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A. I. Sanda Nagoya University
• Discovery of K meson 1947
• Discovery of CP violation 1964
• Discovery of Y(4S) 1980
• Discovery of CP violation in B decays 2000
+
When I was 27, I was excited by
K as this was a loop effect
which will be a critical test of
gauge theory!
e e
2* 22
2 4
( )
( )
( )3
4 sin ( )
s
c
tb ts t
W cs
Br B X
Br B X e
V V X x
V f z
)()(
eXKBrXKBr
c
s
*4td ts
us
V V
V 2ts
cs
V
V
2* 22
2 4
( )
( )
( )3
4 sin ( )
s
c
td ts t
W us
Br K X
Br K X e
V V X x
V f z
5( ) 4.1 10sBr B X
9 4 20( ) 1.7 10 ( )LBr K A
sin2 usW 0 10 4 2( ) 4.1 10LBr K A
K
K
K K
( ) ( ) ( ) ( )
+d(t) 3 ( )
K t a t K b t K c t
e t l
( ) ( )dK t H K t
dt
MixingK K
11 11 12 122 2* *
12 12 22 222 2
| ( ) ( ) | ( ) |
( ) ( )
( ) ( )
2
i i
i i
t a t K b t K
a t a tdi H
b t b tdt
M MiH M
M M
12 2 2
12 2 ( )
W Wn
K n
K F W WF
K H n n H KM P
m m
m m K H F F H K
K F
K F
Wigner-Weisskopf approximation• c(0), d(0), e(0), ・・・ =0
• ｔ >> 強い相互作用の時間スケール
• a(t), b(t) 以外興味がない。
CPT symmetry 11 11 22 222 2
i iM M
CP symmetry 12 12 21 212 2i iM M
* *21 21 21 21
Since and are hermitian,
M
M M
12 12Complex or violate CP symmetryM
aa K b K
b
a adi H
b bdt
11 11 12 122 211 11 21 212 2
21 21 22 222 2
1 0 0 1( ) ( )
0 1 1 0
i ii i
i i
M MM M
M M
CP eigenstate
1
2K K K
0 1 1 1
1 0 1 1
Ｃ ＝
Ｐ ＝
LONG SHORTK Kと
11 2
12
1 1
2
2
2
| |
| | |
| | |
| |
| |
CP K K
CP K
CP K K
K K K
K K
K
K
1
2
2
3
K
K
500
3 420Km MeV
m MeV
1
2
S
L
K K
K K
CP
11 2
12 2
| | | |
| | | |
S
L
K K K K
K K K K
Ｈの固有状態個有値
2
2
:
:
iL L L
iS S S
K m
K m
時間依存性12
12
| ( ) | |
| ( ) | |
S S L L
S S L L
im t t im t tS L
im t t im t tS L
K t e K e K
K t e K e K
12
12
| ( ) (| | ) (| | )
| ( ) ( ) | ( ) |
S S L L
S S S SL L L L
im t t im t t
im t t im t tim t t im t t
K t e K K e K K
K t e e K e e K
11 11 12 122 2
21 21 22 222 2
i i
i i
M M
M M
su
K
d
ｔ
e Lt
Ｋの数
214 ( cos( ))
L SSL
ttte e e mt
K 中間子ー反 K 中間子遷移
CP 保存非保存
この遷移がおこるのは K －反 K だけ三田一郎 名古屋大学大学院 理学研究科
三田一郎 名古屋大学大学院 理学研究科
K 中間子系での CP 非保存はどう理解するのか
振り子は敏感な顕微鏡
K
微小な力も長く待てば観測できるK
tcu ,,s d
d tcu ,, s
W W0K0K
三田一郎 名古屋大学大学院 理学研究科
† † CP h CP h
† † *CPHCP ch c h
* †H ch c h †
particle dynamics
anti-particle dynamics
h
h
ＣＰの破れ*
12 12
*12 12
M M
11 11 12 122 2* *
12 12 22 222 2
| ( ) ( ) | ( ) |
( ) ( )
( ) ( )
2
i i
i i
t a t K b t K
a t a tdi H
b t b tdt
M MiH M
M M
LK 1 2
2 1
| | |
| | |S
L
K K K
K K K
3 2( )(2 10 )
( )L
S
K
K
The Standard Model
0
Tuu cu tu
H cu cc ct
tu tc tt
u Y Y Y u
H c Y Y Y c
t Y Y Y t
+ h.c.
T
W
u d
H c ig s W
t b
+ h.c.
T
m m
W m KM m
mm
u d
H c ig V s W
t b
Ｗｓｄ
ＫＭ行列の位相Phases of the KM matrix
Ｋｍ matrix has 4 parameters
KM matrix has 4 parameters
３ rotation angle３ rotation angle 1 CPV phase1 CPV phase
q e qi ii i
3 x3 unitary matrix has 9 real parametersFor 6 quarks, thereare 5 phases we can adjust
素粒子の種類当時未発見
)( dbB
)( dsK 1980 年には未発見
三田一郎 名古屋大学大学院 理学研究科
より深く CP を理解するために
tcu ,,b d
d tcu ,, b
W W0B0B
0B 0B の遷移
S を ｂ に変えるだけ？
1980 年の計算
三田一郎 名古屋大学大学院 理学研究科
In 1979 we did not know , ij tV M
ARGUS 87
B B
Extremely long Life time - 1ps
G MF2 5
3192
G M
VF bcb
2 5
32
1926 3 ( )| |
bc
d
eue
151, 10 seccb BV
mtm t
m life time
mixing time
Needs time to show interesting physics
214 ( cos( ))
L SSL
ttte e e mt
Experimentalists can only count the number of particlesThey can’t use protractor to measure the phase angle!
Measuring an angle by counting particles in optics
K
Ksin( ) ii Mt e
cos( )Mt K
Ｍａｓｓ ＣＰＶ
0 0
i ie
iie
Ａｍｐｌｉｔｕｄｅ ＣＰＶ
0' established
NA31(93)E832 (99)
0 0
00 0 0
( )'
( )
( )2 '
( )
L
S
L
S
A K
A K
A K
A K
u c t, ,
u c t, ,
s d
W W
d s
csV *cdV
*cdV csV
12M becomes complex
)( KA becomes complex
0'
0'
Penguins and me in Cape Town, Jan., 1999 Penguins and me in Cape Town, Jan., 1999
K
d
b
Bb
c
sd
cdB
c
c
sds K s
SK
B =
B
1
B = 1B =
0
2 B0
LB K
V V V V V Vub ud cb cd tb td* * * 0
( ( ) ) ( ( ) )
( ( ) ) ( ( ) )sin( ) sin
B t K B t K
B t K B t K
m tS S
S S
2 1
Nearly 100% ＣＰＶ
SK
*12
12
( )1 ( )sin(2 ) Im S
S
A B KMM A B K
sin( ) Im[ ]* *
*2 1 V V V
V V Vtb td cb
tb td cb
cdV*
cdV
q e qi ii i
3 x3 unitary matrix has 9 real parametersFor 6 quarks, thereare 5 phases we can
adjust
Three families neededThree families needed
K system
B system
b c
d
u c t, ,
u c t, ,
s d
W W
d s
csV *cdV
*cdV csV
u
( ( ) ) ( ( ) )
( ( ) ) ( ( ) )sin( ) sin
B t K B t K
B t K B t K
m tS S
S S
2 1
*12
12
( )1 ( )sin(2 ) Im S
S
A B KMM A B K
* *
* *cb cs tb ts
cb cs tb ts
V V T V V P
V V T V V P
* * *
* * 2
0
( )
cb cs tb ts tb ts
cb cs tb ts
V V V V V V
V V V V O
ｂ
gluonc
s
*12
12
( )
( )
( ( ) ) ( ( ) )Im
( ( ) ) ( ( ) )A
A B
M
B
MB t B t
B t B t
* *
* *cb cs tb ts
cb cs tb ts
V V T V V P
V V T V V P
( )1
( )
Br B K
Br B
.25P
T
* *
* *
( )
( )ub us tb ts
ub ud tb tu
V V T V V PA B K
A B V V T V V P
4 2
3 3
( )
( )
PT
PT
A B K
A B
Principle of measurement
BB
KS
ｘt
t0 t0
Travels only 20 micronsImpossible to measure
With present technology
8GeVelectron
3GeVpositron
B
B
Travels 200 microns
Asymmetric collider
世界
反世界
三田一郎 名古屋大学大学院 理学研究科
三田一郎 名古屋大学大学院 理学研究科
４００億円
なぜ 21 年かかったのか？１． 1980 年 B 崩壊における大きな CP の破れの予言 B 中間子を発見
３． 1987 年 B- 反 B 遷移が発見された
２． 1983 年 B 中間子の寿命の測定
４．崩壊する前に残す飛跡はわずか 0.02mm
５． 0.01 秒にデータを処理する。 0.02mm の飛跡を追うのは無理６．非対称加速器 飛跡が 0.2mm になる
三田一郎 名古屋大学大学院 理学研究科
Comparison between CP-odd and -even
CP = 1 sample
sin21
= 0.716±0.083
CP = 1 sample
(B0J/KL)
sin21
= 0.78±0.17
∫L dt = 78 fb-1Raw asymmetry
Yamauchi KEK
2 3 212 2
2 4 2 212
3 2
1 ( )
1 (1 )
(1 ) 1
i
KM
A i
V i A i
A i A
- plane
PDG2002 (http://pdg.lbl.gov/2002/kmmixrpp)
+ New Belle result
sin21
=0.719±0.074±0.035
Belle July, 2002
Yamauchi KEK
History of sin21
Yamauchi KEK
* 012
0
0 0
0 0
2
2 2
12
( ( ) ) ( ( ) )
( ( ) ) ( ( ) )
= sin( ) cos( )
| | 1 2Im A
| | 1 | |
(
1
( )
)
CP
M A B
M A
B t B tA
B t B t
S Mt A Mt
S
B
2 2 1A C
SS and and AA
S = 1.21±0.41
A = 0.77±0.27±0.08
0.080.07
A≠0 indicates Direct CPV
i.e., (B0)≠(B0)
∫L dt = 78 fb-1
A> 0 with 99.6%CL.S< 0 with 99.6%CL.5-5 0
Yamauchi KEK
Comparison with BaBar’s result
Yamauchi KEK
CPV in bsss
In the Standard Model,
Ssss = sin21 (bccs)
Asss = ~ 0
B(B0’K0) = 5.8x10-5 : anomalously large
New physics contribution ??Measure its phase.
Yamauchi KEK
CPV inCPV in b b ssssss
SK = 0.73±0.64±0.18
AK = 0.56±0.41±0.12
t (ps)
BKS
∫L dt = 78 fb-1
SKKK = 0.52±0.46±0.11
AKKK = 0.42±0.36±0.09
0.270.030.030.22
BKKKS
t (ps)t (ps)
B’KS
S’K = 0.76±0.36
A’K = 0.26±0.22±0.03
0.050.06
Uncertainty in CP ± fractionsw = (3 )%16
3
Raw asymmetries
S sin21 in bccs (=0.719±0.074±0.035)
Preliminary
Yamauchi KEK
Mission 1
Precision test of KM unitarity.
Mission 2
Mission 3
Search for new physics in B and decays.
Identify SUSY breaking mechanism.
Bread’nd butterfor B factories.
See quantum effect in penguin and box loop.
Very important if New physics = SUSY.
Mission of Super B Factory(ies)
Yamauchi KEK
u c t, ,
u c t, ,
b dW W
d b b b
dd
T.Goto et al.,PRD:035009,02
(|Vub|/|Vcb|)= 0.02 (now)0.005(1ab-1)
3
10°(1ab-1)
mS will be measuredat Tevatron soon.
sin21
=0.082 (now)0.02 (1ab-1)
SUSY scenario vs. B decays (1)
Yamauchi KEK
KEKB upgrade strategy
Present KEKB L=1034
2002 03 04 05 080706 09 10 11
L>1035
L~1036
∫Ldt =300fb-1
One year shutdown to: replace vac. chambers upgrade inj. linac C-band
ILER=1.5A
ILER=9.4A
ILER=20AConstraint: 8GeV x 3.5GeV wall plug pwr.<100MW crossing angle<30mrad
Crabcrossing
Increase no. of RF cavitieslarger beam currentsmaller y*long bunch option
Yamauchi KEK
GUT
Big BangGod
CP
Proton Decay
Baryon number
STANDARD MODEL
Quark Mass
CP violation in K system
50-100%CP violationin B system
strings
We don’t expect new physics effectto be sticking out at few % level.We don’t know if it will stick out at 1%level. But, if that’s the best you can do,we have to go for it!
1. Much work remains after B factory. 2. Precision experiments can reveal new physics if it is out there around 1 TeV.3. I m certain that orders of magnitude more B mesons will be available in the future.
