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%