ФИАН / Nefedyev_Ktp

k

k

q

q

p1

p2

p1

p2

T = −e2Aν (q)εµu¯(p2)

γµ 2(p2k) γν − γν

2(p1k) γµ u(p1).

pˆ2 + m

pˆ1 + m

T = −e2u¯(p2)Aˆ(q)u(p1)

(p2ε )

−

(p1ε )

.

(p2k)

(p1k)

−

e(pε)/(pk)

n + 1

n

±e(pεn+1)/(pkn+1)

T = e

(p2ε )

−

(p1ε )

T0

e

T0

,

(p2k)

(p1k)

ω

dσγ = dσedwγ,

dσe

dwγ = e2

λ

(p2ε )

(p1ε )

2

d3k

= −

α

p2µ

−

p1µ

2

(p2k)

− (p1k)

(2π)3

2ω

(2π)2

(p2k)

(p1k)

ωdωdΩγ

X

ω

ω + dω

2α

2

dω

dwγ =

B(Q )

,

π

ω

Q2 = −(p1 − p2)2

B(Q2)

ω2

p2µ

p1µ

2

B(Q2) ≡ −

Z

−

dΩγ .

8π

(p2k)

(p1k)

Z

1

Ωγ =

4π

(pk)2

ω2p2

1

1

dx

= Z0

,

a1a2

(a1x + a2(1 − x))2

(p1p2)

1

dx

B(Q2) = −1 +

Z0

,

m2

1 + 2x(1 − x)((p1p2) − m2)

x

p = p1x+p2(1−x)

2

Q2 = −(p1 − p2)2

(p1p2) Q 2(p1p2) =

Q2 + 2m2

θ

sh θ = r

4m2 .

Q2

B(Q2) = −1 + ch(2θ) Z0

1

dy

,

ch2 θ − y2 sh2 θ

B(Q2)

B(Q2) = 2θ cth 2θ − 1.

Q2

Q2 m2

B(Q2)

≈

3m22

Q

2

2

ln

Q

m .

m2

2α

2 dω

dIω

dwγ =

|v2 − v1|

≡

,

3π

ω

ω

dIω

v = v1

t = t1

t = t2

ω(t2 − t1) 1

v = v2

|v2 − v1| |v1,2|

1

¨

2

dIω =

6π2

|d(ω)|

dω,

¨

d(ω)

d¨(ω) = ex¨(ω) = e Z

eiωtx¨(t)dt = e Zt1t2

eiωtx¨(t)dt ≈ e Zt1t2

x¨(t)dt = e(x˙ (t2)−x˙ (t1)) = e(v2 −v1),

dIω

dσγ

α2

dσe

e

e3

e4 α2

α

E

dσe = dσMott 1 −

2

B(Q2) ln

,

π

λ

E

dσγ

dσe dσMott

dσphys = dσMott 1 −

α

E

,

2

B(Q2) ln

π

ω0

λ

α ln

ω0

λ

wγn

dσnγ =

dσe

n!

∞

∞ wγn

2α

B(Q2) ln

ω

.

dσphys = n=0 dσnγ = dσe n=0 n!

= dσe exp

π

λ0

X

X

dσe = dσMott exp

−

2π

B(Q2) ln λ .

α

E

λ → 0

dσe

dσphys = dσMott exp −

α

E

Q2 m2 dσMott exp −

α

Q2

E

,

2

B(Q2) ln

2

ln

ln

π

ω0

π

m2

ω0

λ

{|ni}

Y

1

2

X

αn

−

2 |αKλ|

kλ

√

|ni, CkλΦkλ = αkλΦkλ,

Φ = Φkλ, Φkλ = e

n

n!

k,λ

Ckλ

αkλ

Φkλ

S

λ

p1

p2

k1 k2

k1ν Mµν = k2µMµν = 0.

k1ν Mµν

k1ν

kˆ1 = (ˆp1 + kˆ1 − m) − (ˆp1 − m) = S−1(p1 + k1) − (ˆp1 − m),

kˆ1 = −(ˆp2 − kˆ1 − m) + (ˆp2 − m) = −S−1(p2 − k1) + (ˆp2 − m) = −S−1(p1 − k2) + (ˆp2 − m),

Tif = −(4πα)e1ν e2µu¯2Qµν u1,

ˆ

ˆ

+ m

Qµν = γµ

pˆ1 + k1 + m

γν + γν

pˆ1 − k2

γµ.

(p1 + k1)2 − m2

(p1 − k2)2 − m2

1

!

!

1

2

X

X X X

2

2

¯

×

|Tif |

=

2 σ1

2 λ1

σ2 λ2

|Tif

|

=

4

(4πα)

Qµν αβ (Qρω)γδ

X

X

X

X

× eω(k1, σ1)eν (k1, σ1)

eµ(k2, σ2)eρ(k2, σ2)

(uλ1 (p1))δ (¯uλ1 (p1))α (uλ2 (p2))β (¯uλ2 (p2))γ =

σ1

2

¯

σ2

λ1

λ2

αβ (Qρω)γδ (−gων )(−gµρ)(ˆp1 + m)δα(ˆp2 + m)βγ =

= (2πα)

Qµν

2 2

¯

2

2

≡

2 2

= 4π α Sp [(ˆp2 + m)Qµν (ˆp1 + m)Qνµ]

4π α Sp,

= 4π α Sp (ˆp2 + m)Qµν (ˆp1 + m)Qµν

¯

†

= Qνµ.

Qµν ≡

γ0Qµν γ0

s t

u

s = (p1 + k1)2 = (p2 + k2)2, t = (p1 − p2)2 = (k2 − k1)2, u = (p1 − k2)2 = (p2 − k1)2

(p1k1) = (p2k2) =

1

(s

− m2), (p1k2) = (p2k1) = −

1

(u − m2),

2

2

(k1k2) = (p1p2) − m2

= −

t

=

1

(s + u) − m2,

2

2

s + u + t = 2m2

s

= 2m

2

s

tmax

u = 22m2 − s − t

u

= 2m

s

min

−

−

t2

−

4

cos θ = −1

umaxs = m

u

m4

> u > 2m2 − s,

s

x =

s − m2

, y =

m2 − u

,

m2

m2

y

x

6 y 6 x.

1 + x

πr2

4

8

1

8

1

σ =

2 e

1 −

−

ln(1 + x) +

+

−

.

x

x

x2

2

x

2(1 + x)2

s − m2 m2

x 1

34 x

σ

8πα2

8π

re2.

=

3m2

3

ln x + 1

s m2

x 1

2

πα2

ln

s