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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation

1U. Uwer

3. CP violation in the K0 and B0 system

τν−π −τ τν −π−τ

↔P

↔P

Cb Cb

τν+π +τ τν +π+τ

forbidden

forbidden

• C and P violated in weak decays

• CP conserved in weak interaction ? → No !

allowed

τνπτ −− →

3.1 Observation of CP violation (CPV) in KL decays

( ) 1CP21 00 −=−= KKKL

3102~1CP

−

−+

⋅

+=

→

BR

KL ππ

should always decay into 3π:

CP(|3π>)= -1

and never into 2π CP(|2π>)= +1

Christenson, Cronin, Fitch, Turlay, 1964

( ) LL KKKKCP −=−= 00

21

Explanation:

( )1221

1 KKKL εε

++

=1−=CP 1+=CP

Not a CP eigenstate: CP violation !


2U. Uwer

3

3

10)26.067.1()Re(

10)014.0284.2(−

−

⋅±=′

⋅±=

εε

ε

)K(/ sτt∆

1999 0KKpp +−→ π

ππAfter 35 years of kaon physics:

( )1221

1 KKKL εε

++

=

ππππ (mixing)

(Direct CPV)

ε ′

Interpretation of CPV measured in the kaonsystem is difficult. Much easier to understandand to predict in the SM is the B mesonsystem: CPV in the B0 system was observed in 2000.

3.2 CP Violation in the Standard Modell

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

bsd

VVVVVVVVV

bsd

tbtstd

cbcscd

ubusud

'''

Quarks:

Antiquarks:

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

bsd

VVVVVVVVV

bsd

tbtstd

cbcscd

ubusud

***

***

***

'''

Phase angle≠0: complex CKM matrix

Different mixing for quarks and anti-quarks

Origin of CP Violation (CPV)

( ) 0Im ** ≠= kjilklij VVVVJStrength of CPV: Characterized by Jarlskog invariant:

γiubub eVV −=

βitdtd eVV −=

see Wolfensteinparametrization

( ) 510262 10~)(21]Im[ −∗∗ +−== λληλ OAVVVVJ csubcbusIn SM:


3U. Uwer

3.3 Unitarity Triangle

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

tbtstd

cbcscd

ubusud

VVVVVVVVV

V

Unitary CKM matrix: VV† = 1

0=++ ∗∗∗

tbtdcbcdubud VVVVVV

0=++ ∗∗∗

ubtbustsudtd VVVVVV

β

α

γ

*tbtdVV

*cbcdVV

*ubudVV

area = J/2

Important for Bd and Bs decays

→ 6 “triangle” relations:

0=++ ∗∗∗

tbtdcbcdubud VVVVVV

Remaining 4 relations lead to degenerated triangles: same area (J/2) but verydifferent sides.

Rescaled Unitarity Triangle

β

α

γ*

*

cbcd

ubud

VVVV *

*

cbcd

tbtd

VVVV

η

0 1

Im

ρRe

⎥⎥⎦

⎤

⎢⎢⎣

⎡−≡ *

*

argcbcd

ubud

VVVVγ

⎥⎥⎦

⎤

⎢⎢⎣

⎡−≡ *

*

argtbtd

cbcd

VVVVβ

⎥⎥⎦

⎤

⎢⎢⎣

⎡−≡ *

*

argubud

tbtd

VVVVα

0=++ ∗∗∗

tbtdcbcdubud VVVVVV


4U. Uwer

3.4 Observation of CP Violation

1AfB

δφ ii eeA CP2

fB →

)cos(2 21

22

21

2

δφ ++

+=

CPAA

AAA

CP

1AfB

δφ ii eeA CP−2

fB →

)cos(2 21

22

21

2

δφ −+

+=

CPAA

AAAWeak and CP invariant phase difference

Need two phase differences between A1 and A2: Weak difference which changessign under CP and another phase difference (strong) which is unchanged.

“3 Ways” of CP violation in meson decays

≠p/q

0B 0B

q/p

0B0B

f f

)()( 0000 BBPBBP →≠→

)()( fBPfBP →≠→

1≠f

f

AA

Bϕ δ f

weak strong

δϕ ii eeAfBA =→ )(

≠2 2

0Bf f

0B

fA fA

1≠pq

a) Direct CP violation

b) CP violation in mixing


5U. Uwer

c) CP violation through interference of mixed and unmixed amplitudes

f0B

0B

))(())(( 00

00 tfBtfB tt →Γ≠→Γ ==

Asymmetrie modulated by mt∆sin~

Combinations of the 3 ways are possible!

a) Direct CP violation (B system)

B0

gB0

1A−+πK0B

δφ ii eeA CP2

Strong phase difference

δϕ sinsin4 2122

AAAA =−CP Asymmetrie


6U. Uwer

0

0

BB K

Kππ

+ −

− +→→

BB Mio227

]GeV/c[m 2Kπ

511606)/( 00 ±=→ ± mπKBBN

)()()()(

00

00

+−−+

+−−+

→+→→−→

=ππππ

KBNKBNKBNKBNACP

4.2σ009.0030.0133.0 ±±−=CPA

PRL93(2004) 131801.

1≠pq

b) CP (T) violation in mixing

)()( 0000 BBPBBP →≠→

εεη

+−

=≡11

pq

m ( )1221

1 KKK K

K

L εε

++

=

Reminder:

εεε Re4

1Re4

1

1))(())(())(())(()( 24

4

0000

0000

≈+

≈+

−=

→+→→−→

=pq

pqtBBPtBBPtBBPtBBPtA

T violation

Measured using semileptonic decays

))(())(())(())(()(

00

00

00

00

tXBtXBtXBtXBtA

tt

ttSL νν

νν−

=+

=

−=

+=

→Γ+→Γ→Γ−→Γ

=ll

ll

ν+−→ lXB0

ν−+→ lXB 00B 0B


7U. Uwer

CPLEAR( ) 3107.12.6)Re(4 −⋅±=Kε

K0⎯K0 System:B0⎯B0 System:

0017.00007.0Re4

0034.00013.1

0067.00026.0

±−=

±=

±−=

B

SL

pq

A

ε

HFAG 2004

0K

)()() ()() ()(

00

00

00

00exp t

eKeKeKeKtA

etet

etet

νπνπ

νπνπ+−

=−+

=

+−=

−+=

→Γ−→Γ

→Γ−→Γ=

24

21 4 sin 5 10c

t

mqp m

π β −− ≈ ≈ ×

Standard model prediction for B

c) CP violation in interference between mixing and decay

))(/( 0 tKJB sψ→Γ ))(/( 0 tKJB sψ→Γ≠

sKJB ψ/0 →CPηCP=-1

sKJB ψ/0 →

A

2πieAβ2~ iepq

sKJ ψ/0B

0B

A

2πieAβ2~ ieqp −

sKJ ψ/0B

0B

Important variable:AA

pq

CP ⋅≡λ


8U. Uwer

SM prediction of λCP for B0→J/ψKs

βλ i

cdcb

cdcb

tdtb

tdtb

cdcs

cdcs

cscb

cscb

tdtb

tdtb eVVVV

VVVV

VVVV

VVVV

VVVV

AA

pq 2

*

*

*

*

*

*

*

*

*

*

CP−−=−=−==

b

d b

dB0 mixing

pq /

b

d

ccsd

W+

B0 decay

*cscbVVA∝

K0 mixings

d s

d

KK pq /

βiepq 2~

β)sin(2)Im(

1

=

=

CP

CP

λ

λ⇒≈ − βi

tdtd eVV no direct CPV, no CPV in mixing

1−=CPη

Sam

e fo

r all

ccK

0ch

anne

ls

Beside Vtd all other CKM elements are real

Calculation of the time-dependent CP asymmetry

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡∆

−−∆+

+×

+∝→Γ

⎥⎥⎦

⎤

⎢⎢⎣

⎡∆

−+∆−

+×

+∝→Γ

∆−

∆−

tmtmetfB

tmtmetfB

dCP

dCPCP

CP

t

CP

dCP

dCPCP

CP

t

CP

B

B

cos2

1sinIm

21

1))((

cos2

1sinIm

21

1))((

22

2

/0

22

2

/0

0

0

λλ

λ

λ

λλ

λ

λτ

τ

≠

( ) ( )[ ]tmCtmSftBftBftBftBtA dfdf

CPCP

CPCPCP ∆−∆=

→Γ+→Γ

→Γ−→Γ= cossin

))(())(())(())(()( 00

00

Time resolved

Interference= sin2β for B0→J/ψKS

indicates direct CP violationif |q/p|≠1

2

2

2 1

1

1Im2

CP

CPf

CP

CPf CS

λ

λ

λλ

+

−=

+=


9U. Uwer

Measurement of sin2β: Asymmetric e+ e- B factory

GeV3.5−e +e B Mesonen in Ruhe→ Zerfallslänge z≈0

GeV9−e +e

GeV3.5

GeV1.3

Boost β = 0.56 tcz βγ=

GeV58.10ECMS = 50% / 50%

Symmetrisch:

Asymmetrisch:

Zerfallslängez≈250µm

21 vt ⋅

+l

11 vt ⋅ψ/J

sK

2vt ⋅∆

0CP

0tag B)0(B BB ==∆= t

0CP

0tag B)0(B BB ==∆= t

tagBCPB

)sin( β2sin)( mttACP ∆=

Υ(4s)

Erei

gnis

se

Measurement of sin2β: Coherent oszillation


10U. Uwer

B0 →D*+ π-fast→ D0π+soft

→K-π+

→ψ(2S) Ks

→ µ+µ- →π+π-

B0(∆t)CPB

tagB

PRL 94, 161803. BB Mio227

023.0040.0722.02sin ±±=β

sKB ψ→0

)sin( β2sin)( mttACP ∆=

Measurement of sin2β: Golden decay channel

3.5 Experimental status of the Unitarity Triangle

A triple triumph

Standard Model CKM mechanism confirmed

1. Large CP Violation in B decays

2. Large direct CP violation observed

3. CPV parameter related to magnitude of non-CP observables


11U. Uwer

• Baryon number violation

• C and CP Violation

• Departure from thermal equilibrium

Does the Standard Model explain the baryon symmetry in universe?

No

No

• CP violation in quark sector is a factor ~1010 to small.• for MHiggs> 114 GeV: Symmetry breaking = 2nd order phase transition

Attractive: Super-symmetric extensions of Standard Model

• Additional CP violation through supersymmetric particles

• Extended Higgs-sector → strong phase transition

Alternative: Lepto-genesis

Andrei D. Sakharov, 1967

3.6 Baryon asymmetry in the universe

CP - physi.uni-heidelberg.deuwer/lectures/ParticlePhysics/...Advanced Particle Physics: IX. Flavor...

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