View
232
Download
2
Embed Size (px)
Citation preview
Fundamental principles of particle physics
G.Ross, CERN, July08
Fundamental principles of particle physics
G.Ross, CERN, July07
• Introduction - Fundamental particles and interactions
• Symmetries I - Relativity
• Quantum field theory - Quantum Mechanics + relativity
• Theory confronts experiment - Cross sections and decay rates
• Symmetries II – Gauge symmetries, the Standard Model
• Fermions and the weak interactions
Outline
http://www.physics.ox.ac.uk/users/ross/cern_lectures.htm
Fundamental principles of particle physics
G.Ross, CERN, July07
Fundamental Interactions
† Short range
2
2
4
14 137
2 5†
36
†
2
1
10
10
sgs c
eem c
F p
N p
Strength
Strong
Electromagnetic
Weak G m
Gravitational G m
π
π
αα
−
−
==
h
h
:
:
:
:
Fundamental principles of particle physics
G.Ross, CERN, July07
Fundamental Particles
2
2
4
14 137
2 5†
36
†
2
1
10
10
sgs c
eem c
F p
N p
Strength
Strong
Electromagnetic
Weak G m
Gravitational G m
π
π
αα
−
−
==
h
h
:
:
:
:
Fundamental Interactions
Fundamental principles of particle physics
G.Ross, CERN, July07
Fundamental Particles
2
2
4
14 137
2 5†
36
†
2
1
10
10
sgs c
eem c
F p
N p
Strength
Strong
Electromagnetic
Weak G m
Gravitational G m
π
π
αα
−
−
==
h
h
:
:
:
:
Fundamental Interactions
Strength Size
22e4 r 2Energy PE + KE = -
e
pmE π= +
Heisenberg's
Uncertainty principle
p. rΔ Δ ≥h
2 2
2e
4 r 2-
em rE π≈ + h
1 2 3 4 5
-25
-20
-15
-10
-5
E
r
2 2
2 3e
4 r0
em rπ⇒ − =h
2
4 e
eem c m rcπα ≡ ≈ h
h
0Er
∂∂ =
pr r
p⇒ ≥Δ ≥ ≥Δh h
Units
8
34 2
3.10 m/sec
10 kg m /sec
c−
=
=h
Natural Units
Length : LTime : T
Energy : Eor Mass : m
Choose units such that :
2
1 /
1 . ( . / )
c L T
E T M L T
=
= ≡h
1 unit left : choose9 -101 ( 10 electron volts = 1.6 10 J)E GeV= =
Natural Units
-10
-27
1
1 24
1 1.6 10
1 1.8 10
1 0.2
1 0.7 10 sec
energy of GeV J
mass of GeV kg
length of GeV fm
time of GeV
−
− −
;
;
;
;
...typical of elementary particles
2
41
e e
eem c m rc m rπα = =h
h ;
10 5
3
10 10
0.510
atom
e
r m fm
m GeV
−
−
: ;
;
2 24 10e
em πα −= ;
†
†
Dimensionless-same in any units
Fundamental Interactions and sizes
1m rα =
2 24 10e
em πα −= ≈10 5
3
10 10
0.510
atom
e
r m fm
m GeV
−
−
: ;
;
1510 1
1nucleus
p
r m fm
m GeV
−: ;
;
2
4 1gstrong πα = ≈
Atomic binding :
Nuclear binding :
2
2
4
14 137
2 5
2 36
1
10
10
sgs c
eem c
F p
N p
Strength
Strong
Electromagnetic
Weak G m
Gravitational G m
π
π
αα
−
−
==
h
h
:
:
:
:
Elementary particles
, ,e μ τ− − −
2/3 2 /3 2 /3, ,u c t
1/3 1/3 1/3, ,d s b− − −
Leptons :
Quarks :
, ,e μ τν ν ν
Isador Rabi 1937 “Who ordered the muon?”
Elementary particles
, ,e μ τ− − −Leptons :
Quarks : , ,u c t, ,u c t
, ,u c t
, ,d s b, ,d s b
, ,d s b
Hadrons : 3 strong “colour” charges
, ,e μ τν ν ν
Elementary forces
The strength of the force
Nucleus
Exchange forces
1 2 14( ) e e
em rV r π=
Experiments conducted in momentum space :
V
em( q ) : V
em( r )e−ik .r∫ d3r : α
k2
e−
Electromagnetism
Photon “propagator”
Feynman diagram
e1
e2
γ
Nucleus
1 2 14( ) e e
em rV r π=
Experiments conducted in momentum space :
2
. 3( ) ( ) iem emV V e d α−∫ k r
kq r r: :
e−
2 2
" "
Q
virtual photon
≡−k
2( )Q
1Q
R:
Exchange forces
Electromagnetism
e2
e1
γ
μ−
2
2 2
1
64 CM
dM
d E
σπ
=Ω
e+ e−
μ− μ +
Feynman diagram : Transition amplitude <final state| | initial state> IHQM
| | | |I IM H H e eααμ μ γ γ+ − + −∝ < > < >
| | (0,1, ,0)IH e e e iαγ + −< > ∝
| | (0,cos , ,sin )IH e iαμ μ γ θ θ+ −< > ∝
2( ) (1 cos )M RL RL e θ→ = +
θe+
e−
μ +
LH
LH
RH
RH
LH RH
γ
Application to a scattering processes e e μ μ+ − + −→
θe+
e−
μ +
μ−
( )2 2
22
1| 1 cos
4 4 137unpolarisedCM
d e
d E
σ αθ α
π= + = =
Ω
cosθ
21
4( ) sgstrong rV r π= (Q2)
q
q
2 2
" "
Q
virtual gluon
≡−k
In momentum space :
g
2
. 3( ) ( ) sis sV V e d α−∫ k r
kq r r: :
Exchange forces
Strong interactions gs
gs
1 2 14( ) Zg g M r
weak rV r eπ−=
2 2
. 3( ) ( ) weak
Z
iweak weak M
V V e d α−
+∫ k r
kk r r: :
(Q2)
q
e−
" "virtual Z boson
In momentum space :
Z
21
ZF M
G ∝
Exchange forces
Weak force
Yukawa interaction
g1
g2
1 2( ) m mgravity N rV r G=
(Q2)
2m
1m
" "virtual graviton
G
Exchange forces
Gravitational force
11 3 2
1/ 2 19
33
6.610 / .sec ..
( /
.
) 1
.
1
:
.210
0
N Planck
N
Planck
fundamental
ma
G m kg could pr
ss c G GeV M
lengt
ovide scale
h cm l−
−
= =
≡
=
≡
=
h
!Planckor maybe M not fundamental
(Q2)
m2
1m
G1 2( ) m m
gravity N rV r G=
Exchange forces
Gravitational force
References useful for future lectures:
Halzen & Martin, ‘Quarks & leptons’, Wiley, 1984
Aitchison & Hey, ‘Gauge Theories in Particle Physics’, Taylor and Francis, 2005
[Peskin & Schroeder, ‘Quantum Field Theory’, Addison-Wesley, 1995]