String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 - - PowerPoint PPT Presentation
String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 Friday, April 20, 12 String Theory in the LHC Era 1. Electromagnetism and 5. Supersymmetry Special Relativity 2. The Quantum World 6. Einsteins Gravity 3. Why do we need
1
J Marsano (marsano@uchicago.edu)
Friday, April 20, 12
Special Relativity
2
Friday, April 20, 12
3
Richard Feynman Julian Schwinger Sin-Itiro Tomonoga
L ∼ ¯ ψ (iγµDµ − m) ψ − 1 4e2 FµνF µν
Photon Electron Charge Electron mass
Friday, April 20, 12
4
L ∼ ¯ ψ (iγµDµ − m) ψ − 1 4e2 FµνF µν
Photon Electron Charge Electron mass
Friday, April 20, 12
5
Friday, April 20, 12
6
Test to see if various materials glow when exposed to sunlight ...weather was cloudy for several days led to discovery of natural radioactivity!
Friday, April 20, 12
7
Pierre Curie Marie Curie
Friday, April 20, 12
8
Decay classified according to penetration depth
Ernest Rutherford
Sheet of paper Aluminum Lead
Friday, April 20, 12
8
Decay classified according to penetration depth
Photons He nuclei Electrons Ernest Rutherford
Sheet of paper Aluminum Lead
Friday, April 20, 12
9
Decays can change one element into another
Frederick Soddy Ernest Rutherford
e.g. β decay +e− + . . .
60 27Co → 60 28Ni
Friday, April 20, 12
9
Decays can change one element into another
Frederick Soddy Ernest Rutherford
e.g. β decay +e− + . . .
60 27Co → 60 28Ni
# protons + neutrons # protons
Friday, April 20, 12
10
+ e− + . . .
Electron energy should be fixed by change in atomic mass
60 27Co → 60 28Ni
n → p+ + e− + . . .
Friday, April 20, 12
10
+ e− + . . .
Electron energy should be fixed by change in atomic mass
...but it isn’t...varies continuously ...something else is carrying away energy
60 27Co → 60 28Ni
n → p+ + e− + . . .
Friday, April 20, 12
11
Neutrino! Wolfgang Pauli Enrico Fermi
60 27Co → 60 28Ni + e− + νe
Friday, April 20, 12
12
Enrico Fermi
Interaction strength
GF (~c)3 = 1.11637(1) × 10−5 GeV −2 ∼ 1 (300 GeV )2
Fermi constant
60 27Co → 60 28Ni
e− n → p+ + e− + νe n p+
νe
+ e− + νe
Friday, April 20, 12
13
Interaction strength
GF (~c)3 = 1.11637(1) × 10−5 GeV −2 ∼ 1 (300 GeV )2
Fermi constant
Conventional to choose units so that ~ = c = 1 E = hc λ → E ∼ 1 λ
Friday, April 20, 12
13
Interaction strength
GF (~c)3 = 1.11637(1) × 10−5 GeV −2 ∼ 1 (300 GeV )2
Fermi constant
Conventional to choose units so that ~ = c = 1 E = hc λ → E ∼ 1 λ Energy = 1 Distance
Friday, April 20, 12
13
Interaction strength
GF (~c)3 = 1.11637(1) × 10−5 GeV −2 ∼ 1 (300 GeV )2
Fermi constant
Conventional to choose units so that ~ = c = 1 E = hc λ → E ∼ 1 λ Energy = 1 Distance e ∼ r 4π 137
Fermi interaction Electromagnetic interaction
mproton ∼ 0.938 GeV
GF ∼ 1 (300 GeV)2 ∼
2 `proton ∼ 10−13 cm
Friday, April 20, 12
14
No units No characteristic length or energy scale Physical length/energy scale
(Length)2 ∼ (Energy)−2
‘Short range force’ ‘Long range force’
e ∼ r 4π 137
Fermi interaction Electromagnetic interaction
mproton ∼ 0.938 GeV
GF ∼ 1 (300 GeV)2 ∼
2 `proton ∼ 10−13 cm
Friday, April 20, 12
14
No units No characteristic length or energy scale Physical length/energy scale
(Length)2 ∼ (Energy)−2
‘Short range force’ ‘Long range force’
Some funny business around 100 GeV
e ∼ r 4π 137
Fermi interaction Electromagnetic interaction
mproton ∼ 0.938 GeV
GF ∼ 1 (300 GeV)2 ∼
2 `proton ∼ 10−13 cm
Friday, April 20, 12
15
+ e− + νe
60 27Co → 60 28Ni
Friday, April 20, 12
16
60 27Co → 60 28Ni
Friday, April 20, 12
17
Friday, April 20, 12
18
Parity is essentially reflection in a mirror flips right and left
Looking right Looking left For years people assumed that our world respected parity
i.e. the laws of physics do not distinguish right from left
Real world ‘Mirror’ world
Friday, April 20, 12
19
Photo Credit: Alan W. Richards from physics.nist.gov
Yang
Parity seems natural Why should right and left be different?
In 1956, Lee and Yang pointed out that parity of weak interactions hadn’t been strongly tested Many people doubted that parity could actually be violated
Friday, April 20, 12
19
Photo Credit: Alan W. Richards from physics.nist.gov
Yang
Parity seems natural Why should right and left be different?
In 1956, Lee and Yang pointed out that parity of weak interactions hadn’t been strongly tested Many people doubted that parity could actually be violated Feynman bet $50 that parity is not violated in nature
Friday, April 20, 12
20
Photo Credit: Alan W. Richards from physics.nist.gov
Yang
Lee and Yang suggested several experimental tests
Spin
Use fact that parity flips the spin of a particle
Real world ‘Mirror’ world Spin
Friday, April 20, 12
21
Chien-Shiung Wu
60 27Co Nuclei
Spinning
β rays (electrons)
Parity = ⇒ same # of e− going ↑ and ↓
Real world ‘Mirror’ world
Friday, April 20, 12
21
Chien-Shiung Wu
60 27Co Nuclei
Spinning
β rays (electrons)
Parity = ⇒ same # of e− going ↑ and ↓
Left ⬌ Right flips direction of spin
Real world ‘Mirror’ world
Friday, April 20, 12
22
Chien-Shiung Wu
In reality, see more going ↓ than ↑!
60 27Co Nuclei
Spinning
β rays (electrons)
Real world ‘Mirror’ world
Friday, April 20, 12
22
Chien-Shiung Wu
In reality, see more going ↓ than ↑!
60 27Co Nuclei
Spinning
β rays (electrons)
Real world ‘Mirror’ world
Different result in real and mirror worlds
Friday, April 20, 12
23
Chien-Shiung Wu
Yang
Weak interactions can tell right from left!
Friday, April 20, 12
24
→ Weak interactions distinguish left- and right-handed particles
Weak interactions can tell right from left! Spin Momentum Spin Momentum
Participate in Weak Interaction DO NOT Participate in Weak Interaction
Friday, April 20, 12
25
Spin
For a massive particle, the direction of motion depends on the observer!
Looks left-handed to us but if the race car is moving fast enough...... Momentum that we see Race car speed
Friday, April 20, 12
25
Spin
For a massive particle, the direction of motion depends on the observer!
Looks left-handed to us but if the race car is moving fast enough...... Momentum that we see Race car speed Momentum seen by race car
Particle looks right-handed to the race car!
Friday, April 20, 12
26
Spin
For a massive particle, the direction of motion depends on the observer!
We think the left-handed particle should participate in Weak Interaction Momentum that we see Race car speed Momentum seen by race car Race car thinks right-handed particle should not participate in Weak Interaction
Friday, April 20, 12
27
Spin Momentum that we see Race car speed Momentum seen by race car
If particle is massless, it moves at speed of light
Race car can never ‘catch up’ to it we always agree on the ‘handedness’
Friday, April 20, 12
28
to right-handed particles
→ ALL PARTICLES MUST BE FUNDAMENTALLY MASSLESS
Spin Momentum Spin Momentum right-handed left-handed
Friday, April 20, 12
29
→ ALL PARTICLES MUST BE FUNDAMENTALLY MASSLESS
Friday, April 20, 12
30
Start with massless ‘right-handed’ and ‘left-handed’ electrons
eL eR
h
eR and eL
Add a new ‘Higgs field’ that couples to them
Friday, April 20, 12
30
Start with massless ‘right-handed’ and ‘left-handed’ electrons
eL eR
h
eR and eL
Add a new ‘Higgs field’ that couples to them
Electrons can acquire a mass if the vacuum has a ‘bath’ of Higgs fields Like having a constant electric field everywhere in the universe
→ Higgs boson is a small fluctuation of this field
Friday, April 20, 12
31
Crowded room of physicists Einstein walks in People crowd around Einstein and slow him down (Higgs bath in vacuum) (Particle comes along) (Particle becomes massive)
Cartoons from CERN
Friday, April 20, 12
32
Cartoons from CERN
Someone introduces a rumor in the room, say some new discovery at CERN Physicists cluster as the rumor passes through the room (A small excitation is introduced) (The excitation, a Higgs boson, propagates in the room)
Friday, April 20, 12
33
interacting with the ‘Higgs bath’
carries ‘weak charge’
→ REQUIRES FUNDAMENTAL SCALAR PARTICLE: HIGGS BOSON
Spin Momentum Spin Momentum right-handed left-handed
Friday, April 20, 12
34
Peter Higgs Tom Kibble Gerald Guralnik C Richard Hagen Francois Englert Robert Brout
Friday, April 20, 12
35
Friday, April 20, 12
36
Enrico Fermi
Interaction strength
GF ∼ 1 (300 GeV)2
Fermi’s theory is badly behaved if we do scattering experiments at energies much beyond 300 GeV
n → p+ + e− + νe e−
n
p+ νe
Friday, April 20, 12
37
GF ∼ 1 (300 GeV)2
Fermi’s theory is badly behaved if we do scattering experiments at energies much beyond 300 GeV → violates ‘unitarity’
If we sum the probabilities of everything that can happen in a given experiment, the answer better be 1 (i.e. 100%)
Fermi’s theory starts violating this condition for scattering experiments at energies much beyond 300 GeV
e− n p+ νe
Friday, April 20, 12
38
GF ∼ 1 (300 GeV)2
If we sum the probabilities of everything that can happen in a given experiment, the answer better be 1 (i.e. 100%)
Fermi’s theory starts violating this condition for scattering experiments at energies much beyond 300 GeV Very roughly, grows too large at large energy E
e− n p+ νe ’Probability’ ∼ GF E2 ∼ ✓ E 300 GeV ◆2
Friday, April 20, 12
39
GF ∼ 1 (300 GeV)2
Fermi’s theory is an ‘effective theory’, valid only at low enough energies
New physics must appear before we get far above 300 GeV. ‘Naturalness‘ principle says that the new physics should appear very close to 300 GeV
e− n p+ νe
Friday, April 20, 12
40
At high energies, it becomes evident that Fermi’s interaction is mediated by a heavy particle
not too far from 300 GeV
e− n p+
νe
e− W − n p+
νe MW ∼ 80 GeV
Friday, April 20, 12
41
νe e− W + νe νe Z0
In fact we get 3 new heavy particles Like massive photons Carriers of ‘Weak nuclear force’ Mass sets ‘distance scale’ of force
e− W − n p+
νe
n → p+ + e− + νe n + νe → p+ + e− p+
n
n + νe → n + νe
n n
MW ∼ 80 GeV MZ ∼ 91 GeV
Friday, April 20, 12
41
νe e− W + νe νe Z0
In fact we get 3 new heavy particles Like massive photons Carriers of ‘Weak nuclear force’ Mass sets ‘distance scale’ of force
e− W − n p+
νe
n → p+ + e− + νe n + νe → p+ + e− p+
n
n + νe → n + νe
n n
MW ∼ 80 GeV MZ ∼ 91 GeV
e− e− e− e− γ
Friday, April 20, 12
42
Carlo Rubbia Simon van der Meer
UA1 and UA2 SPS: Proton-antiproton collider Now injector for LHC
Friday, April 20, 12
43
e−
νe q q
W e− q q Z e+
Friday, April 20, 12
44
Quantum theory tricky
Hard to give mass to vector particles like photon To get an idea why, we return, to the classical electromagnetic wave (an ensemble of photons)
e− W − n p+
νe
n → p+ + e− + νe
Friday, April 20, 12
45
Light has two physical polarizations (ie ways to oscillate)
Electric field oscillates in horizontal direction Electric field oscillates in vertical direction
Friday, April 20, 12
46
In principle, there is a third polarization: Longitudinal polarization
Some parts of slinky move faster than
→ like polarization along direction of motion
Light cannot do this because every part of the wave moves at a fixed ‘speed of light’ and nothing can go faster
...but a wave made from massive force carriers could do this!
Friday, April 20, 12
47
Photon γ
Long range force
→ Electromagnetism
Weak bosons W ±, Z0
Short range force
Range set by 1 Mass of W ±, Z0
→ Weak nuclear force
n νe e− p+ W −
γ e− e−
2 degrees of freedom 3 degrees of freedom
Friday, April 20, 12
47
Photon γ
Long range force
→ Electromagnetism
Weak bosons W ±, Z0
Short range force
Range set by 1 Mass of W ±, Z0
→ Weak nuclear force
n νe e− p+ W −
γ e− e−
2 degrees of freedom 3 degrees of freedom
Extra degree of freedom can cause unitarity problems in quantum theory
Friday, April 20, 12
48
W-W scattering badly behaved around 1 TeV Divergences from the ‘extra longitudinal mode’ Idea: W and Z fundamentally massless Get mass from Higgs bath
Where does the ‘longitudinal mode’ come from?
Friday, April 20, 12
49
Rolls to nonzero field values
→ Generates ‘Higgs bath’
Motion along bottom
→ Longitudinal modes of
Motion up hill
→ ‘Higgs boson’
W ±, Z0
(rough picture)
‘Spontaneous symmetry breaking’
Friday, April 20, 12
50
Without Higgs, W-W scattering badly behaved around 1 TeV Higgs contributions can cure this
Friday, April 20, 12
51
Friday, April 20, 12
51
1.Mass to ordinary particles 2.Mass to carriers of weak nuclear force
Friday, April 20, 12
52
✓A sin θW + Z0 cos θW √ 2W − √ 2W + −A sin θW − Z0 cos θW ◆ ⊗ A cos θW − Z0 sin θW
Weak bosons SU(2) U(1)
Broken to quantum electrodynamics by Higgs mechanism
Steven Weinberg Abdus Salam Sheldon Glashow
Friday, April 20, 12
53
A Toroidal Lhc ApparatuS Compact Muon Solenoid
Friday, April 20, 12
54
Image from CDF website
p p
Friday, April 20, 12
55
Image from CDF website
h → γγ
Friday, April 20, 12
56
Friday, April 20, 12
56
Friday, April 20, 12
57
[GeV]
H
m 110 115 120 125 130 135 140 145 150
SM
10 1 10 Obs. Exp.
±
± = 7 TeV s
Ldt = 4.6-4.9 fb
2011 Data CLs Limits
Higgs boson mass (GeV)
110 115 120 125 130 135 140 145
S
CL
10
10
10 1
90% 95% 99%
L = 4.6-4.8 fb = 7 TeV s CMS,
Observed Expected (68%) Expected (95%)
Friday, April 20, 12
58
electromagnetism
Friday, April 20, 12