1 YukawaYukawa YukawaYukawa: n-p

m , m, . t=/mc2 R ct =/mc

Klein-Gordon m spin. 2 2 2m c

m=0 / . ( )

2 22 2 0

m ct

=== ()

U(r) r>0 r=0

2

:

22 2

2 2

1( ) ( )U mcU r r U rr r r

= = =

=. .

/0 ( ) R=

4 mcr RgU r e

r= =

2 YukawaYukawa/0 ( ) R= r RgU r e= =

g0 .

( )4 mcr

. / 2U(r)=0 U(r)=Q/4r g0 Yukawa Q

/ . R

R10-15 m .

2 2 197 1401 4

c MeV fmR mc mc mc MeVmc R R fm

= = = = = =

. .

1.4mc R R fm

3 YukawaYukawa

. .

4

qG f( ) . f( ) Fourier:

qqG qG

iq rf(q)=g U(r)e dV GGG g: ( Fourier

)

q g 2 cos dV=r sinq r qr d d dr =GG

U(r) Yukawa ==c=1

q q

20

sin( ) 4 ( )iqr iqr

mrqr e ef q g U r r dr g g e dr

= = G 00 0

( ) 4 ( )2

f q g U r r dr g g e drqr iq

0

2 2( ) g gf q =G

. .

2 2( )q

q m+G .

5

gg gg00 gg gg00,, , ,

pp==qq qq 4 4--..

2 21/( )q m+

g g g g02 2

( ) g gf qq m

= +G

G 02 2( )g gf q

q m= +

G2 2 2q p E=

22q q G

. .

|f(q)|2

6 FeynmanFeynman

. .

7 &

C D

. .

8

C D C D

. .

9

. .

10

.

t= t = .

q2

11

- (/ )

ssee-- ee--

2 2 2 2 + - + - + -p =(p +p ) =p +p +2p p

q2>o timelike

2+ - + -

2

=2m +2(E E +p p ) 4E

G G

e+e+ e+e+ 0 -

tt -

= 2 = 2 :

. .

:

t t /2E/2E

12

FeynmanFeynman A + B C + D

A B + C + D A B + C + D

A, B, C, DA, B, C, D

( ) ( )

() () ((g)g) WW++ WW-- ZZ00

. .

13

FeynmanFeynman

. .

14

FeynmanFeynman

. .

15

FeynmanFeynman FeynmanFeynman ::

--

quarkquark : : ( ( l )l ) (= (=gluon)gluon)

(= ) (= ) = = 00

= = WW++ = = WW--

. .

16

FeynmanFeynman

:: ::

: : Quarks Quarks

:: QuarksQuarks

//

QuarksQuarks 99 99 99

99 99 xx

. .

99 xx xx

17

. .

18

. .

19

. .

20

. e

Compton e.

2

2e

V(r=r ) /m c e 1=c e2 2

e e

V(r r ) /m c e 1 = = =m c m c c 137

= = H 1/2 ~ e

.

e+ e-

. .

21

a + b c + d nb /

ab

a :=navi

/ / dx

a

/ /. d d / nbdx nbdx /

W==navi /

. .

22

.

(long range).

. . .

.

. .

23

, b, , .

b . :

: :

: Rutherford

. .

24

= + + = = /2 /2b = R sin = R sin(/2 - /2) = R cos(/2)

. .

25

RutherfordRutherford

Coulomb q2 q1 .

. .

1 2q qb = c o t ( / 2 )2 E

26

d/d

d = |b db d| d = |sin d d|d = |b db d| d = |sin d d|

d b db = d sin d

. .

d sin d

27

db Rdb Rb = R cos( /2) = - sin( /2)d 2

d b db

2

d b db = d sin d

R sin( ) cos( )2 2

2

R sin( ) cos( )2 2 = 2 sin

R =

22R = =

R =

R4

4

d . .

4

28

RutherfordRutherford21 2 1 2q q q qdbb= cot( /2) csc ( /2) q q q qb= cot( /2) - csc ( /2)

2E d 4Ed b db =

=

2 2 21 2

= d sin d

q q cot( /2)csc ( /2) =

2

21 2

= 8 sin

q q =

E

21 2

2 = 4Esin ( /2)

q q sin = 2 d

. .

40

= 2 d 4E sin ( /2)

29

Luminosity Luminosity LL

dN = L d

, L ( )-1 LHC: L 1034 cm-2s-1

(peak luminosity) / .

. .

. pb-1

30

/M/M Feynman Feynman

, , ss , , MM . .

Feynman.Feynman.

ee-- ee--

q

Feynman.Feynman.

ee ee

q

tt

ee-- ee--

ss ee-- ee--

e+e+ e+e+

M 2 2M 3 3

. .

ttM 3 3

1%