Download PHYS 1443 – Section 501 Lecture #1

PHYS 3446 – Lecture #14
Wednesday, Oct. 25, 2006
Dr. Jae Yu
1. Particle Accelerators
•
•
•
Electro-static Accelerators
Cyclotron Accelerators
Synchrotron Accelerators
2. Elementary Particle Properties
•
•
•
•
•
Forces and their relative magnitudes
Elementary particles
Quantum Numbers
Gell-Mann-Nishijima Relations
Production and Decay of Resonances
Wednesday, Oct. 25, 2006
PHYS 3446, Fall 2006
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Announcements
• Quiz in class next Wednesday, Nov. 1
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Principles of Calorimeters
Total absorption
calorimeter: See
the entire shower
energy
Sampling calorimeter:
See only some fraction
of shower energy
For EM
Absorber plates
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X 0vis
E  fEvis  abs
Evis
X 0  X 0vis
0vis
Evis
For HAD E  fEvis  abs
0  30vis
Example Hadronic Shower (20GeV)
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Particle Accelerators
• How can one obtain high energy particles?
– Cosmic ray  Sometimes we observe 1000TeV cosmic rays
• Low flux and cannot control energies too well
• Need to look into small distances to probe the fundamental
constituents with full control of particle energies and fluxes
– Particle accelerators
• Accelerators need not only to accelerate particles but also to
– Track them
– Maneuver them
– Constrain their motions to the order of 1mm
• Why?
– Must correct particle paths and momenta to increase fluxes and control
momenta
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Particle Accelerators
• Depending on what the main goals of physics are, one needs
different kinds of accelerator experiments
• Fixed target experiments: Probe the nature of the nucleons 
Structure functions
– Results also can be used for producing secondary particles for further
accelerations  Tevatron anti-proton production
• Colliders: Probes the interactions between fundamental
constituents
– Hadron colliders: Wide kinematic ranges and high discovery potential
• Proton-anti-proton: TeVatron at Fermilab, Sp`pS at CERN
• Proton-Proton: Large Hadron Collider at CERN (late 2007)
– Lepton colliders: Very narrow kinematic reach, so it is used for precision
measurements
• Electron-positron: LEP at CERN, Petra at DESY, PEP at SLAC, Tristan at KEK,
ILC in the med-range future
• Muon-anti-muon: Conceptual accelerator in the far future
– Lepton-hadron colliders: HERA at DESY
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Electrostatic Accelerators: Cockcroft-Walton
• Cockcroft-Walton Accelerator
– Pass ions through sets of aligned DC electrodes at successively
increasing fixed potentials
– Consists of ion source (hydrogen gas) and a target with the electrodes
arranged in between
– Acceleration Procedure
• Electrons are either added or striped off of an atom
• Ions of charge q then get accelerated through series of electrodes, gaining kinetic
energy of T=qV through every set of electrodes
• Limited to about 1MeV acceleration due to
voltage breakdown and discharge beyond
voltage of 1MV.
• Available commercially and also used as the
first step high current injector (to ~1mA).
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Electrostatic Accelerators: Van de Graaff
• Energies of particles through DC accelerators are
proportional to the applied voltage
• Robert Van de Graaff developed a clever mechanism to
increase HV
– The charge on any conductor resides on its outermost
surface
– If a conductor carrying additional charge touches another
conductor that surrounds it, all of its charges will transfer to
the outer conductor increasing the charge on the outer
conductor, increasing HV
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Electrostatic Accelerators: Van de Graaff
• Sprayer adds positive charge to
the conveyor belt at corona points
• Charge is carried on an insulating
conveyor belt
• The charges get transferred to the
dome via the collector
• The ions in the source then gets
accelerated to about 12MeV
• Tandem Van de Graff can
accelerate particles up to 25 MeV
• This acceleration normally occurs
in high pressure gas that has very
high breakdown voltage
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Resonance Accelerators: Cyclotron
• Fixed voltage machines have intrinsic
limitations in their energy due to
breakdown
• Machines using resonance principles
can accelerate particles in higher
energies
• Cyclotron developed by E. Lawrence
is the simplest one
• Accelerator consists of
– Two hallow D shaped metal chambers
connected to alternating HV source
– The entire system is placed under
strong magnetic field
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Resonance Accelerators: Cyclotron
• While the D’s are connected to HV sources,
there is no electric field inside the chamber
due to Faraday effect
• Strong electric field exists only in the gap
between the D’s
• An ion source is placed in the gap
• The path is circular due to the
perpendicular magnetic field
• Ion does not feel any acceleration inside a
D but gets bent due to magnetic field
• When the particle exits a D, the direction of
voltage can be changed and the ion gets
accelerated before entering into the D on
the other side
• If the frequency of the alternating voltage is
just right, the charged particle gets
accelerated continuously until it is extracted
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Resonance Accelerators: Cyclotron
• For non-relativistic motion, the frequency appropriate for
alternating voltage can be calculated from the fact that the
magnetic force provides centripetal acceleration for a circular
orbit
v qB
v2
vB
m
r
q
r
c

mc
w
• In a constant angular speed, w=v/r. The frequency of the
motion is
qB

1  q B
f
2


2 mc 2  m  c
• Thus, to continue accelerate the particle the electric field
should alternate in this frequency, cyclotron resonance
frequency
• The maximum kinetic energy achievable for an cyclotron with
2
radius R is
 qBR 
1
1
2
2 2
T

mv

m

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2006 
maxPHYS 3446, Fall R
2
2Jae Yu
mc 2
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Resonance Accelerators: Linear Accelerator
• Accelerates particles along a linear path using resonance principle
• A series of metal tubes are located in a vacuum vessel and connected
successively to alternating terminals of radio frequency oscillator
• The directions of the electric fields changes before the particles exits the
given tube
• The tube length needs to get longer as the particle gets accelerated to
keep up with the phase
• These accelerators are used for accelerating light particles to very high
energies
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Synchroton Accelerators
• For very energetic particles, the relativistic effect must be taken
into account
• For relativistic energies, the equation of motion of a charge q
under magnetic field B is
dv
vB
m
dt
 m v   q
• For v ~ c, the resonance frequency becomes
n
c

1 q 1B
  
2 2  m   c
• Thus for high energies, either B or n should increase
• Machines with constant B but variable n are called synchrocyclotrons
• Machines with variable B independent of the change of n is
called synchrotrons
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Synchroton Accelerators
• Electron synchrotrons, B varies while n is held
constant
• Proton synchrotrons, both B and n varies
• For v ~ c, the frequency of motion can be expressed
• For an electron
1 v
c
f

2 R 2 R
p  GeV / c 
pc
R(m) 

qB 0.3B Tesla) 
• For magnetic field strength of 2Tesla, one needs radius
of 50m to accelerate an electron to 30GeV/c.
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Synchroton Accelerators
• Synchrotons use magnets
arranged in a ring-like
fashion.
• Multiple stages of
accelerations are needed
before reaching over GeV
ranges of energies
• RF power stations are
located through the ring to
pump electric energies into
the particles
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Forewords
• What are elementary particles?
– Particles that make up matter in the universe
• What are the requirements for elementary particles?
– Cannot be broken into smaller pieces
– Cannot have sizes
• The notion of “elementary particles” have changed from
1930’s through present
– In the past, people thought protons, neutrons, pions, kaons, rmesons, etc, as elementary particles
• Why?
– Due to the increasing energies of accelerators that allows us to
probe smaller distance scales
• What is the energy needed to probe 0.1–fm?
– From de Broglie Wavelength, we obtain
P
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
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2006
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c 197fm  MeV 2000MeV / c


c
0.1fm c
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Forces and Their Relative Strengths
• Classical forces:
– Gravitational: every particle is subject to this force, including
massless ones
• How do you know?
– Electromagnetic: only those with electrical charges
– What are the ranges of these forces?
• Infinite!!
– What does this tell you?
• Their force carriers are massless!!
– What are the force carriers of these forces?
• Gravity: graviton (not seen but just a concept)
• Electromagnetism: Photons
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Forces and Their Relative Strengths
• What other forces?
– Strong force
• Where did we learn this force?
– From nuclear phenomena
– The interactions are far stronger and extremely short ranged
– Weak force
• How did we learn about this force?
– From nuclear beta decay
– What are their ranges?
• Very short
– What does this tell you?
• Their force carriers are massive!
• Not really for strong forces
• All four forces can act at the same time!!!
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Forces’ Relative Strengths
• The strengths can be obtained through potential, considering
two protons separated by a distance r.
• Magnitude of Coulomb
and gravitational potential are
2
2
e
e
Fourier x-form
VEM  r  
VEM  r   2
r
q
2
2
G
m
GN m Fourier x-form
Vg  r   N 2
Vg  r  
q
r
– q: magnitude of the momentum transfer
• What do you observe?
– The absolute values of the potential E decreases quadratically with
increasing momentum transfer
– The relative strength is, though independent of momentum transfer
 e2  1
e2
VEM
c5  1  1 1039 GeV 2
36



~
10


2
2 3446, Fall 2006
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Oct.
2006
PHYS
20
2
G25,
m
Vg
c
GN  137  1GeV 2
6.7
N
  mc


Jae Yu
Forces’ Relative Strengths
• Using Yukawa potential form, the magnitudes of strong and
weak potential can be written as
2
VS  r  
g S2
m c 2r

e c
Fourier x-form
r
mW c 2r
2
gW  c
VW  r  
e
r
Fourier x-form
VS  r  
gS
q 2  m2 c 2
gW2
VW  r   2
q  mW2 c 2
– gW and gs: coupling constants or effective charges
– mW and m: masses of force mediators
• The values of the coupling constants can be estimated from
2
2
experiments
g
g
S
c
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W
c
 0.004
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Forces’ Relative Strengths
• We could think of  as the strong force mediator w/
m  140 MeV / c 2
2
m

80
GeV
/
c
• From observations of beta decays, W
• However there still is an explicit dependence on
momentum transfer
– Since we are considering two protons, we can replace the
momentum transfer, q, with the mass of protons
2 2
qc
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2 4
 mp c
 1GeV
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Forces’ Relative Strengths
• The relative strength between EM and strong
potentials is
g S2
2
VS
c
q


2
2
2 2
VEM
c e q  m c
2
gS
c
2 4
m pc
c
2
2 4
2 2
e m p c  m c
 15  137  1  2  103
• And that between weak and EM potentials is
VEM e c q 

c gW2
q
VW
2
2
mW2 c 2
2
2 4
2 2
m
c

m
e c p
Wc

c gW2
m 2p c 4
2
1
1


 802  1.2 104
137 0.004
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Interaction Time
• The ranges of forces also affect interaction time
– Typical time for Strong interaction ~10-24sec
• What is this?
• A time that takes light to traverse the size of a proton (~1 fm)
– Typical time for EM force ~10-20 – 10-16 sec
– Typical time for Weak force ~10-13 – 10-6 sec
• In GeV ranges, the four forces are different
• These are used to classify elementary particles
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Elementary Particles
• Before the quark concepts, all known elementary
particles were grouped in four depending on the
nature of their interactions
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Elementary Particles
• How do these particles interact??
– All particles, including photons and neutrinos, participate in
gravitational interactions
– Photons can interact electromagnetically with any particles
with electric charge
– All charged leptons participate in both EM and weak
interactions
– Neutral leptons do not have EM couplings
– All hadrons (Mesons and baryons) responds to the strong
force and appears to participate in all the interactions
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Elementary Particles: Bosons and Fermions
• All particles can be classified as bosons or fermions
– Bosons follow Bose-Einstein statistics
• Quantum mechanical wave function is symmetric under exchange
of any pair of bosons
 B  x1, x2 , x3 ,...xi ...xn    B  x2 , x1 , x3 ,...xi ...xn 
• xi: space-time coordinates and internal quantum numbers of
particle i
– Fermions obey Fermi-Dirac statistics
• Quantum mechanical wave function is anti-symmetric under
exchange of any pair of Fermions
 F  x1, x2 , x3 ,...xi ...xn    F  x2 , x1, x3 ,...xi ...xn 
• Pauli exclusion principle is built into the wave function
– For xi=xj,
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 F   F
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Bosons, Fermions, Particles and Antiparticles
• Bosons
– All have integer spin angular momentum
– All mesons are bosons
• Fermions
– All have half integer spin angular momentum
– All leptons and baryons are fermions
• All particles have anti-particles
– What are anti-particles?
• Particles that has same mass as particles but with opposite quantum numbers
– What is the anti-particle of
•
•
•
•
A 0 ?
A neutron?
A K0?
A Neutrinos?
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Quantum Numbers
• When can an interaction occur?
– If it is kinematically allowed
– If it does not violate any recognized conservation laws
• Eg. A reaction that violates charge conservation will not occur
– In order to deduce conservation laws, a full theoretical
understanding of forces are necessary
• Since we do not have full theory for all the forces
– Many of general conservation rules for particles are based on
experiments
• One of the clearest conservation is the lepton number
conservation
– While photon and meson numbers are not conserved
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Baryon Numbers
• Can the decay p  e   0 occur?
– Kinematically??
• Yes, proton mass is a lot larger than the sum of the two masses
– Electrical charge?
• Yes, it is conserved
• But this decay does not occur (<10-40/sec)
– Why?
• Must be a conservation law that prohibits this decay
– What could it be?
•
•
•
•
An additive and conserved quantum number, Baryon number (B)
All baryons have B=1
Anti-baryons? (B=-1)
Photons, leptons and mesons have B=0
• Since proton is the lightest baryon, it does not decay.
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Assignments
1. Carry out Fourier transformation and derive
equations 9.3 and 9.5
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