Topics in Contemporary Physics Basic concepts Luis Roberto Flores Castillo Chinese University of Hong Kong Hong Kong SAR January 5, 2015

L. R. Flores CastilloCUHK January 14, 2015 … last time: Historical Overview Historical overview (following D. Griffiths, 2 nd ed.) –“Classical Era” (electron, nuclei, neutrons)( ) –Photons (quantum effects become apparent)( ) –Mesons (from Yukawa to the muon)( ) –Antiparticles (Dirac, Anderson, x-ing symm) ( ) –Neutrinos (β-decays, Pauli’s solution, 2 types)( ) –Strange Particles (new baryons and mesons)( ) –The Eightfold Way (finding structure)( ) –The Quark Model (an explanation)(1964) –The November Revolution (evidence!)( , 1995) –Intermediate Vector Bosons (1983) –The Standard Model (1978-?) 2

L. R. Flores CastilloCUHK January 14, 2015 One point to emphasize Strong interactions conserve strangeness, weak interactions don’t Please notice the “Notice board” from the website 3

L. R. Flores CastilloCUHK January 14, 2015 PART 1 Brief history Basic concepts Colliders & detectors From Collisions to papers The Higgs discovery BSM MVA Techniques The future 4 5σ

L. R. Flores CastilloCUHK January 14, 2015 Outline –Numbers and Units –Elementary particle dynamics (a first quick look at Feynman Diagrams) QED QCD Weak interactions Conservation laws Unification 5

L. R. Flores CastilloCUHK January 14, 2015 On Constants and Units Two of the most used constants in particle physics: c = m/s h = (29) x kg m 2 / s 6 Why no uncertainty on c ?

L. R. Flores CastilloCUHK January 14, 2015 On Constants and Units Two of the most used constants in particle physics: c = m/s h = (29) x kg m 2 / s 7 Very impractical values. Why? Meter: –1790: Length of a pendulum with half-period of one second –1791: One ten-millionth of ¼ Earth’s meridian through Paris –1799: Platinum meter bar (refined in 1889 and 1927) –1960: 1,650, wavelengths of 2p 10  5d 5 of Kr-86 –1983: Length traveled by light in vacuum in 1 / 299,762,458 of a sec –2002: “… as long as GR effects are negligible.”

L. R. Flores CastilloCUHK January 14, 2015 On Constants and Units Similarly, the kg is defined by an object 8 SI: “The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram”

L. R. Flores CastilloCUHK January 14, 2015 On Constants and Units Similarly, the kg is defined by an object 9 Comparisons between official copies show some divergence with time. ~ 5 x (50 μ g in 100 years)

L. R. Flores CastilloCUHK January 14, 2015 On Constants and Units We can choose units so that c, h, … have value 1. The constants chosen to be = 1 determine units of length, mass, time, temperature and electric charge. “Natural” units: Plank units: c = G = ħ = k B = 1 [ħ] = [ momentum x position ] = L T -1 M L = L 2 T -1 M [c] = [ speed ] = L T -1 [G] = ? 10

L. R. Flores CastilloCUHK January 14, 2015 On Constants and Units Gravitational constant: [ F ]= [ G ] M 2 L -2 M L T -2 = [ G ] M 2 L -2 M -1 L 3 T -2 = [ G ] G= (80) x m 3 kg -1 s -2 = (80) x N m 2 kg -2 11

L. R. Flores CastilloCUHK January 14, 2015 On Constants and Units Universal constants can define a length, a mass, a time, and a temperature. 12 Using these as units, all these constants become 1.

L. R. Flores CastilloCUHK January 14, 2015 On Constants and Units Planck units are not adequate for particle physics. Why? Instead, we can start from an adequate unit of energy: 13

L. R. Flores CastilloCUHK January 14, 2015 On Constants and Units In this system, c = ħ = k B = 1 And, by construction, the unit of energy is good for particle physics. 14

Elementary Particle Dynamics 15

L. R. Flores CastilloCUHK January 14, 2015 Brief reminder Matter: quarks & leptons Interactions: Vector bosons (plus the Higgs) Three generations –One neutrino for each charged lepton –Up-type, down-type quarks 16

QED 17

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) All EM phenomena are ultimately reducible to: 18 Time flows horizontally An electron enters, emits (or absorbs) a photon, and exits Any charged particle (lepton, quark, W)

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) Combinations describe more complicated processes: 19 e’s enter, a photon is exchanged (direction?), both exit Coulomb repulsion, or “Møller scattering” Time

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) Same diagram (“Feynman diagram”), rotated Line ‘backward in time’ = antiparticle moving forward in time Above: e +, e - annihilate into a γ, which makes an e + e - pair Coulomb attraction of opposite charges, “Bhabha scattering” 20 Time

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) Very different diagram, also describes Bhabha scattering Both must be included in the calculation 21 Time

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) Other diagrams (same two vertices): 22 Pair annihilation e + + e -  γ + γ Pair production γ + γ  e + + e - Compton scattering e + + γ  e - + γ Crossing symmetry: twisting or rotating the figure

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) … why stop there? With 4 vertices: 23 In all these: e + + e -  e + + e - (Møller scattering) Internal lines: –irrelevant for the observed process –“Virtual particles” –“Mechanism” External lines –Observable particles –Physical process

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) Careful! Only one primitive vertex!! 24

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) Feynman diagrams do NOT represent trajectories Only interactions Each diagram represents a NUMBER “Feynman rules” define how calculate it. For a given process (a set of external lines), the sum of all FD’s with those external lines represents the process There are infinitely many, but each vertex brings a factor α = e 2 /ħc = 1/137 (the fine structure constant) –The sum does converge 25

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) Recently: 12,672 Feynman diagrams for electron’s g-2 Phys Rev Lett 109, (2012) 26 …

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) Energy & momentum should be conserved in each vertex Consequence: –Conserved in the diagram as a whole –The primitive ‘building block’ does not represent a possible process: 27 In CM frame: Energy from mc 2 to more than that. In CM frame: from zero total momentum to a photon.

L. R. Flores CastilloCUHK January 14, 2015 Quantum Electrodynamics (QED) Any charged particle would interact with the photon 28 Pion decay

L. R. Flores CastilloCUHK January 14, 2015 Quick exercise Draw the lowest order Feynman diagram representing “Delbruck scattering”: γ+γ  γ+γ 29

QCD 30

L. R. Flores CastilloCUHK January 14, 2015 Quantum Chromodynamics (QCD) Color plays the role of charge 31 Similar structure, but some important differences: –Three kinds of color –Quark color (but not flavor) may change –Gluons must carry away the difference

L. R. Flores CastilloCUHK January 14, 2015 Quantum Chromodynamics (QCD) Force between quarks, at lower order: 32 Gluons have then two colors (color and anticolor) 3 × 3 = 9 possibilities, but there are 8 gluons

L. R. Flores CastilloCUHK January 14, 2015 Quantum Chromodynamics (QCD) Gluons do carry color (in contrast with photons) 33 Far richer than QED Bound states of gluons possible (“glueballs”) In contrast with α EM (=1/137), α S > 1 !!! What to do?

L. R. Flores CastilloCUHK January 14, 2015 Quantum Chromodynamics (QCD) With α S > 1, it would be impossible to sum diagrams Fortunately, an effect similar to … –Dielectric shielding of a charge –Vacuum polarization plus the features of QCD, end up decreasing the QCD coupling at short distances. i.e., within hadrons (p, n, π, …), quarks interact very weakly. This is called ASYMPTOTIC FREEDOM, and recovers the possibility of calculating the sums. 34

L. R. Flores CastilloCUHK January 14, 2015 Quantum Chromodynamics (QCD) One final difference: naturally occurring particles are colorless. We only observe indirect effects of color. 35

L. R. Flores CastilloCUHK January 14, 2015 Color confinement 36

Weak Interactions 37

L. R. Flores CastilloCUHK January 14, 2015 Weak interactions Leptons have no color, so no strong nuclear interaction Neutrinos have no charge, so no EM interaction But all of them carry the “weak charge” Two types of weak interaction: neutral (Z), charged (W) NEUTRAL 38

L. R. Flores CastilloCUHK January 14, 2015 Neutral Weak Interactions Examples: 39 Neutrino-electron scattering v μ +e -  v μ +e - Neutrino-proton scattering v μ + p  v μ + p

L. R. Flores CastilloCUHK January 14, 2015 Neutral Weak Interactions Any process mediated by the photon can also be mediated by the Z: These diagrams (including the Z instead of the photon) also enter in the sum… but are negligible. 40

L. R. Flores CastilloCUHK January 14, 2015 Charged Weak Interactions LEPTONS: 41 A simple combination: Two leptons of the same generation

L. R. Flores CastilloCUHK January 14, 2015 Charged Weak Interactions Slightly modified: 42

L. R. Flores CastilloCUHK January 14, 2015 Charged Weak Interactions QUARKS: 43 Mixing lepton and quark diagrams:

L. R. Flores CastilloCUHK January 14, 2015 Charged Weak Interactions QUARKS: 44 With u and d bound by the strong force, Time vμvμ μ × × The pair on the right can be μ, v μ :

L. R. Flores CastilloCUHK January 14, 2015 Charged Weak Interactions QUARKS: 45 It also accounts for neutron beta decay: Time (n)

L. R. Flores CastilloCUHK January 14, 2015 On Feynman Diagrams Replacing the lepton vertex with a quark vertex: 46 … which also proceeds by the strong interaction: (this is by far the dominant contribution in this case)

L. R. Flores CastilloCUHK January 14, 2015 Some complications If these vertices did not mix generations, strangeness would never change, but it does: 47 (Λ)

L. R. Flores CastilloCUHK January 14, 2015 … and a solution This mixing of generations posed a problem. Solution: to weak interactions, the quark generations are ‘misaligned’ If the weak force acted on (u,d), (c,s), (t,b) there would be no “inter-generational” mixing However, it acts on rotated versions of d, s and b: (u,d’), (c,s’), (t,b’) 48 Cabibbo-Kobayashi-Maskawa matrix

L. R. Flores CastilloCUHK January 14, 2015 The CKM Matrix If the KM matrix was the unit matrix, –“upness-plus-downness” –“strangeness plus charm” –“topness plus botomness” Would each be conserved (just as e, μ & τ lepton numbers) However, experimentally: 49 With three generations of quarks: three mixing angles + one CP-violating complex phase.

L. R. Flores CastilloCUHK January 14, 2015 Weak and EM couplings of W and Z Similar to gluon-gluon interactions, W and Z couple to one another: 50 Since W is charged, it also couples to the photon:

L. R. Flores CastilloCUHK January 14, 2015 Decays and conservation laws Whenever possible, particles decay into lighter particles i.e., unless prevented by conservation laws Stable particles: Photon: nothing lighter to decay into. Electron: lightest charged particle Proton: lightest baryon Lightest neutrino: lepton number (plus antiparticles) All other particles decay spontaneously 51

L. R. Flores CastilloCUHK January 14, 2015 Decays and conservation laws Each unstable particle has A characteristic lifetime: –μ : 2.2×10 -6 s, –π + : 2.6×10 -8 s, –π 0 : 8.3× s, Predicting these numbers is one of the goals of elementary particle theory 52 Several decay modes: K+ decay: 64% into μ + + v μ 21% into π + +π 0 6% into π + +π + +π - 5% into e + +v e +π 0 …

L. R. Flores CastilloCUHK January 14, 2015 Decays and conservation laws Decays are usually dominated by one of the fundamental forces –If there is a photon coming out … EM –If there is a neutrino coming out … weak –If neither, harder to tell The most striking experimental difference: decay times –strong decays: ~ s (about the time for light to cross a p) –electromagnetic: ~ s –weak: ~ s normally, faster for larger mass differences between original and decay products. 53

L. R. Flores CastilloCUHK January 14, 2015 Decays and conservation laws Energy and momentum –Particles cannot decay into heavier ones Angular momentum From the fundamental vertices: 54

L. R. Flores CastilloCUHK January 14, 2015 Decays and conservation laws Charge: all conserve it strictly (difference carried out by W) Color: difference carried out by the gluon … but, due to confinement: zero in, zero out. Baryon number: number of quarks present is a constant –They come in packages of 3, so we might simply use B = #q/3 –Mesons: zero net quark content, so any number may be produced Lepton number: again, unchanged. –No cross-generation until recently (neutrino oscillations) Flavor –Approximately conserved… because Weak interactions are weak 55

L. R. Flores CastilloCUHK January 14, 2015 About unification Electricity + Magnetism Glashow, Weinberg and Salam: EM + Weak = EW Chromodynamics + EW ? The “running” of the coupling constants hints at it 56

L. R. Flores CastilloCUHK January 14, 2015 About unification Electricity + Magnetism Glashow, Weinberg and Salam: EM + Weak = EW Chromodynamics + EW ? The “running” of the coupling constants hints at it 57 ?

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L. R. Flores CastilloCUHK January 14, 2015 A couple comments Slides: starting next week, the day before class Please look at the notice board section of the website –Announcements about homework and deadlines –Information about exercise classes 59