Сарычева Л.И. Физика фундаментальных взаимодействий
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W Z
W
0
B
0
A Z
0
A = W
0
sin θ
W
+ B
0
cos θ
W
,
Z
0
= W
0
cos θ
W
+ B
0
sin θ
W
.
A Z
0
A
Z
0
θ
W
θ
W
g
W
±
e
e = g sin θ
W
.
ν
µ
+ d −→ µ
−
+ u, ¯ν
e
+ u −→ e
+
+ d
ν
µ
+ u −→ ν
µ
+ u, ¯ν
µ
+ e −→ ¯ν
µ
+ e,
u d
ν
µ
+ u → ν
µ
+ u, ν
µ
+ u → µ
−
+ d.
”
“ θ
c
d
′
= d cos θ
c
+ s sin θ
c
,
s
′
= −d sin θ
c
+ s cos θ
c
,
θ
c
|sin θ
c
| ≈ 0.22 θ
c
≈ 13
◦
e µ τ
ν
e
ν
µ
ν
τ
u d s c b t
j = ¯eν
e
+ ¯µν
µ
+ ˜τν
τ
+
˜
d
′
u + ˜s
′
c +
˜
b
′
t.
d
′
s
′
b
′
”
“
”
“
α =
G
N
m
2
¯hc
≈ 0.53 · 10
−38
,
m = m
p
G
N
∼ 1
×
E
G
−
dE
dx
= Kz
2
Z
A
1
β
2
"
1
2
ln
2m
e
c
2
β
2
γ
2
T
max
I
2
− β
2
−
δ
2
#
,
T
max
=
2m
e
c
2
β
2
γ
2
1+2γm
e
/M+(m
e
/M)
2
K = 4πN
A
r
2
em
e
c
2
= 0.307 /c
2
.
1
2
3
4
5
6
8
10
1.0 10 100 1000 10 0000.1
Pion momentum (GeV/c)
Proton momentum (GeV/c)
1.0 10 100 10000.1
1.0 10 100 10000.1
1.0 10 100 1000 10 0000.1
−dE/dx (MeV g
−1
cm
2
)
βγ = p/Mc
Muon momentum (GeV/c)
H
2
liquid
He gas
C
Al
Fe
Sn
Pb
βγ
b
b b
max
b
min
E
min
E
max
N
A
r
e
m
e
z
Z A β
γ I
T
max
δ
Muon momentum
1
10
100
Stopping power [MeV cm
2
/g]
Lindhard-
Scharff
Bethe-Bloch Radiative
Radiative
effects
reach 1%
µ
+
on Cu
Without δ
Radiative
losses
βγ
0.001 0.01 0.1 1 10 100 1000 10
4
10
5
10
6
[MeV/c] [GeV/c]
1001010.1 100101 100101
[TeV/c]
Anderson-
Ziegler
Nuclear
losses
Minimum
ionization
E
µc
µ
−
−
dE
dx
= a(E) + b(E)E
a(E) b(E)
e
+
e
−
X
0
2 5 10 20 50 100 200
Copper
X
0
= 12.86 g cm
−2
E
c
= 19.63 MeV
dE/dx × X
0
(MeV)
Electron energy (MeV)
10
20
30
50
70
100
200
40
Brems = ionization
I
o
n
i
z
a
t
i
o
n
Rossi:
Ionization per X
0
= electron energy
To
t
a
l
Brems
≈
E
E
xa
ct
bre
m
s
st
ra
h
l
u
n
g
Bremsstrahlung
Lead (Z = 82)
Positrons
Electrons
Ionization
Møller (e
−
)
Bhabha (e
+
)
Positron
annihilation
1.0
0.5
0.20
0.15
0.10
0.05
(cm
2
g
−1
)
E (MeV)
1
0
10 100 1000
1
E
−
dE
dx
(X
0
−1
)
X
0
E
c
e
X
0
=
716, 4
/
2
A
Z(Z + 1) ln( 287/
√
Z)
.
t
Z
5
Z
Z
2
+ Z
2m
e
= 1.022
λ
ph
≃
9
7
X
0
e
+
e
−
t