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miL
Lagrangian of a free Dirac field
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mDiL
FF
4
1
ieAD 5
miL
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AAF field strength
mDiL
FF
4
1
Lagrangian of QED:
e
fieldphotonA
mieAi
:
0)((
8
e
9
fine-structure constant
hce /22
=0.00729735253
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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
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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
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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 .....)(
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Feynman
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gluon
quark
antiquark
8:
3:
3:
G
q
q
63
antibaryonqqq
baryonqqq
mesonqq
)(
)(
)(
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...1)()(
...1)33()33(
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66
qqqq
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„dimesons“
„pentaquarks“
„dibaryons“
)...( qqqq
)...( qqqqq
)...( qqqqqq
88 )()( qqqqqq
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mesonsBB
88 )()( qqqqq
)( suud68
example:
69? 1540 MeV ?
...1
...1
888
88
GGG
GG
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glue mesonsstrong mixing with neutral
quark-antiquark mesons
(thus far not observed)
