning only if Λ ~ weak-scale.

115 What scale do we need Modification? mh = + ~ weak-scale mhclassical ~ Λ² Can avoid need for fine tuning only if Λ ~ weak-scale. Need changes to stop vacuum fluctuations below: 10 3 GeV 1 (10 19 m)

116 What scale do we need Modification? mh = + ~ weak-scale mhclassical ~ Λ² Can avoid need for fine tuning only if Λ ~ weak-scale. Need changes to stop vacuum fluctuations below: 10 3 GeV 1 (10 19 m) new particle h m ~ 1000 GeV h

Dark Matter 117

118 Dark Matter Most natural explanation requires new physics at 10 3 GeV 1 (10 19 m)