STANDARD THEORY

H. Fritzsch

STANDARD - THEORY

quantum chromo

dynamics

electroweak gauge theory

SYMMETRIES

AND QUARKS

Special quantum relativity mechanics

QUANTUM

FIELD THEORY

QUANTUM FIELD THEORY

Standard Theory particle physics

cm1710

1936 =>matter

atomselectrons + nuclei

hydrogen atom

Proton Electron

nucleus protons neutrons

electric force

strong force

1935 Heisenberg / Pauli

1935

strong interactions

- meson exchange -

nucleon nucleon

Hideki Yukawameson

pion

mass: 140 MeV

nucleon 1947

1932 Heisenberg

Isospin

n

pN

pions: triplet eta: singlet

MeV

MeV

548

1400

0

weak decay

elm. decay

MeV

MeV

MeVe

1777:

7.105:

511.0:

LBL Berkeley

Golden gate

1953

pion nucleon

delta quadruplet

01230 MeV

SU(2)representations

singletdoublettriplet

quadruplet*********

24

1950 1 discovery of new particles in cosmic rays

HyperonsK-mesons

1950 =>

Hyperon

MesonK

Hyperon

MesonK

pair production

6 hyperons

0

0

8 baryons

0

0

np

new mesons

MeVKm

KK

KK

495)(

0

0

8 mesons

KK

KK0

0

0

KK

KK0

0

0

??? EIGHT ???

0

0

np

strangenessconserved in processes of

strong interactions

0

1

1

KS

KS

S

Hyperon

MesonK

2)()(

0)()(

KSS

KSS

2

1

S

S

strangenessnot conserved in processes of

weak interactions

weak Decays

0

0

K

K

p

00

0

0 /

n

npS conserved elm. process

S=-2 S=-1

8 baryons

0

0

np

o

o

pn

K

o

oK

K oK

8 mesons => octet

Isospinbreaking about 1%

_______________________________

SU(3)-symmetrybreaking about 20% !

Group theory

U(n) group of complex unitary n

x n matrices

SU(n) n x n matrices

det U = 1

U = exp (iH)

H: Hermitean n x n matrix

matricesnnHermiteantindependenn 2

det U = exp i (trH)

SU(n): det U = 1tr H = 0

matricesnnSU )1(:)( 2

SU(n) (n x n-1) generators

SU(2): 3 SU(3): 8 SU(4): 15 SU(5): 24

SU(2): 3 Hermitean matrices

3 Pauli matrices

10

01

0

0

01

10321

i

i

commutation relations SU(2)

ii

kijkji

i

T

matricesPauli

TiTT

TgeneratorsSU

2

1

:

,

3:)2(

SU(3) 8 Hermitean matrices

8 Gell-Mann matrices

000

010

001

000

00

00

000

001

010

321 i

i

010

100

000

00

000

00

001

000

100

654 i

i

200

010

001

3

1

00

00

000

87 i

i

ijji

i

tr

tr

2

0

ijji

i

tr

tr

2

0

commutation relations SU(3)

ii

kijkji

i

T

matricesMannGell

TifTT

TgeneratorsSU

2

1

:

,

8:)3(

2

3

2

12

11

678458

367156

345257246147123

ff

ff

fffff

:

,

ijk

kijkji

f

TifTT

structure constants

kijkijji d 2

1

3

4

2

1,

2

1

3

1..

:

118 dge

symmetrictotallydijk

s

d

u

3 quarks

triplet fundamental representation

ud

s

isospin

spinU spinV

two of the eight lambda matrices are diagonal:

=> T(3) / Y

a state described by isospin and hypercharge:

yt ,3

ud

s

2

12

1

3

2

3t

yquark triplet

3

1

p

q

steps p / q

irreducible representations

2112

1 qpqpN

number of states in an irreducible representation

each state is described by 3 numbers:

ytt ,, 3

irreducible representation

=> (p,q)

(0,0): singlet(1,0): triplet

(0,1): anti -triplet

a representation is in general complex

pqqp ,,

)0,1(3

)1,0(3

)0,2(6

)1,1(8

o

o

pn

)0,3(10

o

o

o

1232 MeV

1530 MeV

1385 MeV

Decuplet ???

o

o

o

???Decuplet ?

mesons singlets, octets

baryonssinglets, octets, decuplets

triplets? sextets?

77

Three quarks for Muster Mark! Finnegans Wake, page 383

Three quarks for Muster Mark!

Drei Mark für Musterquark!

SU(3)

es

ed

eu

31:

31:

32:

isospind

u

n

p

symmetrySU

s

d

u

)3(

Symmetry breaking

quark masses

m(u)=m(d)=m(s)

SU(3) unbroken

m(u): 5 MeV m(d): 7 MeV m(s): 110 MeV

SU(3) broken

m(u): 5 MeV m(d): 7 MeV

m(d) > m(u)

isospin broken by quark masses m(neutron) > m(proton) !!!

uu

d

d

proton

87

o

o

pn

1

)(

S

uds

strangeness: - minus number of strange quarks !

)( ud)( du

)( us)( ds

)( su )( sd

)( uu

)( dd)( ss

91

o

o

o

(56) - representation40410

2

3

spin

16282

1

spin

)

222(

)(

duuuuduud

uduududuu

uudududuu

p

qq

J

2

1

6

1)634(

18

1

2

1

3

2)0444(

18

1

2

1

21

21

pp

pp

d

u

3/2)2/1(

6/1)2/1(

nn

nn

d

u

qq q

qq m

eeqp

2

1)()()(

qdu

q m

e

m

ep

22

1

3

1

2

1

3

2)(

Np 79.2)(

MeVmq ...336

qq m

e

m

en

23

2

3

2

3

1)6

1(

3

2)(

50.12/3)(/)( np

104

105

transferenergy

photonvirtualofmassq 22 )(

scaling behaviour

cross section

2

)(),(2

22

2

qx

xFqW

J. Bjorken

1967

parton model

partons

quarks

112

Fritzsch / Gell-Mann1970

current commutators near

the light cone abstracted from free quark model

explains scaling ---------behaviour-------------

114

115

1x

x = quark-momentum / proton-momentum

Expected: x => 1/3

observed

1974 : SPEAR

Stanford

e(-) e(+)J/ψ

M= 3.1 GeV

electron-positron-annihilation

J/ψ: 3,1 GeV

quarkcharmc

ccJ

:

/

:)2( decayS

s

c

d

u...

4 Quarks

c: Charm - Quark

D-mesons(masses ~ 1870 MeV)

sDcs

Dcd

Dcu 0

D-mesons decay: weak interactions

0:.. KDge

1977

Fermilabdiscovery

Y

„upsilon“

upsilon meson (ϒ) 9.46 GeV

b – quark charge: -1/3 e / m(b): 4.2 GeV

ϒ= bb

128

bs

c

d

u ?

discovery of t-quark

CDF-detector

m(t): 174 GeV

bt

FNAL 1995

GeVbm

GeVtm

b

t

4,4)(

174)(

t-quark

gold atom

Top – Mass: 174 Gev

t-quarkdecay very fast

no time to form a hadron

=>No T-mesons No T-baryons

bsd

tcu

6 QUARKS