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Nucleons Are Not Elementary Particles!
eep
hadron
jet
Scatter high-energy electrons off
protons. If there is no internal
structure of e- or p, then welldefined “elastic” e- energy for
each angle. See structure!!
scatter probability
excited states of the proton
elastic
x1/8.5
Each line in the
energy
spectrum of
scattered
electrons
ground state of
the proton
Bartel
etal.
PL28B,
148
(1968)
energy of scattered electron
corresponds to
a different
energy state of
the proton.
The Quark Model
The quark model represents a relatively simple picture
of the internal structure of subatomic particles and
makes predictions of their production and decay. It
uses a minimum of adjusted quark parameters and has
great predictive power, e.g., for the composite-particle
masses, magnetic moments, and lifetimes.
There are no contradictions to this model known so far,
(but many questions remain).
Internal Nucleonic Structure
e-
e-
The proton has internal structure,
so-called quarks (u,u,d).
Quarks combine to nucleon states
of different excitations.
Proton is the (u,u,d) ground state
p
1200
MeV
938
MeV
135
MeV
 S=3/2
N S=½
e   (1232)
 

e  p  e  (1450)
e   (1688)

N: one doublet with a splitting of
only m = 1.3 MeV
: one quadruplet with a splitting
of only m = 8 MeV
p S=0
Mesons
The Quark-Lepton Model of Matter
Explains the consistency of the known particles in all of their states.
3 families of quarks (3 “colors” each) and associated leptons.
All are spin-1/2 particles, quarks have non-integer charges
Nucleons (q,q,q)
Mesons (q, q-bar)
q-bar:anti-quark
Leptons
Hadrons
Baryons
Particle Spectrum
Mesons
Simplified scheme of
stable or unstable
subatomic particles.
Y'’
4
Mass (GeV/c2)
Y'
Families have
different interactions,
Leptons: weak+elm,
Hadrons:
weak+elm+strong
J/Y
3
“strange”
2
t
W
X*
Y*

X
8 S
L
N
1
10
K*
w
r
h
K
0
m
n, e
Spin ½
8
p
½
3/2
0
1
Each particle also has
an anti-particle, with
inverse quantum
numbers.
e  e
p p
nn
K  K , etc.
Quark Quantum Numbers
All: spin=1/2, baryon number B=1/3
Flavor
Q/e
M/GeVc-2
T
T3
S
C
B*
Top
u
+2/3
0.005
½
½
0
0
0
0
d
-1/3
0.009
½
-½
0
0
0
0
s
-1/3
0.175
0
0
-1
0
0
0
c
+2/3
1.5
0
0
0
1
0
0
b
-1/3
4.9
0
0
0
0
-1
0
t
+2/3
162
0
0
0
0
0
1
T,T3: isospin; S: strangeness; C: charm; B*: bottom qu.#, Top: top qu.#
Structure of Composite Particles
There are only 3-quark (q,q,q)  Baryons and quark-antiquark ( q, q )
configurations. No free quarks or higher quark multiplicities.
_
_
_
u
d
s
quarks
antiquarks
u
s
d
s= 1/2
s= 0
0 T3 d d
n
u
Sd d
s
S
u u
d p
s d
X- s
S0
u d
s
L0
K0
S+
u u
s
s u
s 0
X
p_u d
_
s d
_
s u K+
p0
_
_
u u d d
_
h
h’
s s
_
s
u
K-
_
u s
p_+
d u
_
K0
s = 3/2
0
T3

0
d d
d
d d
u
S*
d
s d

d u
u
S*0
d
s u
d
X* s
s
S
u S*
s u
u s
s
W
s s
s

u u
u
X*0
Meson Wave Functions
Examples to interpret the graphic shorthand in these figures:
Mesons
p   ud
p
0
p   ud

1

uu  dd
2

simple qq structure
mixed qq state
Meson spins are integer, vector sum of halfinteger quark and anti-quark spins, and their
integer orbital angular momentum l. In ground
state, mostly l =0.
Baryon Wave Functions
Examples to interpret the graphic shorthand:
s  1/ 2 Baryons
p   u u  d 
n   d  d u 
qqq structure
s  3 / 2 Baryons

0


u d d



 u u  d 
aligned qqq state
These Baryon and Meson wave functions are schematic, do
not have proper (anti-)symmetry property required by Pauli
Principle: The total particle wave function
 (all coordinates)   ( space)   ( flavor )   ( spin) 
must be antisymmetric under quark exchange (quarks are fermions)
Pauli Principle and Color Coordinate
Quarks are Fermions
 no two same quarks can be in the same state
d 
d d
have both 3 identical fermions (same
quarks) with same spins (S=3/2) and
isospin (T3=+3/2) states
u 
u u
s3,T
3
s3,T
3
Violates Pauli Principle !?
Conclusion: There must be an additional quantum number (degree of
freedom), “color”. Need 3 colors and their anti-colors
Red
Green
Blue
Red  Cyan, Green  Magenta, Blue  Yellow
Color and complementary color (anti-color) add up to color-less (white)
_
_
_
d
d
d
d quarks
anti-d quarks d
d
d
Color Wave Function
d
d
d
d quarks
anti-d quarks
_
d
_
d
_
d
++ : Flavor and spin configurations symmetric, spatial
configuration symmetric (no orbital angular momentum, l =0)
 color configuration must be antisymmetric. All colors are
present with equal weights. All physical particles are “white.”
Mesons
rr
p   mix of ur d r , ub db , u g d g
Baryons
p  mix of ur ub d g , ubur d g , ur u g db ,...
Necessity of color rules out combinations such as (q),(q, q, q),.....
There are no free quarks  Confinement
Gluons
Bound quark systems (physical particles) by q-q interactions.
Field quanta: 8 Gluons (not actually pions!)
Spin and parity 1- like a photon.
Gluons carry color and the corresponding anticolor.
Color can be transferred but particle remains colorless.
_
q
qc’
qc
gluon emission
changes color
q
q-qbar creation
self coupling
of the color charges
Usual conservation laws apply to reactions between quarks.
time
Gluon Exchange
b
_
b
g
_
g
b
_
b
g
b
_
r
_
d
b
g
r
u
p
g
r
u
b
Gluons are exchanged back
and forth between q-q,
g
changing q colors and
momenta dynamically
r, g, and b are visited with
equal probability
r
u
p
d
Baryon Production with Strong Interactions
Typically: Energetic projectile hits nucleon/nucleus,
new particles are produced.
Rules for strong interactions:
•Energy, momentum, s, charge, baryon numbers, etc., conserved
•q existing in system are rearranged, no flavor is changed
•q-q-bar pairs can be produced
p
p
u
u
d
_
d
u
time 
annihilation
d, d-bar
u
u
s
_
s
u
creation
s, s-bar
S
Example
p  p   S  K 
K
time 
Baryon Resonances
p
p+
_
d u
u u d
Typically: Energetic projectile hits
nucleon/nucleus, intermediate
particle is produced and decays into
other particles.
Example
p  p      p  p 
u u
u
++
++ produced as short-lived intermediate state,
t = 0.5·10-23s
corresp. width of state: G = ħ/t = 120 MeV
u u d
p
_
d u
p+
This happens with high probability when a
nucleon of 300 MeV/c, or a relative energy of
1232 MeV penetrates into the medium of a
nucleus.  Resonance
Confinement and Strings
Why are there no free quarks? Earlier: symmetry arguments.
Property of gluon interaction between color charges (“stringlike character).
Q: Can one dissociate a qq pair?
field lines: color strings
energy in strings
proportional to length
0.9GeV/fm
successive q/q-bar creation, always in pairs!
Leptons
Leptons have their own quantum number, L, which is conserved.
It seems likely, but is not yet known, whether electronic, muonic
and tau lepton numbers are independently conserved in reactions
and decays.
Conservation Laws
Quantum numbers are additive.
Anti-quarks have all signs of quark quantum numbers reversed,
except spin and isospin.
Derived quantities:
Charge
Q  e T3  (1 2) B  S  C  B * Top
Hypercharge Y  B  S
In a reaction/transmutation, decay, the following quantities
are conserved (before=after):
•The total energy, momentum, angular momentum (spin),
•The total charge, baryon number, lepton number
Conservation Laws in Decays
Decay
A  B + C
possible, if
mAc2 ≥ mBc2 + mCc2
Otherwise, balance must be
supplied as kinetic energy.
Relativistic energy of particle
with rest mass m, momentum p :
E
 pc 
2
  mc

2 2
 Ekin  mc 2
Example: Conservation of charge, baryon number, lepton number in
neutron decay.
n  p  e   n e n  decay
p  m   n  n m m  capture
B 1 1  0  0  1
Le  0  0  1  1  0
1  0  1 0
Lm  0  1  0  1
Q 0  e e 0  0
e e  00
Weak Interactions
10-5 weaker than strong interaction, small probabilities for
reaction/decays. Mediated by heavy (mass ~100GeV)
intermediate bosons W± ,Z0.
Weak bosons can change quark flavor
d
u
W+
u
up-down
conversion
carries +e
u
Z0
W-
s
strange-non-strange
conversion
carries –e
u
no flavor change
carries no charge
Decays of W± and Z0 Bosons
Hadronic decays to quark pair are dominant (>90%), leptonic
decays are weak. All possible couplings:




l
,
n

e
,
n
,
m
,
n
,
t
,n t  leptonic decays
  
e 
m 

W 
 q, q    d , u  ,  s, c  ,  b, t  hadronic decays
  l ,n    e  ,n e  ,  m  ,n m  , t  ,n t 


W 
 q , q '   d , u  ,  s , c  ,  b , t 
 l , l    e  , e   , n e ,n e  ,  m  , m  ), (n m ,n m  ,

0


Z 
t
,
t
 ), (n t ,n t 

 q, q   (d , d ), (u, u ),  s, s ), (c, c  , (b, b ), (t , t )
Examples of Weak Decays
Can you predict, which (if any) weak boson effects the change?
_
p
ne

p
n
e
m
ne
?
?
time
?
n
n-decay?
p
n
neutrino scattering
off protons?
nm
e-
neutrino-induced
reaction off e-?
Examples of Weak Decays
Answer: Yes, all processes are possible. These are the bosons,
p
e-
_ p
ne
n
ne
m
W+
Z0
time
W-
n
n-decay
p
n
nm
e-
neutrino scattering
neutrino-induced
off protons
reaction off e-
Method:
•Balance conserved quantities at the vortex, where boson originates.
Remember W± carries away charge ±|e|.
•Balance conserved quantities at lepton vortex.
Particle Production
probability
In electron-positron collisions,
particle-anti-particle pairs can be
created out of collision energy,
either via electromagnetic or weak
interaction.
 collision energy (GeV)
m+
m-
e+
electromagnetic
e-
Z0
e+
weak
m+
m-
Z0
g
e-
antifermion
fermion
e-
e+
example
The Standard Model
The body of currently accepted views of structure and interactions of
subatomic particles.
Interactions
Interaction
Coupling
Charge
Field Boson
Mass/
GeVc-2
Jp
strong
color
gluons (8)
0
1-
elmgn
electric (e)
photon (g)
0
1-
weak
weak
W+, W-, Z0
100
1
Weak
interactions
violate certain
symmetries
(parity, helicity)
see later
Particles
Fermions
Family
Q/e
Color
Spin
Weak
Isospin
Quarks
u c t
d s b
+2/3
-1/3
r, b, g
½
½
Leptons
ne nm nt
e m t
0
-1
none
½
½
The Standard Model ct’d
Combine weak and elm interactions “electro-weak”
Type of isospin-symmetry: same particles carry weak and elm charge.
Vqq
Force range
Electromagnetic: ∞
0
1 fm
2mqc2
r
Weak: 10-3fm
Strong qq force increases with
distance
There are no free quarks. All free physical particles are colorless.
The End