1 Atmospheric Atmospheric Neutrinos, Neutrinos, Muons, etc. Muons, etc. Proton hits in atm Proton hits in atm Produces, Produces, , n, , n, etc… etc… p p e e
Jan 23, 2016
11
Atmospheric Atmospheric Neutrinos, Neutrinos,
Muons, etc.Muons, etc.
Proton hits in atm Proton hits in atm Produces, Produces, , n, etc…, n, etc…
pp ee
22
Production of ParticlesProduction of Particlesby cosmics raysby cosmics rays
Primary cosmic rays:
+
+
e+
e
_
n
K
90% protons, 9% He nuclei
Air nuclei (Nitrogen & Oxygen)
33
Quantum Field Theories Quantum Field Theories included in Standard Modelincluded in Standard Model
QED=QuantumElectro Dynamics
QCD=QuantumChromo Dynamics
Electro-Weak
44
55
Models used to described general Models used to described general principlesprinciples
ClassicalClassical
MechanicsMechanics
Quantum Quantum
MechanicsMechanics
RelativisticRelativistic
MechanicsMechanics
Quantum Quantum
Field TheoryField Theory
What is missing? …What is missing? … Quantum Quantum GravityGravity
Small
Fa
st
66
Remember that in Special Remember that in Special RelativityRelativity
We have time dilation:We have time dilation:– t = t = T’ T’
We have space contraction:We have space contraction:– L = L’ / L = L’ /
Where Where = v/c and = v/c and = 1/sqrt(1 – = 1/sqrt(1 – 22) … what is ) … what is this in terms of energy, momentum & massthis in terms of energy, momentum & mass
77
Time Dilation Time Dilation t’ = tThe “clock” runs slower for an observer not in the “rest” frame
in atmosphere: Proper Lifetime= 2.2 x 10-6 s
c0.66 km decay path = c average in labaverage in lab
“ “lifetime” decay pathlifetime” 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
.999 22.4 49 s 15 km
=pc/E=pc/E=E/mc=E/mc22
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DecaysDecaysWe usually refer the decay time in the We usually refer the decay time in the particle’s rest frame as its particle’s rest frame as its proper timeproper time which which we denote we denote . .
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Time Dilation IITime Dilation IIShort-lived particles like tau and B. Lifetime 10-12 sec c0.03 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/v = .4 psL
Twin Paradox. If travel to distant planet at v~c then age less on spaceship then in “lab” frame
1010
Study of Decays (Study of Decays (AAB+C+…B+C+…) )
Decay rate Decay rate : “: “The probability per unit time that a The probability per unit time that a particle decaysparticle decays””
Lifetime Lifetime : “: “The average time it takes to decayThe average time it takes to decay” (at ” (at particle’s rest frame!)particle’s rest frame!)
Usually several decay modesUsually several decay modes
Branching ratio BRBranching ratio BR
We measure We measure tottot (or (or ) and BRs; we calculate ) and BRs; we calculate ii
1
toti
itot 1 and
toti i) modedecay (BR
t)0N(N(t)tNN -e dd
1111
as decay widthas decay widthUnstable particles have no fixed Unstable particles have no fixed mass due to the uncertainty mass due to the uncertainty principle:principle:
The Breit-Wigner shape:The Breit-Wigner shape:
We are able to measure only We are able to measure only one of one of , , of a particle of a particle( 1GeV( 1GeV-1-1 =6.582 =6.582××1010-25 -25 sec ) sec )
tm
220
2
max )2()Mm(
)2(N)m(N
MM00
NNmaxmax
0.5N0.5Nmaxmax
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Muon Muon decaydecay
± e± + + Cosmic ray muon stopping
in a cloud chamber anddecaying to an electron
decay electron track
Muon lifetime at rest: = . x - s . sMuon decay mean free path in flight:
c
cm
p
m
p
c-decay
2/v1
v
muons can reach the Earth surface after a path 10 km because the decay mean free path is stretched by the relativistic time expansion
p : muon momentum
c . km
Muon spin = ½
Decay electron momentum distribution
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Lepton Number ConservationLepton Number Conservation Electron, Muon and Tau Lepton Number
LeptonLepton Conserved Conserved QuantityQuantity
Lepton Lepton NumberNumber
ee--
LLee
+1+1
ee +1+1
LL
+1+1
+1+1
LL
+1+1
+1+1
Anti-Anti-LeptonLepton
Conserved Conserved QuantityQuantity
Lepton Lepton NumberNumber
ee++
LLee
-1-1
ee -1-1
LL
-1-1
-1-1
LL
-1-1
-1-1
We find that Le , L and L are each conserved quantities
1414
Basic principles of particle detectionBasic principles of particle detectionPassage of charged particles through matterInteraction 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
proportional to (electric charge) of incident particle
Mean energy loss rate – dE dx
for a given material, function only of incident particle velocity
typical value at minimum:
dE dx = – MeV (g cm)
What causes this shape?
Momentum
pK
e
1515
Many detectors based on Many detectors based on IonizationIonization
Charged particlesCharged particles– interaction with interaction with
materialmaterial
++
+
++
++
+++
++
+----
----
--
---
-
“track of ionisation”
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Ionization & Energy lossIonization & Energy loss
Important for all Important for all charged particlescharged particles
2
)(2ln 2
222
2
I
mcDn
dx
dE e
• Bethe-Bloch Equation
velocity
Mean ionization potential(10ZeV)
Density of electrons
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IonizationIonization
In low fields the ions eventually recombine In low fields the ions eventually recombine with the electronswith the electrons
However under higher fields it is possible However under higher fields it is possible to separate the chargesto separate the charges
E++++++++
------- -
------- -
------- -
------- -
------- -
------- -
------- -
------- -
------- -
------- -
------- -
------- -
------- -
Note: e-’s and ions generally move at a different rate
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UnitsUnitsParticle Physicists use Natural Units:Particle Physicists use Natural Units:
Hence, we write the masses of some Hence, we write the masses of some standard particles in terms of energy standard particles in terms of energy (MeV, GeV):(MeV, GeV):
fmMeV3.197
MeVs10582.6Js100546.12
12234
c
h
c
kg10672.1MeV/.938
kg10109.9MeV/511.0272
312
cm
cm
p
e