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

Transcription

1 How and Why to go Beyond the Discovery of the Higgs Boson John Alison University of Chicago

2 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

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

4 Reminder: Last Week 2012: Discovered new particle consistent with expectations κ F v F m or κ V v V m ATLAS s = 7 TeV, fb s = 8 TeV, 20.3 fb Observed SM Expected -1-1 W Z t µ τ b Fig. 12 Confidence intervals in the (µ,m H ) plan n 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

5 What it Took: In Numbers - >10,000 scientists and engineers from 85 countries - 27 kilometer particle accelerator - Protons moving at % 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

6 What it Took: In Numbers - >10,000 scientists and engineers from 85 countries - 27 kilometer particle accelerator - Protons moving at % 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

7 What it Took: In Numbers - >10,000 scientists and engineers from 85 countries - 27 kilometer particle accelerator - Protons moving at % 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

8 What it Took: In Numbers - >10,000 scientists and engineers from 85 countries - 27 kilometer particle accelerator - Protons moving at % 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

9 What it Took: In Numbers - >10,000 scientists and engineers from 85 countries - 27 kilometer particle accelerator - Protons moving at % 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

10 Today s Lecture Problems with the Standard Model 10

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

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

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

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

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

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

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

18 (In principle) Failure WW scattering ~unexplored LHC Length Scales Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally GeV 1 (10 36 m) weak-scale nuclei Planck ( p scale G N ) atoms cells 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

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

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

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

22 (In principle) Failure WW scattering ~unexplored Fundamental Length Scales LHC Standard Model (After Higgs Discovery) Standard Model (Before Higgs Discovery) Directly Probed Experimentally GeV 1 (10 36 m) 10 3 GeV 1 (10 19 m) 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

23 (In principle) Failure WW scattering ~unexplored 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 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

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

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

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

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

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

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

30 Problem with the Planck Scale 30

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

32 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

33 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 G N (l Pl ) 2 (10 20 GeV 1 ) 2 1 Distance GeV 1 m p 33

34 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 G N (l Pl ) 2 (10 20 GeV 1 ) 2 1 Distance GeV 1 m p 34

35 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 G N (l Pl ) 2 (10 20 GeV 1 ) 2 1 Distance GeV 1 m p 35

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

37 37 Probing Smaller Distance Scales GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 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 38 Probing Smaller Distance Scales GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 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 39 Probing Smaller Distance Scales GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 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 40 Probing Smaller Distance Scales GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 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

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 41

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 42

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 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

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 m 1 r r p G N l Pl 44

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 45

46 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

47 Probing Smaller Distance Scales GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 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

48 Probing Smaller Distance Scales GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 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

49 Probing Smaller Distance Scales GeV 1 (10 36 m) Planck 10 3 GeV 1 (10 19 m) Weak 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

50 Probing Smaller Distance Scales GeV 1 (10 36 m) 10 3 GeV 1 (10 19 m) Lower Limit to Spacetime 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

51 Problems with Weak and Hubble Scales 51

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

53 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

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

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

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

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

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

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 Λ ~ E/V ~ 1/L^4 (V ~ L³) (E ~ 1/L) 59

60 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

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 ) 61

62 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

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 L L E V 1 L 4 (V L 3 ) (E 1 L ) Λ much bigger 63

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 Λ much bigger V 1 1 L 4 (V L 3 ) (E 1 L ) `Pl 4 64

65 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

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) 66

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 Doubling time ~ 1/ (GN Λ) ~1 (lpl² Λ) 67

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 1 p GN 1 p `Pl 2 68

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 s 69

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 s (would be bad for atoms/planets/people ) 70

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 s (would be bad for atoms/planets/people ) - Conservative cut-off at 100 GeV: t Double 10 ns 71

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 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

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 `Pl 2 - Naive cut off at lpl: t Double 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 years cut off of 10µm! 73

74 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 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 years cut off of 10µm! 74

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

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

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

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 78

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 = `Pl digits ΛQM 79

80 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 = `Pl digits ΛQM `Pl digits ΛClassical 80

81 Cosmological Constant Problem How do we deal with this in the current theory? Λ = ΛQM + ΛClassical Fine Tuning from the vacuum fluctuations = Constant. Input parameter to theory `Pl digits ΛQM `Pl digits ΛClassical 81

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

83 Vacuum Fluctuations: Higgs Particle Closely related problem 83

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

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

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

87 Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) mh² = digits digits `Pl 2 `Pl 2 Top h h ~ Λ² mh GeV 87

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

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

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

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 = digits `Pl 2 `Pl 2 - Estimated mass corrections unreasonably large - Instability of the Higgs mass h Top ~ Λ² mh GeV new heavy particle h h mh ~ m h 91

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 = digits Top Including 2 physics h at smaller scales h (vibrations/ `Pl air molecules / atoms) - Quickly lead to instability ~ Λ² mh 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

93 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 = Top Including 2 physics h at smaller scales h (vibrations/ `Pl air molecules / atoms) - Quickly lead to instability ~ Λ² mh 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

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

95 Vacuum Fluctuations: Higgs Particle Closely related problem Vacuum fluctuations of Higgs mass (mh²) mh² = digits 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 GeV new heavy particle h mh ~ m h 95

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 96

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 97

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 98

99 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 GeV m 99

100 100 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 GeV m Measured scale of: 10 3 GeV m

101 101 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 GeV m Measured scale of: 10 3 GeV m Λ ~ lpl would be bad for atoms/planets/people all blackholes

102 102 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 GeV m Measured scale of: 10 3 GeV m Λ ~ lpl would be bad for atoms/planets/people all blackholes 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 GeV m Measured scale of: 10 3 GeV m Λ ~ lpl would be bad for atoms/planets/people all blackholes Expect: ~ 1 F G F EM (`Pl 2 2 ) 103

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 GeV m Measured scale of: 10 3 GeV m Λ ~ lpl would be bad for atoms/planets/people all blackholes Expect: ~ 1 F G F EM (`Pl 2 2 ) Observe:

105 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 GeV m Measured scale of: 10 3 GeV 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?

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 G r atom Naively, r Λ ~ lpl : G atom 1 `Pl Measured scale of: 10 3 GeV m GeV 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?

107 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 GeV 1 (10 36 m) Planck scale G Naively, r Λ ~ lpl : G atom 10 3 GeV 1 (10 19 m) r atom 1 `Pl Measured scale of: 10 3 GeV m weak scale GeV 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? GeV 1 (10 25 m) Hubble scale 107

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

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

110 110 Length Scales Quantum Mechanics + Space-time leads us to expect: Planck scale ~ weak scale ~ Hubble scale We observe: 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

111 111 Length Scales Quantum Mechanics + Space-time leads us to expect: Planck scale ~ weak scale ~ Hubble scale We observe: 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

112 112 What scale do we need Modification? mh = +

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

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

115 115 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)

116 116 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

117 Dark Matter 117

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