Transcript Master Class 2002

Master Class – Lancaster Package
 Particle Physics Basics
How do we identify particles?
How do we measure properties of particle?
What are the rules?
 Conservation Laws:
Energy
Momentum
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Conservation of Momentum
 Momentum
Classically (Newton)

p  mv (mass times velocity)
The sum of the momentum before and after a collision of
particles is conserved.
Consider a moving particle striking a stationary particle
m2
m1, speed v1

m1, speed u
Can calculate mass of particle 1,
if measure one final velocity
and both angles
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m2, speed v2
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Reference Calculations
Momentum before collision : x direction : m1u
y direction : 0
After collision : x direction : m1v1 cos   m2v2 cos   m1u
: y direction : m1v1 sin   m2v2 sin   0
m v sin 
Solve using y direction to : v2  1 1
m2 sin 
get equation for m2v2 :
1
2 1
2 1
Use Energy Conservati on : m1u  m1v1  m2v2 2
2
2
2


2
2
 m1v1   sin  
2
2
: m1 u  v1   m2 
 

m
 sin  
(Kinetic Energy) : m1 u 2  v12  m2v2 2

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

2 
2
2 m2  sin  
: u  v1
 m1
2  sin  
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Application
 Start Lancaster Particle class
 Hit Graphics:
Choose value of u1 (u) and fire
Use Excel Spread sheet to calculate m1 (enter “measured values”,
Look at bottom of page for Billiards)
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Relativity
 Major Result:
Mass and Energy are Equivalent
 
E   pc   mc
2
2
2 2
Lead to Particle and anti-particles
Convert into energy
 Two types of experiments:
Fixed Target:
Colliding Beams
Colliding beams are more difficult to build. Then why do we prefer
to use colliding beams.
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Particle Creation
 Use the second page of the package
Electrons have a mass of 0.5 MeV/c2
Muons have mass of 105 MeV/c2
 Determine using the two options in the package
the beam energy in an electron positron collision:
Fixed target
Colliding Beams
 Why are the numbers different?
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How to Measure Momentum?
 Most Particles are Charged.
If a charged particle moves through in a magnetic field

it experiences a field
F  vqB  ma

 
F  qv  B
So the acceleration is proportional to the magnetic
field and perpendicular to the direction of motion.
Magnetic Field into Page
Momentum given by:
Velocity in direction of
arrow.
 How can we measure Momentum
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Dashed Arrow: Force
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Charged Particle in a Magnetic Field
 In the Program the momentum is given by the following
p  0.3Br
equation:
P = momentum (in GeV/c)
B strength of magnetic field in Tesla
R = radius of curve in metres
 So we can calculate the momentum if we can measure the
radius of the curve made by the particle in the magnetic
field
 Simple Mathematics: x2 + y2 = r2
Pick three points on a circle and you get a radius
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Charged Particle II
 Use the package, charged particles
Choose Magnetic Field strength of around 3 Tesla
Choose Incident beam energy of 3 GeV
Click on Fire to produce an event
Click radius, the use the mouse to select three points
on a track
Best choose three points equally separated and as far apart as
possible (do not use the circle at the end)
 From the radius the momentum is calculated
(see page 2 of spreadsheet)
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Charged Particle III

Now we calculate the total energy of the particle
assuming that it is one of the four following particles:
1)
2)
3)
4)

Muon: mass 105 MeV/c2
Pion: mass 140 MeV/c2
Kaon: mass 494 MeV/c2
Proton: mass 938 MeV/c2
We use the equation: E2 = (pc)2 + (mc2)2 to calculate the
beam energy.
 The spreadsheet does this four times
 Which of the above particles best agrees with the chosen beam
energy
 Can you guess which particle it is?
 (Note it will be difficult to separate muons and pions)
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Particle Lifetimes
 Most Particles are unstable – I.e they decay.
Important property is the lifetime of the particle
Quantum Mechanical Effect – Decay is random
We have to measure many decays and take the average to determine a
real lifetime (in fact we need to fit the data)
Relativistic Effects are important:
Need to take account time dilation etc.
Ebeam
 
mK c 2
L
Use the mass and lifetime page

2
of the package
c  1
Choose a high beam energy
(The particle will travel further before decaying)
Click fire then length
Click on both Crosses to get the length before decay:
Enter into a zero length measurement cell,  will be calculated
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Masses  The kaon decays to two pions:
K 0    
 By measuring the momentum and the angle between the
two pions we can calculate the mass of the kaon if we
know the mass of the pion:
mK c 2  2m2 c 4  2 p1 p2 cos  E1E2
 (Take this formula as a given)
Enter the measured radii and opening angle for each measurement
on the sheet.
Make ten measurements
Get average mass.
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