Italian Physical Society International School of Physics “Enrico Fermi”
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Transcript of Italian Physical Society International School of Physics “Enrico Fermi”
CP ViolationTopics to be covered
Lecture 11. Introduction• Why study CP violation?• Grand view - Sakharov's ideas2. Symmetries • Mechanics • Electrodynamics• Quantum mechanics time reversal operator anti-unitary operator
Lecture 2• Edm• Krammer’s degeneracy• Particle physics• How do you measure pion spin?• How do you show that pion is a pseudos
calar?• G-parity• C,P,T in particle physics
Lecture 3
3. K meson system
• τ-θ Puzzl• Weak interaction• CPT • Mixing 4. CP violation• Asymmetry in partial widths• Role of final state interaction• Hyperon decays• Watson's theorem
Lecture 4•Regeneration•Explain Eq. 7.8 and Fig 7,.1•Discovery of CP violation Cronin-Fitch experiment•Direct•indirect
• In this section, we refrain from deriving the expression for ε and ε' etc.
Lecture 5CP violation in B decays
Towards building the B factoryEPR paradox Experiments at the B factory without much about the KM formalism
13.7 billion years
270
2810 cm
4310Time(sec)
3410
Temp( )℃3010 2610
1m410 cmradius
1010protons and neutrons
1510
100Km
Light
elements
1310410
1 billion
years
Stars and m
ilky w
ay
5 billion years
Supernova and heavy
elements
We are here
100910
Nucleosythesis of
Helium
Black-body radiationThe universe is filled with 3 °K (-270℃) photons
Generation of light elements
Expanding universeMeasuring the speed of expansion
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
10-1 1 10 102 103
Rigidity (GV)
Ant
ihel
ium
/hel
ium
flux
ratio
He/He limit (95% C.L.)
Evenson (1972)
Evenson (1972)
Smoot et al. (1975)
Smoot et al. (1975)
Badhwar et al. (1978)
Aizu et al. (1961)
Buffington et al. (1981)
Golden et al. (1997)
Ormes et al. (1997) BESS-95
T. Saeki et al. (1998) BESS-93~95
J . Alcaraz et al. (1999) AMS01
BESS-1993~2000Preliminary
M. Sasaki (2000)BESS-93~98
BESS-Polar (2003, 20 days)
PAMELA (2002~, 3 years)
AMS02 (2004~, 3 years)
KEK/IPNS Yoshida
2.No primary anti-particle in cosmic rays BESS experiment KEK/IPNS
Really absent?
Alpha Matter SpectrometerSpace Shuttle NASA program
SEMINAR – EXPERIMENTS ON ANTIMATTER SEARCHES IN SPACE Battison
16
29
3
80
10 sec
10
270
200 /
10 ,
0 ,
t
r cm
T C
cm
p n
p n
Why there is no anti-universe
三田一郎 名古屋大学大学院 理学研究科
1. Anti-baryon has to disappear. So, there has to be baryon number violation
2. Only anti-baryon has to disappear. So, there has to be CP violation
3. Created asymmetry will be washed out if the universe is in equilibrium. So, baryon has to be created out of equilibrium.
X qe
X qe
®
®
88 80
88
10 10
10
N
N
= +
=
88 80 88
88 80 8810 10 1010 10 10
810
N NN N
+ --+ + +
-
=
=
These annihilationsProduce light
16
29
3
80
10 sec
10
270
200 /
10 ,
0 ,
t
r cm
T C
cm
p n
p n
GUT
God
CP
Proton Decay
Baryon number
STANDARD MODEL
Quark Mass
CP violation in K system
CP violation in K system
50-100%CP violationin B system
50-100%CP violationin B system
strings
Newton’s Equation
2
2
d rF m
dt
Show that this equation is invariant under parity Show that this equation is invariant under time reversal
Symmetries and quantum mechanics
i iΩ
:
:
:
P r r
C e e
T t t
[H,Ω ]=0
1 1
| ; | ;
| ; | ;
| ; | ;
i t H tt
i t H tt
i t H tt
ψ and Ω ψ are both solutions to the Schorodinger Eq.
† †ψ ψ =ψ Ω Ω ψ Ω Ω =1So, you can’t tell the difference!
d
d
= -
=+
P x x
so we take 1
i
i
e
e
1
X x
P XP X
XP x PX x
x
xP
x
x
P x x
XP x xP x
2 -1 †P =1, P=P , P=P
1 1
| ; | ;
| ; | ;
| ; | ;
i t H tt
Pi P P t PHP P tt
i P t HP tt
(1) I f [P,H]=0
(2) i | , H | ,t
x H x = x H x
Show that
H( ) H( x)
then i ( , ) H(x)
x i | , H
( , )
:
| ,
t
t
P t P t
P t dy x y y t
t x t
P
x
xy y
y y
y y
¶=
¶¶
=¶
- -
= -
¶- = -
¶
ò
h
h
h
†
(3) ( ) is also solution to the Schordinger equation.
(1) P P
(
2) ( ) ( )
x x x x
Sho t
x
w h
x x
at
y
y y y y
y y± ± ± ±
±
±
±
- = = =±
- =±
&&
1(3) P is also a solition
2y y y
±é ù= ±ë û
( ) ( )x H y H x x y
2 2 2
22 2 2
p e eH A p p A A e
m mc mc
e e
A A
1CHC H
If charge of a particle is flipped, and the externalall fields are flipped, the motion is invariant.
Time reversal and quantum mechanics
* *
O=UK K is a complex conjugate operator
K α|a>+β|b>=α K|a>+β K|b>
†
|b>=O|b>
|a>=O|a>
|<a|b>|=|<a|O O|b>|=|<a|b>|
†<a|O O|b>=<a|b>
† *<a|O O|b>=<a|b>
†
† * † * †
K acts always to the lef t
[α <a|+β<b|]K =α <a|K + β <b|K
-1K =K2K =1
T=K
-1 -1
i |ψ(t)>=H|ψ(t)>t
Ti T T|ψ(t)>=THT T|ψ(t)>t
-i T|ψ(t)>=HT|ψ(t)>t
T|ψ(t)>=|ψ(-t)>
ψ(-t) = dx' x' x' ψ(-t)
T ψ(t) =T dx' x' x' ψ(t) = dx' x' x' ψ(t) *
ò
ò ò
Show that x,p =i is consistent with time reversal.
Transf ormation of Schrodinger equation under T
Transf ormation of the wave f unction under T
ψ(x,-t)=ψ(x,t)*
i |ψ(-t)>=H|ψ(-t) > t
T ψ(t) =T dx' x' x' ψ(t) = dx' x' x' ψ(t) *ò ò
T (t) =T dy' y' y' (t) = dy' y' y' (t) *ff fò ò
†(t) T T ψ(t) = ' ' ' ( ) ' ' x' ψ(t) *dx dy y t y xff ò
†(t) T T ψ(t) =ψ(t) (t)ff
1. If T=K, from the definition of operator P, show that T-1PT=-P.
2. From the definition of J=rxP, show that T-
1JT=-J
' cos sin 0
' sin cos 0 around the z axis
' 0 0 0
' cos 0 sin
' 0 1 0 around th
' sin 0 cos
x x
y y
z z
x x
y y
z z
V V
V V
V V
V V
V V
V V
e y axis
' 1 0 0
' 0 cos sin around the x axis
' 0 sin cos
x x
y y
z z
V V
V V
V V
ziJe
Rotation operator
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 1 0 0 0 0z x y
i i
J i J i J
i i
1 if T=KTJ T J
x y
0 0 0 0 0 0 0
0 0 J 0 0 J 0 0 0
0 0 0 0 0 0 0z
i i
J i i
i i
x y
1 0 0 0 1 0 0 01 1
0 0 0 J 1 0 1 J 02 2
0 0 1 0 1 0
So we of ten use
0 0
:
z
i
J i i
i
But in quantum mechanics
fi rst question we ask:
what operator can we diagonalize
together with H.
2[ , ] 0H J
Then we have to change
p
T=K
ex yT i J K
[ , ] 0H J
[ , ]i j ijk kJ J i J