PHYS 3446 – Lecture #16
Wednesday, Nov. 1, 2006
Dr. Jae Yu
1. Elementary Particle Properties
•
•
•
•
•
Forces and their relative magnitudes
Elementary particles
Quantum Numbers
• Baryon
• Lepton numbers
• Strangeness
• Isospin
Gell-Mann-Nishijima Relations
Production and Decay of Resonances
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
1
Announcements
•
LPCC Workshop
–
–
–
•
Time: 10am – 5pm, Saturday, Nov. 4
Place: CPB 303
Lunch and refreshments will be provided
Bring your PDG booklet to class all the time
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
2
Forewords
• What are elementary particles?
– Particles that make up all the 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
• What allowed this to happen?
– The increasing energies of accelerators allows us to probe smaller
distance scales
• What is the energy needed to probe 0.1–fm?
– From de Broglie Wavelength, we obtain
P
Wednesday, Nov. 1, 2006

PHYS 3446, Fall 
2006
Jae Yu
c 197fm  MeV 2000MeV / c


c
0.1fm c
3
Forces and Their Relative Strengths
• Classical forces:
– Gravitational Force: all matters are subject to this force, including
massless ones
• How do you know that even massless ones get affected?
– Lights bends around heavy planets or even a black hole
– Electromagnetic Force: 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 yet seen but just a concept)
• Electromagnetism: Photons
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
4
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!!!
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
5
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
ke
ke
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 from the above?
– The absolute values of the potential energy decreases quadratically
with increasing momentum transfer
– The relative strength is independent of momentum scale
 e2  k
ke 2
VEM
c5  1  1 1039 GeV 2
36



~
10


2
2


2
Wednesday,
Nov.
2006
PHYS
6
2 3446,
GN1, m
Vg
c
GNFall 2006
6.7
  mc
 137  1GeV


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
mp c 2r

e c
Fourier x-form
r
mW c 2r
2
gW  c
VW  r  
e
r
Fourier x-form
VS  r  
VW  r  
gS
q 2  mp2 c 2
gW2
q 2  mW2 c 2
– gW and gs: coupling constants or effective charges
– mW and mp: masses of force mediators
• The values of the coupling constants can be estimated from
2
2
experiments
g
g
S
c
Wednesday, Nov. 1, 2006
 15
PHYS 3446, Fall 2006
Jae Yu
W
c
 0.004
7
Forces’ Relative Strengths
• We could think of p as the strong force mediator w/
mp  140MeV / c 2
• From observations of beta decays, mW  80GeV / c 2
• 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
qc 
2 2
Wednesday, Nov. 1, 2006
2 4
mpc
 1GeV
2
PHYS 3446, Fall 2006
Jae Yu
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Forces’ Relative Strengths
• The relative strength between EM and strong
potentials is
g S2
2
q
c
VS


2
2 2
2
c e q  mp c
VEM
2
gS
c
2 4
m pc
c
2
2 4
2 2
e m p c  mp 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
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
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Interaction Time
• The ranges of forces also affect interaction time
– Typical time for strong interaction ~10-24sec
• What is this time?
• A time that takes light to traverse the size of a proton (~1 fm)
– Typical time for EM interaction ~10-20 – 10-16 sec
– Typical time for Weak interaction ~10-13 – 10-6 sec
• In GeV ranges, the four forces are different
• These are used to classify elementary particles
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
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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
Interactions
G, EM
Charged:G, EM, W
Neutral: G, W
G, EM, W, S
G, EM, W, S
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
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Elementary Particles: Bosons and Fermions
• All particles can be classified as bosons or fermions
– Bosons (integer spin) follow Bose-Einstein statistics
• Quantum mechanical wave function is symmetric under the
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 (half integer spin) obey Fermi-Dirac statistics
• Quantum mechanical wave function is anti-symmetric under the
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,
Wednesday, Nov. 1, 2006
 F   F
PHYS 3446, Fall 2006
Jae Yu
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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 have the same masses as particles but with opposite
charges and quantum numbers
– What is the anti-particle of
•
•
•
•
A p0? p 0
A neutron? n
0
A K0? K
A Neutrinos? 
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
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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
experimental observations
• One of the clearest conservation is the lepton number
conservation
– While photon and meson numbers are not conserved
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
14
Baryon Numbers
• Can the decay p  e  p 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 (probability<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.
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
15
Lepton Numbers
• Quantum number of leptons
– All leptons carry L=1 (particles) or L=-1 (antiparticles)
– Photons or hadrons carry L=0
• Lepton number is a conserved quantity
– Total lepton number must be conserved
– Lepton numbers by species must be conserved
– This is an empirical law necessitated by experimental observation (or
lack thereof)
• Consider the decay e   e   p   p 
– Does this decay process conserve energy and charge?
• Yes
– But it hasn’t been observed, why?
• Due to the lepton number conservation
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
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Lepton Number Assignments
Leptons
Le
Lm
Lt
L=Le+Lm+Lt
e- (e+)
1 (-1)
0
0
1 (-1)
 e  e 
1 (-1)
0
0
1 (-1)
m m
0
1 (-1)
0
1 (-1)
 m  m 
0
1 (-1)
0
1 (-1)
t t
 
0
0
1 (-1)
1 (-1)
t t 
0
0
1 (-1)
1 (-1)
(anti-leptons)
 
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
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Lepton Number Conservation
• Can the following decays occur?
Decays
m   e  
m   e  e  e
m   e   e   m
Le
0 1 0
0 1 1 1
0 1 1  0
Lm
1 0  0
1 0  0  0
1 0  0 1
Lt
000
0000
0000
L=Le+Lm+Lt
11 0
1 111
1 111
– Case 1: L is conserved but Le and Lm not conserved
– Case 2: L is conserved but Le and Lm not conserved
– Case 3: L is conserved, and Le and Lm are also conserved
Wednesday, Nov. 1, 2006
PHYS 3446, Fall 2006
Jae Yu
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