Transcript for_lab
Atmospheric Neutrinos, Muons, etc. Proton hits in atm Produces, p, L, n, etc… L pp p e 1 Production of Particles by cosmics rays Primary cosmic rays: 90% protons, 9% He nuclei Air nuclei (Nitrogen & Oxygen) p+ n L + K _ e e+ 2 Quantum Field Theories included in Standard Model QED=Quantum Electro Dynamics QCD=Quantum Chromo Dynamics Electro-Weak 3 4 Models used to described general principles Small Fast Classical Mechanics Quantum Mechanics Relativistic Mechanics Quantum Field Theory What is missing? … Quantum Gravity 5 Remember that in Special Relativity We have time dilation: – t = g T’ We have space contraction: – L = L’ / g Where b = v/c and g = 1/sqrt(1 – b 2) … what is this in terms of energy, momentum & mass 6 Time Dilation t’ = g t The “clock” runs slower for an observer not in the “rest” frame in atmosphere: Proper Lifetime t = 2.2 x 10-6 s ct = 0.66 km b g decay path = bgtc average in lab “lifetime” decay path .1 1.005 2.2 s 0.07 km .5 1.15 2.5 s 0.4 km .9 2.29 5.0 s 1.4 km .99 7.09 16 s 4.6 km 49 s 15 km .999 22.4 b=pc/E g=E/mc2 7 Decays We usually refer the decay time in the particle’s rest frame as its proper time which we denote t. 8 Time Dilation II Short-lived particles like tau and B. Lifetime = 10-12 sec ct = 0.03 mm time dilation gives longer path lengths measure “second” vertex, determine “proper time” in rest frame If measure L=1.25 mm and v = .995c L t(proper)=L/vg = .4 ps Twin Paradox. If travel to distant planet at v~c then age less on spaceship then in “lab” frame 9 Study of Decays (AB+C+…) Decay rate G: “The probability per unit time that a particle decays” dN = GNdt N(t) = N(0)e - Gt Lifetime t: “The average time it takes to decay” (at t=1 G particle’s rest frame!) Usually several decay modes BR (decay mode i) = Gi Gtot Branching ratio BR We measure Gtot (or t) and BRs; we calculate Gi Gtot = Gi and t = 1 Gtot i 10 G as decay width Unstable particles have no fixed mass due to the uncertainty principle: Nmax m t The Breit-Wigner shape: N(m ) = N max G 0.5Nmax ( G 2) 2 (m M 0 ) 2 ( G 2) 2 We are able to measure only one of G, t of a particle M0 ( 1GeV-1 =6.582×10-25 sec ) 11 Muon decay ± e± ++ Cosmic ray muon stopping in a cloud chamber and decaying to an electron Decay electron momentum distribution Muon spin = ½ Muon lifetime at rest: t = 2.197 x 10 - 6 s 2.197 s Muon decay mean free path in flight: decay = vt 1-v / c 2 = pt m = p t c m c decay electron track p : muon momentum tc 0.66 km muons can reach the Earth surface after a path 10 km because the decay mean free path is stretched by the relativistic time 12 expansion Lepton Number Conservation Electron, Muon and Tau Lepton Number Anti- Conserved Lepton Conserved Lepton Lepton Quantity Number Lepton Quantity Number ee t t Le L Lt +1 e+ +1 e +1 +1 +1 t +1 t Le L Lt We find that Le , L and Lt are each conserved quantities -1 -1 -1 -1 -1 -1 13 Basic principles of particle detection Passage of charged particles through matter Interaction with atomic electrons ionization (neutral atom ion+ + free electron) excitation of atomic energy levels (de-excitation photon emission) Ionization + excitation of atomic energy levels energy loss Mean energy loss rate – dE /dx K p p e Momentum proportional to (electric charge)2 of incident particle for a given material, function only of incident particle velocity typical value at minimum: dE /dx = 1 – 2 MeV /(g cm2) What causes this shape? 14 Many detectors based on Ionization Charged particles – interaction with material -+ +-+ -+ -+ + -+ + + -+ -+ + +-“track of ionisation” 15 Ionization & Energy loss Density of electrons Important for all charged particles dE Dne = 2 dx b 2mc 2 b 2g 2 (g ) 2 b ln I 2 • Bethe-Bloch Equation velocity Mean ionization potential (10ZeV) 16 Ionization In low fields the ions eventually recombine with the electrons However under higher fields it is possible to separate the charges -+------------------------+-+- -- -- --- ----+------------------------+-+- -- -- --- ----+----- ---- ---------------+ E Note: e-’s and ions generally move at a different rate 17 Units Particle Physicists use Natural Units: = c =1 34 22 h 2p = 1.0546 10 Js = 6.582 10 MeVs c = 197.3 MeV fm Hence, we write the masses of some standard particles in terms of energy (MeV, GeV): me = 0.511MeV/ c = 9.109 10 2 m p = 938. MeV/ c = 1.672 10 2 31 27 kg kg 18