1
2
3
miL
Lagrangian of a free Dirac field
4
mDiL
FF
4
1
ieAD 5
miL
6
AAF field strength
mDiL
FF
4
1
Lagrangian of QED:
e
fieldphotonA
mieAi
:
0)((
8
e
9
fine-structure constant
hce /22
=0.00729735253
10
11
Feynman diagram
Quantum Field Theory:
Finestructure constant function of energy or scale due to quantum fluctuations of electron-positron pairs
=> partial screening of bare charge of the electron at distances less than the compton wavelength of the electron
12
M. Gell-Mann / F. Low ( 1954 )
+
3
2
( , ) ( )ln( / )
( ) ...12
r
de q e e
d q M
QED
ee
+
LEP
( ) 1/127.8ZM
Abelean gauge theory:
gauge bosons interact only with the fermions
Non-Abelean gauge theories
18
19
20
21
non-Abelean gauge theory
gauge bosons interact with the fermions and with the gauge bosons
aa
a
a
GGqmAigiqL4
1)
2(
8 gluons
g
4
2gs
LEP experiments:
118.0s
at 91 GeV
cbabc
aaa AAgfAAG
...12/)( 23 ee
...16/)( 23 gcg
as
MeV3835213
222 /ln/2 QbQ os
fnb3
2110
experiment =>
2
2
2
ln
4.1)(
QQs
3 Quarks: u,d,s
violation of „scaling“
p: proton momentum
x p: quark momentum
0 < x < 1
+ …++ …+
2
+
2
scaling violations in QCD
quarks emit gluons! 0.0 0.2 0.4 0.6 0.8 1.00
2
4
6
x
F2
Q1
Q2 > Q1
The structure function data exhibit systematic violations of Bjorken scaling
MeV250
scaling violations
quark – antiquark potential
Large distance: linear term
rkr
rrV s
)(
3
4)(
rkrV .....)(
54
55
56
Feynman
57
58
59
60
61
62
gluon
quark
antiquark
8:
3:
3:
G
q
q
63
antibaryonqqq
baryonqqq
mesonqq
)(
)(
)(
64
...1)()(
...1)33()33(
66
66
qqqq
65
„dimesons“
„pentaquarks“
„dibaryons“
)...( qqqq
)...( qqqqq
)...( qqqqqq
88 )()( qqqqqq
67
mesonsBB
88 )()( qqqqq
)( suud68
example:
69? 1540 MeV ?
...1
...1
888
88
GGG
GG
70
71
glue mesonsstrong mixing with neutral
quark-antiquark mesons
(thus far not observed)