Кварковая_структура_адронов

integratthe resultonherevariable(for the divergen e ofofveaxialtor urrrrentt)willequalbe tononzerozero, .butOr vithene vfor

. Thesameonserhoiatione of

ofurrentve toris automatiurrent is moreally importantonserved ifbeweausewill ofmakethistheurrentgaugeisinvariantoupled toregulmasslessrizationphotonof our. Theintegrals,ve tor

by P uli-Willars method, for example. So, we will subtra t from our

triangle

diagram the same

ˆthat will beˆ subtraas ted ·

.

will rewrite

i

(2π)4

we In the expression(pˆ + k2) − (pˆ − k1)

diagram with massive ele tron ( mass M ) and put M → ∞

0 Z

((p+k2)−(p−k1))µT

γα pˆ + kˆ2

− M γµγ5 pˆ − kˆ1

− M γβ pˆ − M Aα(k2)Aβ (k1)eik1z eik2z d

k1d

k2

2

I − IM = 0, where

1

1

1

0

0

4

4

d4p

and will get

ˆ

ˆ

ˆ

ˆ

(pˆ + k2) − (pˆ − k1) = (pˆ + k2 − M ) − (pˆ − k1 + M ) + 2M

For the

integral

k1δ

k2δ

d4p

(p − k1)2 − M 2 +

(p + k2)2 − M 2 p2 − M 2 .

remainingIM = Z

4iǫαβγδ pγ

0 and F 0

an in next orders of perturbation theory be renormalized, so that

d4p

Z

is

1

1

1

ik1z eik2z d4k1d4k2

pˆ + kˆ2 − M

pˆ − kˆ1

− M

ˆ − M

α

β

(2π)4

2

T r γα

2M γ5

γβ

A0

(k2)A0

(k1)

the result0

nite and for

M → ∞ we get

urrent

¯

2

˜0µν

µ

0

0

Both let

∂

(ψγµγ5ψ) =

16π2

Fµν F

.

µν

massless

µA

qu2arks

Now10onservation.2 Anomalyus nsiderfnine

urrentsaxialontributing¯QCD with

2

in QCDquarkswith. Naivelymasslesswe shouldquarksexpe t

axialofsu hsinglet

µ

˜

µν

∂

(ψγµγ5ψ) =

16π

2 Fµν F

.

trdi gramein thatavor givesand theolor

a

λ

dtrianglbythe

nomalousdexesof term

the divergen, e of axial.

j

= qγ¯ µγ5

a = 0, .., 8

Theurrental isulationnowmodiof the

T r

2

· T r

2 2

= r

δ

· 2 .

2

λa

ti

tj

3

a0

δij

So, singlet axial urrent in QCD with massless quarks is not onserved

< 0|Gµν G

|η0

> indi

41gluoni

η0-meson is nonzero.

and singlet

∂µjµA0

= 2 r

2

6π2 Gµνa

G˜aµν

1

3

2

η0-meson an be massive

if the matrix element< 0|∂ jµA|η0 >= √2 fP mη0

= 2 r

2 16π2

< 0|Gµν G˜

|η0 >

1

1

3

2

µ

0

2

a

aµν

a ˜aµν

ating

ontent of