Atmospheric Neutrinos, Muons, etc.

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Atmospheric Neutrinos, Muons, etc.

• Proton hits in atm
• Produces, p, L, n, etc
• ? p?
• ? ? ??
• ? ? e??

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Production of Particlesby cosmics rays
Primary cosmic rays
90 protons, 9 He nuclei
Air nuclei (Nitrogen Oxygen)
?
?
e
??
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Quantum Field Theories included in Standard Model
QEDQuantum Electro Dynamics
QCDQuantum Chromo Dynamics
Electro-Weak
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Models used to described general principles
Small ?
Classical Mechanics Quantum Mechanics
Relativistic Mechanics Quantum Field Theory
Fast ?
Quantum Gravity
What is missing?
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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

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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

bpc/E gE/mc2
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Decays

• We usually refer the decay time in the particles
  rest frame as its proper time which we denote ?.
  

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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 L1.25 mm and v .995c t(proper)L/vg
.4 ps
L
Twin Paradox. If travel to distant planet at vc
then age less on spaceship then in lab frame
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Study of Decays (A?BC)

• Decay rate G The probability per unit time that
  a particle decays
• Lifetime t The average time it takes to decay
  (at particles rest frame!)
• Usually several decay modes
• Branching ratio BR
• We measure Gtot (or t) and BRs we calculate Gi

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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 6.58210-25 sec )

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Muon decay
Decay electron momentum distribution
Muon spin ½
Muon lifetime at rest ?? 2.197 x 10 - 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
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Lepton Number Conservation
Electron, Muon and Tau Lepton Number
Lepton Conserved Quantity Lepton Number
e- Le 1
ne Le 1
m- Lm 1
nm Lm 1
t- Lt 1
nt Lt 1
Anti-Lepton Conserved Quantity Lepton Number
e Le -1
ne Le -1
m Lm -1
nm Lm -1
t Lt -1
nt Lt -1
We find that Le , Lm and Lt are each conserved
quantities
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Basic principles of particle detection
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?

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Many detectors based on Ionization

• Charged particles
• interaction with material

track of ionisation
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Ionization Energy loss
Density of electrons

• Important for all charged particles

• Bethe-Bloch Equation

velocity
Mean ionization potential (10ZeV)
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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






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Units

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