String Theory in the LHC Era

Transcription

1 String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1

2 String Theory in the LHC Era 1. Electromagnetism and Special Relativity 2. The Quantum World 3. Why do we need the Higgs? 4. The Standard Model and Beyond 5. Supersymmetry 6. Einstein s Gravity 7. Why is Quantum Gravity so Hard? 8. String Theory and Unification 9. String Theory and Particle Physics 2

3 Quantum Electrodynamics (QED) works incredibly well Electron L (i µ D µ m) Electron mass Photon 1 4e 2 F µ F µ Charge Sin-Itiro Tomonoga Julian Schwinger Richard Feynman 3

4 Electron L (i µ D µ m) Electron mass Photon 1 4e 2 F µ F µ Charge Mass without Higgs... so why all the fuss... 4

5 Quantum Electrodynamics works fine without a Higgs...but nuclear interactions don t 5

6 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

7 Pierre Curie Marie Curie A. Henri Becquerel Radioactivity! 7

8 Decay classified according to penetration depth Sheet of paper Ernest Rutherford Aluminum Lead 8

9 Decay classified according to penetration depth He nuclei Sheet of paper Ernest Rutherford Aluminum Lead Electrons Photons 8

10 Decays can change one element into another Frederick Soddy Ernest Rutherford e.g. decay 60 27Co! 60 28Ni +e

11 Decays can change one element into another Frederick Soddy Ernest Rutherford e.g. decay # protons + neutrons 60 27Co! 60 28Ni # protons +e

12 60 27Co! 60 28Ni + e +... n! p + + e +... Why? Electron energy should be fixed by change in atomic mass 10

13 60 27Co! 60 28Ni + e +... n! p + + e +... Why? Electron energy should be fixed by change in atomic mass...but it isn t...varies continuously G. J. Neary, Roy. Phys. Soc. (London), A175, 71 (1940)....something else is carrying away energy 10

14 60 27Co! 60 28Ni + e + e Neutrino! Wolfgang Pauli 11 Enrico Fermi

15 60 27Co! 60 28Ni + e + e n! p + + e + e e Enrico Fermi n p + e Fermi constant Interaction strength G F (~c) 3 = (1) 10 5 GeV 2 1 (300 GeV ) 2 12

16 Fermi constant Interaction strength G F (~c) 3 = (1) 10 5 GeV 2 1 (300 GeV ) 2 Conventional to choose units so that ~ = c =1 E = hc! E 1 13

17 Fermi constant Interaction strength G F (~c) 3 = (1) 10 5 GeV 2 1 (300 GeV ) 2 Conventional to choose units so that ~ = c =1 E = hc 1 Energy =! E 1 Distance 13

18 Fermi constant Interaction strength G F (~c) 3 = (1) 10 5 GeV 2 1 (300 GeV ) 2 Conventional to choose units so that ~ = c =1 E = hc 1 Energy =! E 1 Distance G F 1 (300 GeV) cm 2 e r Fermi interaction Electromagnetic interaction m proton GeV 13 `proton cm

19 No units No characteristic length or energy scale Long range force G F 1 (300 GeV) cm 2 e r Fermi interaction m proton GeV Electromagnetic interaction `proton cm (Length) 2 (Energy) 2 Physical length/energy scale Short range force 14

20 No units No characteristic length or energy scale Long range force G F 1 (300 GeV) cm 2 e r Fermi interaction m proton GeV Electromagnetic interaction `proton cm (Length) 2 (Energy) 2 Physical length/energy scale Short range force Some funny business around 100 GeV (more on this later) 14

21 60 27Co! 60 28Ni + e + e Weak nuclear force Quantum Electrodynamics works perfectly well without a Higgs boson...but the Weak nuclear force doesn t! 15

22 60 27Co! 60 28Ni Weak nuclear force Focus on two puzzles: Parity violation (problems with mirrors) Unitarity violation (problems with probabilities) 16

23 1. Parity Violation (problems with mirrors) 17

24 Parity is essentially reflection in a mirror flips right and left Real world Mirror 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

25 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 C. N. Yang from physics.nist.gov Many people doubted that parity could actually be violated 19

26 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 C. N. Yang from physics.nist.gov Many people doubted that parity could actually be violated Feynman bet $50 that parity is not violated in nature 19

27 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 C. N. Yang Real world from physics.nist.gov Spin Spin Mirror world 20

28 Parity =) same # of e going " and # Real world Mirror world rays (electrons) Spinning 60 27Co Nuclei Chien-Shiung Wu 21

29 Parity =) same # of e going " and # Real world Mirror world rays (electrons) Spinning 60 27Co Nuclei Chien-Shiung Wu Left Right flips direction of spin 21

30 In reality, see more going # than "! Real world Mirror world rays (electrons) Spinning 60 27Co Nuclei Chien-Shiung Wu 22

31 In reality, see more going # than "! Real world Mirror world rays (electrons) Spinning 60 27Co Nuclei Chien-Shiung Wu Different result in real and mirror worlds 22

32 T. D. Lee Text Chien-Shiung Wu C. N. Yang Weak interactions can tell right from left! 23

33 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 Interaction 24 DO NOT Participate in Weak Interaction

34 For a massive particle, the direction of motion depends on the observer! Momentum that we see Looks left-handed to us but if the race car is moving fast enough... Spin Race car speed 25

35 For a massive particle, the direction of motion depends on the observer! Momentum that we see Looks left-handed to us but if the race car is moving fast enough... Spin Momentum seen by race car Race car speed Particle looks right-handed to the race car! 25

36 For a massive particle, the direction of motion depends on the observer! Momentum that we see We think the left-handed particle should participate in Weak Interaction Spin Momentum seen by race car Race car speed Race car thinks right-handed particle should not participate in Weak Interaction 26

37 If particle is massless, it moves at speed of light Momentum that we see Spin Momentum seen by race car Race car speed 27 Race car can never catch up to it we always agree on the handedness

38 Spin Spin Summary of Parity Puzzle: Momentum Momentum 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

39 ALL PARTICLES MUST BE FUNDAMENTALLY MASSLESS Wait what?!?!?!?!? 29

40 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 that couples to them h h 30

41 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 that couples to them h h 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

42 Crowded room of physicists (Higgs bath in vacuum) Einstein walks in (Particle comes along) Cartoons from CERN People crowd around Einstein and slow him down 31 (Particle becomes massive)

43 What about the Higgs boson? Someone introduces a rumor in the room, say some new discovery at CERN (A small excitation is introduced) Physicists cluster as the rumor passes through the room (The excitation, a Higgs boson, propagates in the room) Cartoons from CERN 32

44 Spin Spin Resolution of Parity Puzzle: Momentum Momentum left-handed right-handed Massless (charged) particles are right-handed or left-handed Pairs of massless particles can become massive by interacting with the Higgs bath Weak force can violate parity because the Higgs field carries weak charge REQUIRES FUNDAMENTAL SCALAR PARTICLE: HIGGS BOSON 33

45 Not just Higgs...3 Papers and 6 Authors First Francois Englert Robert Brout Peter Higgs Tom Kibble Gerald Guralnik C Richard Hagen Second 34 Third

46 2. Unitarity Violation (problems with probabilities) 35

47 n! p + + e + e e n p + e Enrico Fermi Interaction strength G F 1 (300 GeV) 2 Fermi s theory is badly behaved if we do scattering experiments at energies much beyond 300 GeV 36

48 Fermi s theory is badly behaved if we do scattering experiments at energies much beyond 300 GeV violates unitarity Unitarity If we sum the probabilities of everything that can happen in a given experiment, the answer better be 1 (i.e. 100%) n e G F 1 (300 GeV) 2 e p + Fermi s theory starts violating this condition for scattering experiments at energies much beyond 300 GeV 37

49 Unitarity If we sum the probabilities of everything that can happen in a given experiment, the answer better be 1 (i.e. 100%) n e G F 1 (300 GeV) 2 e p + Fermi s theory starts violating this condition for scattering experiments at energies much beyond 300 GeV Very roughly, Probability G F E 2 E 300 GeV 2 grows too large at large energy E 38

50 Naturalness G F 1 (300 GeV) 2 n e e p + 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 39

51 n p + e At high energies, it becomes evident that Fermi s interaction is mediated by a heavy particle e p + M W 80 GeV n W not too far from 300 GeV e e 40

52 p + M W 80 GeV p + n W e n W + e e n! p + + e + e n + e! p + + e e In fact we get 3 new heavy particles Like massive photons Carriers of Weak nuclear force n Z 0 e n M Z 91 GeV Mass sets distance scale of force e n + e! n + e 41

53 p + M W 80 GeV p + n W e n W + e e n! p + + e + e n + e! p + + e e In fact we get 3 new heavy particles e e Like massive photons Carriers of Weak nuclear e force n Z 0 e n M Z 91 GeV Mass e sets distance scale of force e n + e! n + e 41

54 W and Z bosons discovered at CERN in 1983 Carlo Rubbia Simon van der Meer UA1 and UA2 SPS: Proton-antiproton collider Now injector for LHC 42

55 q W e q Z e q e q e + 43

56 p + Quantum theory tricky n W Hard to give mass to vector particles like photon e n! p + + e e + e To get an idea why, we return, to the classical electromagnetic wave (an ensemble of photons) 44

57 Light has two physical polarizations (ie ways to oscillate) Electric field oscillates in horizontal direction Electric field oscillates in vertical direction 45

58 In principle, there is a third polarization: Longitudinal polarization Some parts of slinky move faster than others...gives a lump that propagates 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! 46

59 Massless force carriers Photon Massive force carriers Weak bosons W ±,Z 0 2 degrees of freedom 3 degrees of freedom Long range force Short range force Range set by 1 Mass of W ±,Z 0 Electromagnetism Weak nuclear force p + n W e e e 47 e

60 Massless force carriers Photon Massive force carriers Weak bosons W ±,Z 0 2 degrees of freedom 3 degrees of freedom Extra degree of freedom can cause Long range force unitarity problems in quantum Short range force theory Range set by 1 Mass of W ±,Z 0 Electromagnetism Weak nuclear force p + n W e e e 47 e

61 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? 48

62 Higgs to the rescue (rough picture) Rolls to nonzero field values Generates Higgs bath Motion along bottom Longitudinal modes of W ±,Z 0 Motion up hill Higgs boson Spontaneous symmetry breaking 49

63 Without Higgs, W-W scattering badly behaved around 1 TeV Higgs contributions can cure this 50

64 Summary of our Two Puzzles: Parity violation (problems with mirrors) Does not allow massive particles Mass from interaction with Higgs bath Unitarity violation (problems with probabilities) Fermi s theory breaks down at high energies Requires massive force carriers (like massive photons) Mass from Higgs field 51

65 Summary of our Two Puzzles: Parity violation (problems with mirrors) Does not allow massive particles Mass from interaction with Higgs bath Unitarity violation (problems with probabilities) Fermi s theory breaks down at high energies Requires massive force carriers (like massive photons) Mass from Higgs field Higgs solves two problems of mass: 1.Mass to ordinary particles 2.Mass to carriers of weak nuclear force 51

66 Electroweak theory Photon Weak bosons A sin W + Z 0 cos W p 2W p 2W + A sin W Z 0 cos W A cos W Z 0 sin W SU(2) U(1) Broken to quantum electrodynamics by Higgs mechanism 52 Sheldon Glashow Abdus Salam Steven Weinberg

67 Looking for the Higgs ATLAS A Toroidal Lhc ApparatuS CMS Compact Muon Solenoid 53

68 p p 54 Image from CDF website

69 Look for Higgs through its decay products Best channel is h! 55 Image from CDF website

70 56

71 56

72 95% CL Limit on / SM 10 Obs. Exp. -1 Ldt = fb ±1 ± 2 s = 7 TeV 1 ATLAS Preliminary 2011 Data of SM Higgs hypothesis CMS, s = 7 TeV -1 L = fb Observed Expected (68%) Expected (95%) 90% 95% 99% CL S CLs Limits m H [GeV] Higgs boson mass (GeV) 57

73 SUMMARY Radioactive decay requires new weak interaction Fermi wrote down a quantum model that works for sufficiently low scales Weak interaction introduces two puzzles related to mass Weak interactions violate parity Nature distinguishes between right and left Massive particles can be left-handed or right-handed to different observers All particles must be fundamentally massless Particles get mass from a Higgs bath in the vacuum Excitations are Higgs bosons! Fermi s theory of Weak interactions violates unitarity Probability of all events is not 1...requires new physics at a higher scale New physics is set of massive force carriers Force carriers get mass through Higgs mechanism Resulting Electroweak theory unifies Weak interactions and electromagnetism 58