Download 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 (AB+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
tc  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
ee


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 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
dE Dne

= 2
dx
b
  2mc2 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