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Topics in Contemporary Physics Basic concepts Luis Roberto Flores Castillo Chinese University of Hong Kong Hong Kong SAR January 5, 2015 … last time: Historical Overview Historical overview (following D. Griffiths, 2nd 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) The November Revolution (evidence!) Intermediate Vector Bosons The Standard Model L. R. Flores Castillo CUHK (1897-1932) (1900-1924) (1934-1947) (1930-1956) (1930-1962) (1947-1960) (1961-1964) (1964) (1974-1983, 1995) (1983) (1978-?) January 14, 2015 2 One point to emphasize • Strong interactions conserve strangeness, weak interactions don’t • Please notice the “Notice board” from the website L. R. Flores Castillo CUHK January 14, 2015 3 PART 1 • Brief history • Basic concepts • Colliders & detectors 5σ • From Collisions to papers S ATLA (*) 15 GeV d Selecte s=7 2000 1800 TeV, s=8 ò TeV, ò Ldt = -1 5.9 fb 1600 1400 1200 1000 800 600 10 ATLAS 400 5 150 0 GeV) sample 2 126.5 and 201 fit (m H = 2011 usive Data Bkg incl -1 Sig + nomial 4.8 fb er poly Ldt = 4th ord n diphoto 2400 2200 / Events -1 fb t = 4.8 V: òLd -1 5.8 fb Ldt = TeV: ò Te s=7 s=8 ®4l 100 nary Prelimi 200 250 0 ] [GeV 200 m100 4l - Bkg Even • The Higgs discovery c. Un Syst. 20 H®ZZ Data V ts/5 Ge (*) Data ZZ round s, tt Backg Z+jet round V) Backg 25 Ge l (m H=1 Signa 25 150 140 -100 100 160 V] mg g [Ge 130 0 120 110 • BSM • MVA Techniques • The future L. R. Flores Castillo CUHK January 14, 2015 4 Outline – Numbers and Units – Elementary particle dynamics (a first quick look at Feynman Diagrams) • QED • QCD • Weak interactions • Conservation laws • Unification L. R. Flores Castillo CUHK January 14, 2015 5 On Constants and Units Two of the most used constants in particle physics: • c = 299 762 458 m/s • h = 6.62606957(29) x 10-34 kg m2 / s Why no uncertainty on c ? L. R. Flores Castillo CUHK January 14, 2015 6 On Constants and Units Two of the most used constants in particle physics: • c = 299 762 458 m/s • h = 6.62606957(29) x 10-34 kg m2 / s 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: 1,650,763.73 wavelengths of 2p105d5 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 Castillo CUHK January 14, 2015 7 On Constants and Units Similarly, the kg is defined by an object SI: “The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram” L. R. Flores Castillo CUHK January 14, 2015 8 On Constants and Units Similarly, the kg is defined by an object Comparisons between official copies show some divergence with time. ~ 5 x 10-8 (50 μg in 100 years) L. R. Flores Castillo CUHK January 14, 2015 9 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 = kB = 1 [ħ] = [ momentum x position ] = L T-1 M L = L2 T-1 M [c] = [ speed ] = L T-1 [G] = ? L. R. Flores Castillo CUHK January 14, 2015 10 On Constants and Units • Gravitational constant: m1m2 F =G 2 r [F] M L T-2 M-1 L3 T-2 G L. R. Flores Castillo = [ G ] M2 L-2 = [ G ] M2 L-2 =[G] = 6.67384(80) x 10-11 m3 kg-1 s-2 = 6.67384(80) x 10-11 N m2 kg-2 CUHK January 14, 2015 11 On Constants and Units Universal constants can define a length, a mass, a time, and a temperature. Using these as units, all these constants become 1. L. R. Flores Castillo CUHK January 14, 2015 12 On Constants and Units Planck units are not adequate for particle physics. Why? Instead, we can start from an adequate unit of energy: L. R. Flores Castillo CUHK January 14, 2015 13 On Constants and Units • In this system, c = ħ = kB = 1 • And, by construction, the unit of energy is good for particle physics. E = mc 2 2 4 2 2 E =m c +p c 2 E =m +p 2 2 2 E =n L. R. Flores Castillo CUHK January 14, 2015 14 Elementary Particle Dynamics 15 Brief reminder • Matter: quarks & leptons • Interactions: Vector bosons (plus the Higgs) • Three generations – One neutrino for each charged lepton – Up-type, down-type quarks L. R. Flores Castillo CUHK January 14, 2015 16 QED 17 Quantum Electrodynamics (QED) All EM phenomena are ultimately reducible to: • Time flows horizontally • An electron enters, emits (or absorbs) a photon, and exits • Any charged particle (lepton, quark, W) L. R. Flores Castillo CUHK January 14, 2015 18 Quantum Electrodynamics (QED) • Combinations describe more complicated processes: Time • e’s enter, a photon is exchanged (direction?), both exit • Coulomb repulsion, or “Møller scattering” L. R. Flores Castillo CUHK January 14, 2015 19 Quantum Electrodynamics (QED) Time • • • • 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” L. R. Flores Castillo CUHK January 14, 2015 20 Quantum Electrodynamics (QED) Time • Very different diagram, also describes Bhabha scattering • Both must be included in the calculation L. R. Flores Castillo CUHK January 14, 2015 21 Quantum Electrodynamics (QED) Other diagrams (same two vertices): Pair annihilation Pair production e+ + e- ® γ + γ γ + γ ® e+ + e- Compton scattering e+ + γ ® e- + γ Crossing symmetry: twisting or rotating the figure L. R. Flores Castillo CUHK January 14, 2015 22 Quantum Electrodynamics (QED) … why stop there? With 4 vertices: • 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 Castillo CUHK January 14, 2015 23 Quantum Electrodynamics (QED) • Careful! Only one primitive vertex!! L. R. Flores Castillo CUHK January 14, 2015 24 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 = e2/ħc = 1/137 (the fine structure constant) – The sum does converge L. R. Flores Castillo CUHK January 14, 2015 25 Quantum Electrodynamics (QED) … • Recently: 12,672 Feynman diagrams for electron’s g-2 • Phys Rev Lett 109, 111807 (2012) L. R. Flores Castillo CUHK January 14, 2015 26 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: In CM frame: Energy from mc2 to more than that. L. R. Flores Castillo CUHK In CM frame: from zero total momentum to a photon. January 14, 2015 27 Quantum Electrodynamics (QED) • Any charged particle would interact with the photon Pion decay L. R. Flores Castillo CUHK January 14, 2015 28 Quick exercise • Draw the lowest order Feynman diagram representing “Delbruck scattering”: γ+γ ® γ+γ L. R. Flores Castillo CUHK January 14, 2015 29 QCD 30 Quantum Chromodynamics (QCD) • Color plays the role of charge • 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 Castillo CUHK January 14, 2015 31 Quantum Chromodynamics (QCD) • Force between quarks, at lower order: • Gluons have then two colors (color and anticolor) • 3 × 3 = 9 possibilities, but there are 8 gluons L. R. Flores Castillo CUHK January 14, 2015 32 Quantum Chromodynamics (QCD) • Gluons do carry color (in contrast with photons) • Far richer than QED • Bound states of gluons possible (“glueballs”) • In contrast with αEM (=1/137), αS > 1 !!! What to do? L. R. Flores Castillo CUHK January 14, 2015 33 Quantum Chromodynamics (QCD) • With αS > 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. L. R. Flores Castillo CUHK January 14, 2015 34 Quantum Chromodynamics (QCD) • One final difference: naturally occurring particles are colorless. • We only observe indirect effects of color. L. R. Flores Castillo CUHK January 14, 2015 35 Color confinement L. R. Flores Castillo CUHK January 14, 2015 36 Weak Interactions 37 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 L. R. Flores Castillo CUHK January 14, 2015 38 Neutral Weak Interactions • Examples: Neutrino-electron scattering Neutrino-proton scattering vμ+e- ® vμ+e- vμ + p ® vμ + p L. R. Flores Castillo CUHK January 14, 2015 39 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. L. R. Flores Castillo CUHK January 14, 2015 40 Charged Weak Interactions LEPTONS: A simple combination: Two leptons of the same generation L. R. Flores Castillo CUHK January 14, 2015 41 Charged Weak Interactions • Slightly modified: m ® e + nm + ne - L. R. Flores Castillo CUHK - January 14, 2015 42 Charged Weak Interactions QUARKS: Mixing lepton and quark diagrams: L. R. Flores Castillo CUHK January 14, 2015 43 Charged Weak Interactions QUARKS: Time μ × × With u and d bound by the strong force, The pair on the right can be μ, vμ: L. R. Flores Castillo CUHK vμ p ® e +ne p ® m + nm - January 14, 2015 - 44 Charged Weak Interactions QUARKS: Time (n) It also accounts for neutron beta decay: + - n ® p + e +ne L. R. Flores Castillo CUHK January 14, 2015 45 On Feynman Diagrams Replacing the lepton vertex with a quark vertex: … which also proceeds by the strong interaction: D ® p +p (this is by far the dominant contribution in this case) 0 L. R. Flores Castillo + CUHK - January 14, 2015 46 Some complications • If these vertices did not mix generations, strangeness would never change, but it does: L ® p +p + - W- ® L + K - (Λ) L. R. Flores Castillo CUHK January 14, 2015 47 … 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’) Cabibbo-Kobayashi-Maskawa matrix L. R. Flores Castillo CUHK January 14, 2015 48 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: With three generations of quarks: three mixing angles + one CP-violating complex phase. L. R. Flores Castillo CUHK January 14, 2015 49 Weak and EM couplings of W and Z • Similar to gluon-gluon interactions, W and Z couple to one another: • Since W is charged, it also couples to the photon: L. R. Flores Castillo CUHK January 14, 2015 50 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 L. R. Flores Castillo CUHK January 14, 2015 51 Decays and conservation laws Each unstable particle has • A characteristic lifetime: – μ: 2.2×10-6 s, – π+: 2.6×10-8 s, – π0: 8.3×10-17 s, • Several decay modes: • K+ decay: • 64% into μ+ + vμ • 21% into π++π0 • 6% into π++π++π• 5% into e++ve+π0 •… • Predicting these numbers is one of the goals of elementary particle theory L. R. Flores Castillo CUHK January 14, 2015 52 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: ~ 10-23 s (about the time for light to cross a p) – electromagnetic: ~ 10-16 s – weak: ~ 10-13 s normally, faster for larger mass differences between original and decay products. n ® p + e +ne + L. R. Flores Castillo CUHK - January 14, 2015 53 Decays and conservation laws • Energy and momentum – Particles cannot decay into heavier ones • Angular momentum • From the fundamental vertices: L. R. Flores Castillo CUHK January 14, 2015 54 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 L. R. Flores Castillo CUHK January 14, 2015 55 About unification • • • • Electricity + Magnetism Glashow, Weinberg and Salam: EM + Weak = EW Chromodynamics + EW ? The “running” of the coupling constants hints at it L. R. Flores Castillo CUHK January 14, 2015 56 About unification • • • • Electricity + Magnetism Glashow, Weinberg and Salam: EM + Weak = EW Chromodynamics + EW ? The “running” of the coupling constants hints at it ? L. R. Flores Castillo CUHK January 14, 2015 57 58 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 L. R. Flores Castillo CUHK January 14, 2015 59