Topics in Contemporary Physics Basic concepts 2 Luis Roberto Flores Castillo Chinese University of Hong Kong Hong Kong SAR January 16, 2015

L. R. Flores CastilloCUHK January 16, 2015 PART 1 Brief history Basic concepts Colliders & detectors From Collisions to papers The Higgs discovery BSM MVA Techniques The future 2 5σ

L. R. Flores CastilloCUHK January 16, 2015 … last time: Basic concepts 1 Numbers and units –Definition of some units –“Natural units” –HEP units Elementary particle dynamics –QED –QCD –Weak interactions (following D. Griffiths, 2 nd ed., Chapter 2) 3

L. R. Flores CastilloCUHK January 16, 2015 Reminder: units “Natural units”: –Plank units (based on c, ħ, k B, G) –Particle Physics units (based on c, ħ, k B, E=1eV; ) 4 Using these units, c = ħ = k B = 1

L. R. Flores CastilloCUHK January 16, 2015 Reminder: interactions 5 QED: QCD: Weak: W/Z:W/Z/ γ:

L. R. Flores CastilloCUHK January 16, 2015 Reminder: building processes All processes in nature can be built from these vertices (as far as we can tell so far). Physical processes are defined by the “external lines” –observable particles define initial and final states –their masses are the “correct” ones Transition amplitudes (from initial to final state): weighted sum of all possible histories between them. 6

L. R. Flores CastilloCUHK January 16, 2015 Reminder: adding possible histories 7 + …

L. R. Flores CastilloCUHK January 16, 2015 Quick exercises 8 ( n: udd, p: uud, ) vμvμ μ × × (n)

L. R. Flores CastilloCUHK January 16, 2015 Quick exercises 9 (Λ) ( Λ: udd, p: uud, Ω - : sss, ) (Λ)

L. R. Flores CastilloCUHK January 16, 2015 A few key concepts W bosons carry away the “missing” charge [only one type of charge, so just the difference is needed] quarks carry away the color change. [with three colors, change of color needs bi-color gluons] 10 hence, they also interact strongly

L. R. Flores CastilloCUHK January 16, 2015 A few key concepts Color confinement 11 Asymptotic freedom (which “saved” QCD [or, rather, the infinite sum of ever more complex diagrams] ) Source: Phys.Rev. D86 (2012)

L. R. Flores CastilloCUHK January 16, 2015 A few key concepts Formally, the W boson can only link ‘up-type’ quarks (u,c,t) into the corresponding ‘down-type’ (d,s,b). However, experimentally, some times it mixes generations Solution: the weak force “sees” slightly rotated versions of the down quarks: 12 Cabibbo-Kobayashi-Maskawa matrix

L. R. Flores CastilloCUHK January 16, 2015 Today’s outline Conservation laws Unification Relativistic Kinematics 13

Decays and conservation laws 14

L. R. Flores CastilloCUHK January 16, 2015 Stable particles 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 their antiparticles) All other particles decay spontaneously 15

L. R. Flores CastilloCUHK January 16, 2015 Decays 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 (lifetimes and branching ratios) is one of the goals of elementary particle theory. 16 Several decay modes, each with its own probability (“branching ratio”). For example, K + decays: 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 16, 2015 Nature of decays Each decay is usually dominated by one of the fundamental forces 17 Σ - : dds, n: udd, p:uud, Δ ++ : uuu, π: uū

L. R. Flores CastilloCUHK January 16, 2015 Decay lifetimes How to tell which force dominates a decay? –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. 18 m p +m e ≅ m n,  τ(n ) ~ 15 minutes!

L. R. Flores CastilloCUHK January 16, 2015 Decays and conservation laws Energy and momentum –Particles cannot decay into heavier ones Angular momentum From the fundamental vertices: 19

L. R. Flores CastilloCUHK January 16, 2015 Decays and conservation laws Charge: –strictly conserved –if there is a charge difference, it is carried out by a W boson 20

L. R. Flores CastilloCUHK January 16, 2015 Decays and conservation laws Charge Color: the color difference is carried out by the gluon … but, due to confinement: zero in, zero out. 21

L. R. Flores CastilloCUHK January 16, 2015 Decays and conservation laws Charge, Color Baryon number: the number of quarks present is constant –In packages of 3 or 0; we might simply use B = #q / 3 –Mesons: zero net quark content, so any number may be produced (as long as energy is conserved) 22

L. R. Flores CastilloCUHK January 16, 2015 Decays and conservation laws Charge, Color, Baryon number Lepton number: again, unchanged: –Lepton in  lepton out (even if a different one) –No cross-generation until recently (neutrino oscillations) If generations were unmixed, e, μ, τ conserved separately 23

L. R. Flores CastilloCUHK January 16, 2015 Decays and conservation laws Charge, Color, Baryon number, Lepton number Flavor –Conserved in strong & EM vertices, but not in Weak ones –A weak vertex may turn u into d, or even into s –Weak interactions are very weak, so flavor is approximately conserved. This was Gell-Mann’s reason to postulate “strangeness” Strong interactions dominate production, not decay 24

L. R. Flores CastilloCUHK January 16, 2015 Decays and conservation laws To explain that strange particles are always produced in pairs, Gell- Mann postulated conservation of strangeness This is only approximate; this 2 nd decay can occur weakly, but (strangeness-conserving) strong processes are much more likely. In contrast, particles may only have the option of decaying weakly: Λ is the lightest strange baryon Should decay to (p or n)+meson The lightest strange meson is the K, but m p + m K > m Λ Only decays to non-strange particles can proceed: 25

L. R. Flores CastilloCUHK January 16, 2015 About unification Electricity+magnetism, space+time, acceleration+gravity Glashow, Weinberg and Salam: EM+Weak = EW Chromodynamics + EW ? The “running” of the coupling constants hints at it 26

L. R. Flores CastilloCUHK January 16, 2015 About unification Electricity + Magnetism Glashow, Weinberg and Salam: EM + Weak = EW Chromodynamics + EW ? The “running” of the coupling constants hints at it 27 ?