Gauge Theories

1

2

3

miL

Lagrangian of a free Dirac field

4

mDiL

FF

41

ieAD 5

miL

6

AAF field strength

mDiL

FF

41

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

rd e q e e

d q MQED

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

GGqmAigiqL41)

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

fnb32110

experiment =>

2

22

ln

4.1)(Q

Qs

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

rkrrrV s )(

34)(

rkrV .....)(

54

55

56

Feynman

57

58

59

60

61

62

gluon

quark

antiquark

8:3:3:

Gqq

63

antibaryonqqq

baryonqqqmesonqq

)()()(

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

GGGGG

70

71

glue mesonsstrong mixing with neutral

quark-antiquark mesons

(thus far not observed)