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. Einstein’s Gravity 3. Why do we need the Higgs? 7. Why is Quantum Gravity so Hard? 4. The Standard Model and Beyond 8. String Theory and Unification 9. String Theory and Particle Physics 2 Friday, April 20, 12
Quantum Electrodynamics (QED) works incredibly well Electron Photon ψ ( i γ µ D µ − m ) ψ − 1 L ∼ ¯ 4 e 2 F µ ν F µ ν Charge Electron mass Julian Richard Sin-Itiro Schwinger Feynman Tomonoga 3 Friday, April 20, 12
Electron Photon ψ ( i γ µ D µ − m ) ψ − 1 L ∼ ¯ 4 e 2 F µ ν F µ ν Charge Electron mass Mass without Higgs...... so why all the fuss...... 4 Friday, April 20, 12
Quantum Electrodynamics works fine without a Higgs ...but nuclear interactions don’t 5 Friday, April 20, 12
Test to see if various materials glow when exposed to sunlight A. Henri Becquerel ...weather was cloudy for several days led to discovery of natural radioactivity! 6 Friday, April 20, 12
Pierre Curie Marie Curie A. Henri Becquerel Radioactivity! 7 Friday, April 20, 12
Decay classified according to penetration depth Sheet of paper Ernest Rutherford Aluminum Lead 8 Friday, April 20, 12
Decay classified according to penetration depth He nuclei Sheet of paper Ernest Rutherford Aluminum Lead Electrons Photons 8 Friday, April 20, 12
Decays can change one element into another Frederick Soddy Ernest Rutherford e.g. β decay 60 60 27 Co → 28 Ni + e − + . . . 9 Friday, April 20, 12
Decays can change one element into another Frederick Soddy Ernest Rutherford e.g. β decay # protons + neutrons 60 60 27 Co → 28 Ni # protons + e − + . . . 9 Friday, April 20, 12
+ e − + . . . 60 60 27 Co → 28 Ni n → p + + e − + . . . Why? Electron energy should be fixed by change in atomic mass 10 Friday, April 20, 12
+ e − + . . . 60 60 27 Co → 28 Ni n → p + + e − + . . . Why? Electron energy should be fixed by change in atomic mass ...but it isn’t...varies continuously ...something else is carrying away energy G. J. Neary, Roy. Phys. Soc. (London), A175, 71 (1940). 10 Friday, April 20, 12
28 Ni + e − + ν e 60 60 27 Co → Neutrino! Wolfgang Pauli Enrico Fermi 11 Friday, April 20, 12
+ e − + ν e 60 60 27 Co → 28 Ni n → p + + e − + ν e e − p + n Enrico Fermi ν e Interaction strength Fermi constant 1 G F ( ~ c ) 3 = 1 . 11637(1) × 10 − 5 GeV − 2 ∼ (300 GeV ) 2 12 Friday, April 20, 12
Fermi constant Interaction strength G F 1 ( ~ c ) 3 = 1 . 11637(1) × 10 − 5 GeV − 2 ∼ (300 GeV ) 2 Conventional to choose units so that ~ = c = 1 E = hc E ∼ 1 → λ λ 13 Friday, April 20, 12
Fermi constant Interaction strength G F 1 ( ~ c ) 3 = 1 . 11637(1) × 10 − 5 GeV − 2 ∼ (300 GeV ) 2 Conventional to choose units so that ~ = c = 1 1 E = hc E ∼ 1 Energy = → Distance λ λ 13 Friday, April 20, 12
Fermi constant Interaction strength G F 1 ( ~ c ) 3 = 1 . 11637(1) × 10 − 5 GeV − 2 ∼ (300 GeV ) 2 Conventional to choose units so that ~ = c = 1 1 E = hc E ∼ 1 Energy = → Distance λ λ r 1 4 π 10 − 16 cm � 2 � G F ∼ (300 GeV) 2 ∼ e ∼ 137 Fermi interaction Electromagnetic interaction ` proton ∼ 10 − 13 cm m proton ∼ 0 . 938 GeV 13 Friday, April 20, 12
No units No characteristic length or energy scale ‘Long range force’ r 1 4 π 10 − 16 cm � 2 � G F ∼ (300 GeV) 2 ∼ e ∼ 137 Fermi interaction Electromagnetic interaction ` proton ∼ 10 − 13 cm m proton ∼ 0 . 938 GeV (Length) 2 ∼ (Energy) − 2 Physical length/energy scale ‘Short range force’ 14 Friday, April 20, 12
No units No characteristic length or energy scale ‘Long range force’ r 1 4 π 10 − 16 cm � 2 � G F ∼ (300 GeV) 2 ∼ e ∼ 137 Fermi interaction Electromagnetic interaction ` proton ∼ 10 − 13 cm m proton ∼ 0 . 938 GeV (Length) 2 ∼ (Energy) − 2 Some funny business Physical length/energy scale around 100 GeV ‘Short range force’ (more on this later) 14 Friday, April 20, 12
+ e − + ν e 60 60 27 Co → 28 Ni Weak nuclear force Quantum Electrodynamics works perfectly well without a Higgs boson ...but the Weak nuclear force doesn’t! 15 Friday, April 20, 12
60 60 27 Co → 28 Ni Weak nuclear force Focus on two puzzles: • Parity violation (problems with mirrors) • Unitarity violation (problems with probabilities) 16 Friday, April 20, 12
1. Parity Violation (problems with mirrors) 17 Friday, April 20, 12
Parity is essentially reflection in a mirror flips right and left ‘Mirror’ world Real world For years people assumed that our world respected parity i.e. the laws of physics do not distinguish right from left Looking right Looking left 18 Friday, April 20, 12
T. D. Lee 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 Photo Credit: Alan W. Richards from physics.nist.gov C. N. Yang Many people doubted that parity could actually be violated 19 Friday, April 20, 12
T. D. Lee 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 Photo Credit: Alan W. Richards from physics.nist.gov C. N. Yang Many people doubted that parity could actually be violated Feynman bet $50 that parity is not violated in nature 19 Friday, April 20, 12
T. D. Lee Lee and Yang suggested several experimental tests Use fact that parity flips the spin of a particle Photo Credit: Alan W. Richards from physics.nist.gov C. N. Yang ‘Mirror’ world Spin Spin Real world 20 Friday, April 20, 12
same # of e − going ↑ and ↓ Parity = ⇒ Real world ‘Mirror’ world β rays (electrons) Chien-Shiung Wu Spinning 60 27 Co Nuclei 21 Friday, April 20, 12
same # of e − going ↑ and ↓ Parity = ⇒ Real world ‘Mirror’ world β rays (electrons) Chien-Shiung Wu Spinning 60 27 Co Nuclei Left ⬌ Right flips direction of spin 21 Friday, April 20, 12
In reality, see more going ↓ than ↑ ! Real world ‘Mirror’ world β rays (electrons) Chien-Shiung Wu Spinning 60 27 Co Nuclei 22 Friday, April 20, 12
In reality, see more going ↓ than ↑ ! Real world ‘Mirror’ world β rays (electrons) Chien-Shiung Wu Spinning 60 27 Co Nuclei Different result in real and mirror worlds 22 Friday, April 20, 12
T. D. Lee Chien-Shiung Wu Text C. N. Yang Weak interactions can tell right from left! 23 Friday, April 20, 12
Weak interactions can tell right from left! → Weak interactions distinguish left- and right-handed particles Spin Spin Momentum Momentum left-handed right-handed Participate in Weak DO NOT Participate in Weak Interaction Interaction 24 Friday, April 20, 12
For a massive particle, the direction of motion depends on the observer! Momentum that we see Spin Looks left-handed to us but if the race car is moving fast enough...... Race car speed 25 Friday, April 20, 12
For a massive particle, the direction of motion depends on the observer! Momentum that we see Spin Looks left-handed to us but if the race car is moving fast enough...... Momentum seen by race car Race car speed Particle looks right-handed to the race car! 25 Friday, April 20, 12
For a massive particle, the direction of motion depends on the observer! Momentum that we see Spin We think the left-handed particle should participate in Weak Interaction Momentum seen by race car Race car speed Race car thinks right-handed particle should not participate in Weak Interaction 26 Friday, April 20, 12
If particle is massless, it moves at speed of light Momentum that we see Spin Momentum seen by race car Race car speed Race car can never ‘catch up’ to it we always agree on the ‘handedness’ 27 Friday, April 20, 12
Spin Spin Momentum Momentum Summary of Parity Puzzle: left-handed right-handed • Massless particles can be right-handed or left-handed • A massive particle can have either ‘handedness’ depending on the observer • The weak interaction couples only to left-handed and not to right-handed particles → ALL PARTICLES MUST BE FUNDAMENTALLY MASSLESS 28 Friday, April 20, 12
→ ALL PARTICLES MUST BE FUNDAMENTALLY MASSLESS Wait what?!?!?!?!? 29 Friday, April 20, 12
How to generate mass? Start with massless ‘right-handed’ and ‘left-handed’ electrons e R e R and e L e L Add a new ‘Higgs field’ h h that couples to them 30 Friday, April 20, 12
How to generate mass? Start with massless ‘right-handed’ and ‘left-handed’ electrons e R e R and e L e L Add a new ‘Higgs field’ h h 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 30 Friday, April 20, 12
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