Кварковая_структура_адронов

mesonsof mesonstheandmassbaryonsformula.Thasresultpredi wastedtheGellmass-Mannofnondiagonal- Okubo masssymformulaeetryviolation.Inthe inasetheofmassesvetor

SU (3)

The mixing theory then

of

ω8 - meson to be ω8

= 929M eV .

for this mass of nondiagon

l

ω0

-

ω0 = 900M eV ,

and

ω0 - meson

mixing of ω8 and ω0 -

esons pr du es the diagonal φ

- mesons with observed masses. Thestrangesult that

ω8

- meson is more he vy than

ω0

- meson was

an unexpe ted one be ause

ot ω

- meson ontains more strange quarks than

in theuraldegto nera

y thatof the

e

rease of

quark massve torthat

f nonstrange quarkmesonwould.Theresultiti

ω8

ω0

Onwouldthehavontrarythenonetinthe(oatse

plus-eudosmesonssinglet)alar(of mesodegenerates ) and

that

ω8

ndtofω0

mω8 → mω0

mesonsin the. SU (3) - symmetry limit we

strange quarks

han

mη8

<< mη0 although η8 - meson ontains ore

range quark-

o that of nons

η0

mesonwould.Thenresultitis innaturaltheintorreasonasexpeoft that the de re

e of st ange quark mass

he

mη0 −

η8 mass di eren e

and that in

- symmetry limit we would have the o tet of pseudo alar mesons with masses

mπ

and

udos alar singlet with mass

SU (3)

mη0

>>

part of

π . For this

it is widely a epted to think that some

η0 - meson (and hen e of η′

- meson) is presented by the gluoni omponent . .

1

¯

˜

where the symbol

η0 = α √3

( ¯ + dd + ss¯) + βGG,

the

mesonsmesonsmixing angle

.

The6.2 informationMixing onofGG˜pseudosnotesthealarpseudos alar glueball with quantum numbers J P C = 0−+

θP de ned by the formulae

η = co θP η8 + sinθP η0

an be obtained not only fr m mass formulae′

where 8

0

η = −sinθP

η

+ cosθP

η ,

the tra sition of

|θP | ≈ 10

. The amplitude of

m sons . There are three pseudos alar symmetryonstantsde ayi

the de ays of pseudos alar

g to twobutphotonsalsofrom- π0

, η, η′

qq¯ pair to two photons i

proportional to the ele tri harge of q

2

only. Inbythethelimitvaluesof exaof t

SU (3)

-

the amplitudes of

π0, η8

η0

→ 2γ

transitions woul

q

≡ gqq¯

- quark squared

di er

gπ0 , gη8 , gη0

1

2

2

1

4

1

1

gπ0 =

√2

(

u

−

d) =

√

( 9

−

9 ) =

√

3

2

2

1

2

2

2

1 4

1

1

1

The violation of

gη8

=

√

(eu

+ e

− 2es ) =

√

(

9

+

9

− 2 9 ) =

√

3

.

6

6

6

1

2

2

2

1

4

1

1

2

gη0 =

√

(eu + e + es ) =

√

(

9

+

9

+ 9 ) =

√

3

3

3

3

SU (3) - symmetry

ontributes at least two modi ations. First, the de aying parti les

η and η′ are the mixtures of η8 and η0 and

1

1

2

gη = cosθP gη8 + sinθP gη0

=

3 (

√

cosθP +

√

sinθP )

6

3

.

22

1

1

2

gη′ = −sinθP gη8 + cosθP gη0

=

3

(−

√

sinθP +

√

cosθP )

6

3

A(P

2γ)

˜

2

Here (

→

P P Fµν Fµν

1

gP mP

3 .

2

2

(P → 2γ) |A(P → 2γ)|

gP mP

2mP

˜

Fµν )Fµν is (dual) tensor of ele tromagneti eld. So, we have the ratios

that predi ts

η

= gη2

mη3

= (cosθP + 2√

sinθP )2

1

mη3

,

2

3 mπ3 0

π0

gπ20 mπ3 0

θP ≈ 13.3

and

2

3

√

3

η′

gη′

mη′

2 1

η′

that predi ts

2cosθP )

= g2

π0

m3

= (−sinθP + 2

3

3

,

π0

π0

π0

th

xp

= 4.28KeV ). If the se ond ratio was used for the

determination ofη′ angle= 757 π0 = 5.92KeV ( η′

ΘP

the

sult would be θP ≈ 24.9o

in disagre ment with the re ult |θP | ≈ 10

of mass formulae. The possible reason of this dis greement an be the presen e of gluoni omponent

η′ - meson dis ussed above. Let us assume that in the mixtur

1

. Then˜the width

annihilate to two ¯

the gluoni omponent does not η0 = α

√

( u¯ + dd +

s¯) + βGG

3

photons

th′ is equal to

η

and should be equ l to

ηth′ = α25.92KeV

2

exp

. Thus we

have the se ond argum interestingfavor ofto explain omponentthe experimentalin width

Let6omponent.3us Mixingnow isonsidera

α

≈ 72%

gluoni

η′

η′ = 4.28KeV

proportional

the quark harge q

studied

ele tromagnet

ve

≡ hqq¯ . In the ase- paof irexannt SUhilation(3) - symmetryeleonwe-positronwould

p ir is

ω = cosθV

ω0

+ inθV ω8

ρ0, ω8, ωo0 - mesons and their ouplings

with

φ = −sinθV ω0

+ cosθV ω8

strange|θV quarks| ≈ 40 ais dl

seve torthe ideal mixing with θV

al ≈ 35

for whi h ω - me on d es not ontain

mixingto ele trof n--positronmesonmesonsdoespairnot.Theanbeontainamlitunonstrangeinof

qua ks. Likedeheaysasef vef torpseudmesonsalar-

annihiladiagonalmesons he

φ

23

1

2

1

1

hρ0 =

√

( 3

−1

(

−

3 )) =

√

2

2

1

2

1

1

hω8 =

√6

(

3

+ (

−

)

2(

3 )) = √

6

1

(

2

1

−

−1

hω0 =

√3

3

+ (

−

3 ) + (

−

3 )) = 0.

Le ture 7. Magneti moments of baryons

harges. The le tromagneti urrent of quarks

has- quarksthefollowingdier onlySU (3)by-thestruvaluesture of their ele tri

7.1 SU (3) symmetri limit for magneti moments of baryons

of

qu.hadLikerksons.theInsymmetryinsidethease multipletslimitofmassofofstrformulae.ngOneintofraletthetionusmoststartprediimpressivefromts thetherelationsexamplequarklevel,foris thevafromiousmagnetielephysitromagnetialomentshara teristiofurrentbaryonss

SU (3)

onstru t

SU (3) - symmetry u, d,

of quarks. In parti ular, for the o tet of baryonsSUthat(3)is- transformationsby the asmatrixeletromagneti urrent

2

1

¯

des ribed

j

3 uγ¯ µ

u

− 3

dγ

d

sγ

µ =

1

µ

¯− 3

¯

µ

=

or

= uγ¯ µ −

3

(¯uγµu + dγµ

+ ¯γµ )

wi h

jµ

1

−

1

α

sameConsideringtransformathehadronspropertieswewill

= Jµ1

3

(Jµα).

respethet toele tromagneti urrent of hadrons that possesses the

Σ−

independent

B βbe=

−√2 +

√6

2Λ

,

Σ0

Λ

+

µ

and µ′

√

2

+

√

6

Σ

are the ombinations of ele tri and magneti formfa tors

α

Σ0

Λ

the ele tromagneti urrent an

presented by two

avor stru tures

Ξ−

Ξ0

−√6

¯α

1

1 ¯α

B

β

where the quantities

< jµ >B = B

1

µB α − 3

B

β µ

α

+

,

1

1

+B¯

β µ′ Bβ 1 −

3 B¯α β µ′ Bβ α,

µ = γµf1(q2) + σµν qν f2(q2

Here

µ′

= γµf1′(q2) + σµν qν f2′(q2 .

ombinationshenitefourobinationsomentumoftransferedtwoeletrito the( baryon. Ele tri

andmagneti formfa tors of baryons

are theq isde

following

of

say,

µ,µ′

andexpressed

)

)

f2(q

f2′ (q

)

de) formfanite tors. In a ordanofonstane to

the ele f1(q

f1′

(q

)

his

2

2

2

2