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Nuclear Physics I (PHY 551)
Joanna Kiryluk
Spring Semester Lectures 2014
Department of Physics and Astronomy, Stony Brook University
Lecture 3:
2. Nucleon Structure –continued
§  Elementary Particles, Fundamental Interactions
and the Standard Model
§  Form factors
Textbook: Wong, Chapter 2
1
The Standard Model
A theory which explains what is the matter made of and how
subatomic particles interact with each other. The Standard
Model is a Quantum Field Theory:
the union of Quantum ChromoDynamics (QCD) and the
electro-weak theory. Standard
Model does not include gravity!
+ Higgs boson
the first elementary spin 0 particle
observed
2
3
Feynman diagrams
§ 
§ 
§ 
§ 
pictorial representations of particle interactions
forces are described by exchange of particles
primarily applied to Quantum Field Theory
mathematical tool for calculating amplitudes for a given process
Feynman diagram elements
4
Feynman diagrams
§ 
§ 
§ 
§ 
pictorial representations of particle interactions
forces are described by exchange of particles
primarily applied to Quantum Field Theory
mathematical tool for calculating amplitudes for a given process
x
Quantum Electro-Dynamics
(QED)= relativistic quantum
field theory of electrodynamics
q = p1 + p3 = p2 + p4
t
M.Peskin, D. Schroeder, An Introduction to Quantum Field Theory
Feynman diagrams provide physical insight into the nature
5
of particle interactions.
quark, lepton, neutrino
photon, boson Z, W+, W(virtual – “off mass-shell” particles)
gluon
Vertex: point where fermion and boson lines connect.
Energy, momentum, charge, lepton and baryon
numbers are conserved.
Caution: Different plotting conventions in different books (calculations give the
same results). It is important to understand how to read these plots.
Example:
e+ + e− → µ + + µ −
e+
γ*
e-
µ-
µ+
time
Convention 1
e+ and e- (and µ+ and µ-) move
forward in time. we’ll use this
convention in this lecture, less
confusing
quark, lepton, neutrino
photon, boson Z, W+, W(virtual – “off mass-shell” particles)
gluon
Vertex: point where fermion and boson lines connect.
Energy, momentum, charge, lepton and baryon
numbers are conserved.
e+
γ*
µ+
annihilation
eγ*
µ-
e-
e-
µ+
µ+
scattering
9
Feynman diagrams
Process amplitude ~
(single boson exchange)
~
1

'
' µ
' 
q = (ν , q ) = ( k − k ) = ( E − E , p − p )
µ
k
k’
α = e 2 4π
α = e 2 4π
Coulomb scattering
2
2
dσ dq ~ α q
4
10
Feynman diagrams
Amplitude: M=
+
+
+
+ …..
Perturbative expansion (terms with αn)
Cross section: dσ~|M|2
11
Electroweak Interactions
Charged currents interactions:
Examples:
Or
Neutral currents interactions:
eν
e
e-
Example:
Muon decay
W- νe
µ-
νµ
Helicity
! Ĥ, Ŝ # ≠ 0
Z$
"
" Ĥ, Ŝ ⋅ p̂$ = 0
#
%
Sz – not a “good quantum number” because Sz and
Hamiltonian don’t commute.
The component of particle’s spin along its momentum
is a good quantum number.
Helicity = projection of particle’s spin on it’s momentum direction.
Note: different
notations/definitions
 


S⋅p
S⋅p
σ⋅p

1) h ≡ 
2) h ≡   3) h ≡ 
S= σ (spin 1 / 2 particle)
p
p
2
S p
σ = Pauli matrices
For a spin 1/2 particle helicity
1 or
2) and 3) h = ±1
1) h = ±
2
13
h-positive
h-negative
Helicity
Helicity = projection of particle’s spin on it’s momentum direction.
Note: different notations/definitions
 
 

S⋅p
S⋅p
σ⋅p
1) h ≡ 
2) h ≡   3) h ≡ 
p
p
S p
 1
S= σ (spin 1 / 2 particle)
2
Definition 1) used in e.g.
§  M.Peskin, D. Schroeder “An Introduction to Quantum Field Theory”,
§  wikipedia
Definition 2) used in e.g.
§  B. Povh, K. Rith, C. Scholz, F. Zetsche “Particles and Nuclei”
§  E. Henley, A. Garcia “Subatomic Physics”
§  D. Griffiths “Introductory to Elementary Particles”
Definition 3) used in
§  S. Wong “Introductory Nuclear Physics”
In this course we will follow definition 2), 3)
14
Neutrinos in the mirror
Real world
left-handed
Negative helicity
Mirror world
right-handed
Positive helicity
Neutrinos in the mirror
Right-handed neutrino
Left-handed neutrino
does not exits
Right-handed anti-neutrino
Left-handed anti-neutrino
does not exits
Helicity Structure in Weak Interactions
In the ultra-relativistic limit only left-handed particles and right-handed antiparticles participate in charged current weak interactions. Weak interaction
bosons (Spin=1) are left-handed.
e− + ν e → W −
W-
Valid weak interaction
Mirror
W-
Does not occur
(parity is violated in weak interactions)
Feynman Diagram of the neutron Beta decay
−
n → p + e +νe
at partonic level:
d → u +W → u + e + νe
€
W-
νe
e
−
Weak Bosons resonance production
Example: e+ + e− → q + q
e+
q
q
e-
q- q
time
At sqrt(s)~MZ production of real Z0 boson
Weak boson discovered at SPS (Super Synchrotron Collider)
at CERN in the 1980’s
19
leptons
Force carriers
quarks
Elementary
particles
1st
2nd 3rd
3 generations
20
QED vs QCD
QED
Photons do not carry electric
charge
Gluons carry color charge
QCD
RB
21
QCD potential
4 αs
VQCD ( r ) = −
+ kr
3 r
k ~ 1 GeV / fm
§  QED-like at short distance r ≤ 0.01 fm
§  Quarks are tightly bound α s ~ 0.2
§  String tension: potential increases linearly at large distance
r ≥ 1 fm
Potential similar for baryons and mesons
Force between 2 quarks at large distance:
F = dVQCD dr
22
Strong interactions: gluons exchange
QCD is a gauge theory of the SU(3) gauge group obtained by taking the
color charge to define a local symmetry.
3x3 color combinations
gluon octet
gluon singlet
no color
does not exist
nucleon
What holds the nucleon?
23
Strong force carrier – the gluons
§ 1979 The first direct experimental evidence of gluons found, when three-jet
events were observed at the e+e- collider PETRA @ DESY
jet1
jet2
gluon bremsstrahlung
jet3
§  The angular distribution of the jets proved that the gluon is a spin 1 particle.!
This discovery marked the beginning of intensive tests of QCD
Strong force carrier – the gluons
An angular distribution of jets compared to QCD
calculations with a spin 0 and a spin 1 gluon.
25
Soft processes
(not described by QCD)
26
QED vs QCD
QED
DOES NOT EXIST
Photons interact only with
charged particles
DOES EXIST
QCD
Gluons interact with colorcharged particles (quarks
and gluons)
27
The gluon in the strong force
Confinement
The photon does not carry
electric charge.
αem = e2/4π ~ 1/137
Coupling constant: numerical coefficient that occur as
a parameter whenever there’s an interaction.
Strength of interaction ~ magnitude of a coupling constant
The gluon in the strong force
The photon does not carry
electric charge.
αem = e2/4π ~ 1/137
The gluon carries color
charge itself.
α ~ 1(large!)
Solution: running αs
α →α s (Q2 )
Extra diagrams depend on energy:
QCD at 10GeV = QCD at 1GeV , but with
smaller coupling constant
€
Running coupling and asymptotic freedom in QCD
2
α s (Q ) =
1
33 − 2n f
Q2
× ln 2
12π
Λ
The couplings, which set the strength for
the interactions, change their value if one
probes smaller distances with higher
energies.
where: nf=number of quarks with mass<Q and Λ~230 MeV
€
30
€
Extra
Running coupling and asymptotic freedom in QCD
1
2
α s (Q ) =
2
33 − 2n f
Q
× ln 2
12π
Λ
# −1 &
Λ 2 = µ 2 exp %
2 (
B
α
(
µ
)'
$ s
Λ ~ 230MeV
The effective strong coupling decreases with energy (typical for non-Abelian fields,
self-copupling gluons)
Q 2 →∝ α → 0
s
α em (Q 2 ) =
asymptotic freedom
α (µ )
( 1
" Q 2 %+
*1− α (µ )ln $ 2 '# µ &,
) π
α (µ = 1MeV ) = 1 137 (atomic physics)
α (M Z = 90GeV ) = 1 129 (LEP e+e- accelerator)
The effective em coupling increases with energy
(or decreasing with smaller Q2)
α em (Q12 )
α em (Q22 )
Q12 < Q22
31
Confinement: a crucial feature of QCD
(but no rigorous theoretical proof exists)
electron
nucleus
We can extract an electron from
an atom by providing energy
neutral atom
But we cannot get free quarks out of hadrons: “colour confinement”
quark-antiquark pair
created from vacuum
quark
“white” proton
(confined quarks)
Strong colour field 2
E=
mc
Energy
grows
with
separation!
“white”
proton
“white” π0
(confined quarks)
C.Lourenco (CERN)