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Atmospheric Neutrinos, Muons, etc.

Atmospheric Neutrinos, Muons, etc. Proton hits in atm Produces, p, L , n, etc…  p      e. n. . K. _.  e.  . Production of Particles by cosmics rays. Primary cosmic rays:. 90% protons, 9% He nuclei. Air nuclei (Nitrogen & Oxygen).  +.  +. e +.  .

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Atmospheric Neutrinos, Muons, etc.

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  1. Atmospheric Neutrinos, Muons, etc. • Proton hits in atm • Produces, p, L, n, etc… •  p      e

  2. n  K _ e  Production of Particlesby cosmics rays Primary cosmic rays: 90% protons, 9% He nuclei Air nuclei (Nitrogen & Oxygen) + + e+ 

  3. Quantum Field Theories included in Standard Model QED=Quantum Electro Dynamics QCD=Quantum Chromo Dynamics Electro-Weak

  4. Models used to described general principles Small  Fast  Quantum Gravity What is missing? …

  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 • m in atmosphere: Proper Lifetime t = 2.2 x 10-6 s • ct = 0.66 km decay path = bgtc b g average in lab “lifetime” decay path .1 1.005 2.2 ms 0.07 km .5 1.15 2.5 ms 0.4 km .9 2.29 5.0 ms 1.4 km .99 7.09 16 ms 4.6 km .999 22.4 49 ms 15 km 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 .

  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 t(proper)=L/vg = .4 ps L Twin Paradox. If travel to distant planet at v~c then age less on spaceship then in “lab” frame

  9. Study of Decays (AB+C+…) • Decay rate G: “The probability per unit time that a particle decays” • Lifetime t: “The average time it takes to decay” (at particle’s rest frame!) • Usually several decay modes • Branching ratio BR • We measure Gtot (or t) and BRs; we calculate Gi

  10. Nmax G 0.5Nmax M0 G as decay width • Unstable particles have no fixed mass due to the uncertainty principle: • The Breit-Wigner shape: • We are able to measure only one of G, t of a particle ( 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 track p: muon momentum c0.66 km Decay electron momentum distribution Muon spin = ½ Muon lifetime at rest:  = 2.197x10 - 6 s 2.197s Muon decay mean free path in flight:  muons can reach the Earth surface after a path  10 km because the decay mean free path is stretched by the relativistic time expansion

  12. Lepton Number Conservation Electron, Muon and Tau Lepton Number We find that Le , Lm and Lt are each conserved quantities

  13. Basic principles of particle detection Ionization + excitation of atomic energy levels energy loss Passage of charged particles through matter Interaction with atomic electrons K p ionization (neutral atom  ion+ + free electron) p e excitation of atomic energy levels (de-excitation  photon emission) m Momentum Mean energy loss rate – dE /dx • 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 cm-2) 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 • 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 Note: e-’s and ions generally move at a different rate + + E + + + + + +

  17. Units • Particle Physicists use Natural Units: • Hence, we write the masses of some standard particles in terms of energy (MeV, GeV):

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