Fundamental principles of particle physics...Fundamental principles of particle physics G.Ross,...
Transcript of Fundamental principles of particle physics...Fundamental principles of particle physics G.Ross,...
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
sg
s c
eem c
F p
N p
Strength
Strong
Electromagnetic
Weak G m
Gravitational G m
!
!
"
"
#
#
=
=
!
!
"
"
"
"
Fundamental principles of particle physics
G.Ross, CERN, July07
Fundamental Particles
2
2
4
14 137
2 5†
36
†
2
1
10
10
sg
s c
eem c
F p
N p
Strength
Strong
Electromagnetic
Weak G m
Gravitational G m
!
!
"
"
#
#
=
=
!
!
"
"
"
"
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
sg
s c
eem c
F p
N p
Strength
Strong
Electromagnetic
Weak G m
Gravitational G m
!
!
"
"
#
#
=
=
!
!
"
"
"
"
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
sg
s c
eem c
F p
N p
Strength
Strong
Electromagnetic
Weak G m
Gravitational G m
!
!
"
"
#
#
=
=
!
!
"
"
"
"
Fundamental Interactions
Strength Size
22e4 r 2
Energy PE + KE = - e
p
mE
!= +
Heisenberg's
Uncertainty principle
p. r! ! " !
2 2
2
e
4 r 2-
em r
E!
" +!
1 2 3 4 5
-25
-20
-15
-10
-5
E
r
2 2
2 3
e
4 r0
em r!
" # =!
2
4e
e
em c m rc!" # $
!
!
0E
r
!
!=
pr r
p! " # " "#
! !
Units
8
34 2
3.10 m/sec
10 kg m /sec
c
!
=
=!
Natural Units
Length : LTime : T
Energy : Eor Mass : m
Choose units such that :
2
1 /
1 . ( . / )
c L T
E T M L T
=
= !!
1 unit left : choose 9 -101 ( 10 electron volts = 1.6 10 J)E GeV= =
Natural Units
8 23
34 2 34 15
1 3.10 m/sec = 3.10 fm/sec
1 10 kg m /sec = 10 J/sec GeV fm
c
!
= =
= =! "
-10
-27
1
1 24
1 1.6 10
1 1.8 10
1 0.2
1 0.710 sec
energy of GeV J
mass of GeV kg
length of GeV fm
time of GeV
!
! !
!
!
!
!
...typical of elementary particles
2
4
1
e e
e
em c m rc m r!" = =
!
!"
10 5
3
10 10
0.510
atom
e
r m fm
m GeV
!
!
! "
"
2 2
410
e
em !"
#= !
†
†
Dimensionless-same in any units
Fundamental Interactions and sizes
1
m r! =
2 2
410
e
em !"
#= $
10 5
3
10 10
0.510
atom
e
r m fm
m GeV
!
!
! "
"
1510 1
1
nucleus
p
r m fm
m GeV
!! "
"
2
41
g
strong !" = #
Atomic binding :
Nuclear binding :
2
2
4
1
4 137
2 5
2 36
1
10
10
sg
s c
eem c
F p
N p
Strength
Strong
Electromagnetic
Weak G m
Gravitational G m
!
!
"
"
#
#
=
=
!
!
"
"
"
"
Elementary particles
, ,e µ !" " "
2/3 2 /3 2 /3, ,u c t
1/3 1/3 1/3, ,d s b
! ! !
Leptons :
Quarks :
, ,e µ !
" " "
Isador Rabi 1937 “Who ordered the muon?”
Elementary particles
, ,e µ !" " "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 !
" " "
√α
√α The strength of the forceγ
Nucleus
Exchange forces
1 2 14
( )e e
em rV r
!=
Experiments conducted in momentum space :
V
em( q ) ! V
em( r )e! ik .r
" d3r ! #
k2
e!
Electromagnetism
Photon “propagator”
Feynman diagram
√α
√α
γ
Nucleus
1 2 14
( )e e
em rV r
!=
Experiments conducted in momentum space :
2
. 3( ) ( ) i
em emV V e d !"
#k r
kq r r! !
e!
2 2
" "
Q
virtual photon
! "k
2( )Q
1Q
R!
Exchange forces
Electromagnetism
µ !
2
2 2
1
64CM
dM
d E
!
"=
#
e+
e!
µ ! µ+
Feynman diagram : Transition amplitude <final state| | initial state> I
HQM
| | | |I I
M H H e e!
!µ µ " "+ # + #$ < > < >
| | (0,1, ,0)I
H e e e i!" + #
< > $
| | (0,cos , ,sin )I
H e i!µ µ " # #+ $
< > %
2( ) (1 cos )M RL RL e !" = +
!
e+
e!
µ+
LH
LH
RH
RH
LHRH
!
Application to a scattering processes e e µ µ+ ! + !"
21
4( ) sg
strong rV r
!= (Q2)
q
√α
√α
q
2 2
" "
Q
virtual gluon
! "k
In momentum space :
g
2
. 3( ) ( ) si
s sV V e d
!"
#k r
kq r r! !
Exchange forces
Strong interactions
1 2 14
( ) Zg g M r
weak rV r e
!
"=
2 2
. 3( ) ( ) weak
Z
i
weak weakM
V V e d!"
+#k r
k
k r r! !
(Q2)
q
√α
√α
e!
" "virtual Z boson
In momentum space :
Z
2
1
ZF MG !
Exchange forces
Weak force
Yukawa interaction
1 2( )m m
gravity N rV r G=
(Q2)
2m
√α
√α
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!
!
= =
"
=
"
=
!
!Planckor maybeM not fundamental
(Q2)
2m
√α
√α
1m
G1 2( )m m
gravity N rV r G=
Exchange forces
Gravitational force