11

Weak CP Violation in Kaon and B Systems

Hai-Yang Cheng

Academia Sinica

CPV in kaon system

DCPV & Mixing-induced CPV in B decays

Lattice JC, May 25, 2007

2

Consider neutral K’s decays to pions

Since mK=497 MeV, m=137 MeV, K0,K0 ,

CP| = |, CP| = -|

K0 and K0 can have mixing through weak interaction

K0 K0 (Pais, Gell-Mann)

Let CP|K0=|K0,

CP|K1 = |K1, with K1 = (K0+K0)/2

CP|K2 = -|K2, K2 = (K0-K0)/2

Hence, K1 and K2 , but K2 is not allowed.

K1 & K2 have widely different lifetimes, K1=KS, K2=KL due to

phase space effects : L/S 580

CP Violation in Kaon System

_

_

_

_

_

If CP is good KL cannot decay into

_

3

Discovery of CP Violation• Phys. Rev. Lett. 13, 138 (1964)

3102 K“K 2

0” → ~ 1/300 !CP

4

5

3-00

00

00 102.3|| with ,)(

)( ,

)(

)(

S

L

S

L

KA

KA

KA

KA

KL K2+ K1, KS K1+ K2 with ||

KL K1 K2

indirect (mixing) CPV (CPV in mass matrix)

Two possible sources of CP violation:

'2 ' 00

A fit to K data yields

||=(2.2320.007)10-3, Re(’/)=(1.660.26)10-3

with : mixing-induced CPV, ’: direct CPV

direct CPV (CPV in decay amplitude)

6

Fermilab CERN

KTeV: Bob Hsiung

(NA31)(E731)

7

CERN & Femilab expt’l didn’t agree until 1999

Direct CP Violation: Re(’/)

(1988)

(1993)

8

600

00

10)6.05.5()()(

)()(

)/'Re(

KK

KKAdir

CP

Direct CPV in neutral kaon decays:

In kaon system, ’<< due mainly to I=1/2 rule; ’ vanishes in absence of I=3/2 interaction

Penguin diagram was first discussed by

Shifman, Vainshtein, Zakharov (‘75) motivated

by solving I=1/2 puzzle in kaon decay

I=1/2 puzzle: why 450)(

)(0

0

K

KS

Lattice: David Lin,…

9 Taipei: Chinese J. Phys. 38, 1044 (2000)

10

Lattice calculation of ’/

Using domain wall fermion, RBC obtained Re(’/)= - (4.0±2.3)10-4

A similar negative central value by CP-PACS (Computational Physics by Parallel Array Computer System)

Recently, RBC concluded that no reliable estimate of <+-|O6|K0> (and hence QCD penguin contribution to ’/) can be made within quenched approximation

11

Direct CP violation in charged kaon system

Dalitz plot distribution for K→ is parametrized as (Weinberg ‘60)

)(3

1 ...,

)(1|| 32102

032 ssssm

ssgM

A difference between g+ & g- signals direct CP violation

SM ⇒ Agc for K±→±+- & Ag

n for K± →±00 of order 10-5

At NLO, Agc= -(2.4±1.2)x10-5, Ag

n=(1.1±0.7)x10-5 (Gamiz, Prades,Scimemi)

Preliminary NA48/2 results (03+04)

Agc= -(1.3±2.3)x10-4 Ag

n=(2.1±1.9)x10-4

gg

ggAg

12

CP Violation in Standard Model

tbtstd

cbcscd

ubusud

CKM

L

L

L

CKMLLL

VVV

VVV

VVV

VchW

b

s

d

Vtcug

L

..),,(2

VCKM is the only source of CPV in flavor-changing process in the SM. Only charged current interactions can change flavor

Elements depend on 4 real parameters: 3 angles + 1 CPV phase

iiii

ii

iiCKM

scwith

eescsccss

eesscccsc

ssscc

V

sin ,cos

ccssc

scscc

323213223121

233213232112

31131

First proposed by Kobayashi & Maskawa (73)

CKM= Cabibbo-Kobayashi-Maskawa

小林‧益川

1>>1>>2>>3

13

M. Kobayashi & T. Maskawa, Prog. Theor. Phys. 49, 652-657 (73):

before charm (J/) discovery by Ting & Richter in 1974

K. Niu ( 丹生潔 ) et al. at Nagoya had found evidence for a charm production in cosmic ray data, Prog. Theor. Phys. 46, 652 (73).

KM pointed out that one needs at least six quarks in order to accommodate CPV in SM with one Higgs doublet

14

CKM 2006, Nagoya

15

Some disadvantages for VCKM:

Determination of 2 and in particular 3 is ambiguous

Some elements have comparable real & imaginary parts

cc

sc

323122132121

233212132121

31331

ii

ii

i

MKC

esscscesccss

esssccesscss

essccc

V

A new parametrization similar to the one originally due to Maiani

(76) was proposed by Chau ( 喬玲麗 ) & Keung ( 姜偉宜 ) (84)

CKM= Chau-Keung-Maiani

1>>s1>>s2>>s3

adapted by PDG as a standard parametrizarion

16

mixing CPV () direct CPV (’)

Can one observe similar mixing-induced & direct CPV in B systems ?

mtSmtAftBftB

ftBftBtA ffCP

sincos))(())((

))(())(()(

00

00

Af meaures direct CPV, Sf is related to CPV in interference between mixing & decay amplitude

According to SM, CPV in B decays can be of order 10%!

17

In July 2000, BaBar & Belle announced first hints of CPV in B0 meson system, namely, the golden mode B0 J/KS

SK=0.687 0.032, CK 0

Indirect CPV in KS, 0KS, f0KS, KS were also measured recently

What about direct CPV in B decays ?

It has been claimed by Bigi, Sanda (81) a large CPV in B0J/KS

with SK 0.65- 0.80

18

sinsin )()(

)()(

fBfB

fBfBACP B f

Need at least two different B f paths with different strong & weak phases

strong phase weak phase

ei(+)

It is difficult to estimate direct CP reliably because strong phases are beyond our control.

19

22 |||| , AAbeaAbeaA ii

22)()( |||| , AAbeaAbeaA ii

20

Direct CP asymmetries

(CDF) 08.015.039.0)(

(BaBar) 07.022.011.0

(Belle) 06.023.091.0)(

04.013.0)(

05.019.0)(

31.0)(

11.029.0)(

07.019.0)(

0.09)0.55 : Belle0.090.21 :(BaBar 07.038.0)(

013.0095.0)(

0

0

0

0*0

11.010.0

0

0

0

KBA

DDBA

BA

KBA

KBA

KBA

BA

BA

KBA

s

first confirmed DCPV (2004)

large discrepancy

» 3

21

Three popular models in recent years: QCD factorization (QCDF): Beneke, Buchalla, Neubert, Sachrajda (99)

PQCD approach based on kT factorization theorem developed by

Keum, Li, Sanda (01) -- Introduce parton’s transverse mometum to regulate endpoint div. -- Form factors for B light meson are perturbatively calculable -- Large strong phase stemming from annihilation diagrams

)()(1||0||

...)()()(),,(

)()(||

1122

21

21

2

1

2

b

QCDs

MMBII

MIBM

M

mOOBjMjM

yxyxdxdyTd

xxdxTFfBOMM

TI:

TII:

22

SCET (Bauer,Pirjol,Rothstein,Stewart)

All the terms are factorized into two types of form factors

FB(0)=+J

Acc: charming penguin (nonfactorizable)

Annihilation is real ⇒ strong phases come from charming penguin

23

738

1218

3.15.9

(%) Expt

0

0

0

B

B

KB

723

7.1

517

pQCD

1.02.0

6.5

0.6

4.5

QCDF

2.131.00.31.28.123.08.21.2

5.111.03.12.07.111.06.11.0

7.85.02.21.15.96.05.21.1

10.3

9.12

4.1

QCDF(S4)

pQCD (Keum, Li, Sanda): A sizable strong phase from penguin-induced annihilation by introducing parton’s transverse momentum

QCD factorization (Beneke, Buchalla, Neubert, Sachrajda):Because of endpoint divergences, QCD/mb power corrections due to annihilation and twist-3 spectator interactions can only be modelled

QCDF (S4 scenario): large annihilation with phase chosen so that a correct sign of A(K-+) is produced (A=1, A= -55 for PP, A=-20 for PV and A=-70 for VP)

Comparison with theory: pQCD & QCDF

1 with )1(ln HA,,

0

,,

HAiHA

BHA e

m

y

dyX

input

24

SD perturbative strong phases:

penguin (BSS) vertex corrections (BBNS)

weak

strong

Nonperturbative LD strong phases induced from power corrections especially from final-state rescattering

annihilation (pQCD)

Need sizable strong phases to explain the observed direct CPV

If intermediate states are CKM more favored than final states, e.g. BDDsK

large strong phases

large corrections to rate

25

FSI as rescattering of intermediate two-body states

[HYC, Chua, Soni]

FSIs via resonances are assumed to be suppressed in B decays due to the lack of resonances at energies close to B mass.

FSI is assumed to be dominated by rescattering of two-body intermediate states with one particle exchange in t-channel. Its absorptive part is computed via optical theorem:

i

ifTiBMfBMm )()( 2

• Strong coupling is fixed on shell. For intermediate heavy mesons,

apply HQET+ChPT

• Cutoff must be introduced as exchanged particle is off-shell

and final states are hard

Alternative: Regge trajectory [Nardulli,Pham][Falk et al.] [Du et al.] …

26

Dispersive part is obtained from the absorptive amplitude via dispersion relation

''

)'( 1)(

22 ds

ms

sMmmMe

s BB

= mexc + rQCD (r: of order unity)

or r is determined form a 2 fit to the measured rates

r is process dependent

n=1 (monopole behavior), consistent with QCD sum rules

Once cutoff is fixed CPV can be predicted

subject to large uncertainties and will be ignored in the present work

Form factor is introduced to render perturbative calculation meaningful

n

QCD

n

t

m

t

mtF

2

22

)(

LD amp. vanishes in HQ limit

27

All rescattering diagrams contribute to penguin topology

fit to rates rD = rD* 0.69

predict direct CPV

B B

28

BR

SD

(10-6)

BR

with FSI

(10-6)

BR

Expt

(10-6)

DCPV

SD

DCPV

with FSI

DCPV

Expt

B 16.6 22.9+4.9-3.1 24.11.3 0.01 0.026+0.00

-0.002 0.010.03

B0 13.7 19.7+4.6-2.9 18.20.8 0.03 -0.15+0.03

-0.01 -0.100.02

B0 9.3 12.1+2.4-1.5 12.10.8 0.17 -0.09+0.06

-0.04 0.050.03

B0 6.0 9.0+2.3-1.5

11.51.0 -0.04 0.022+0.008-0.012

For simplicity only LD uncertainties are shown here

FSI yields correct sign and magnitude for A(+K-) !

K puzzle: A(0K-) A(+ K-), while experimentally they differ

by 5Gronau argued that this is not a puzzle if |C| » |T|

_

_

_

_

29

)0(0 tB

• Both B0 and B0 can decay to f: CP eigenstate.

• If no CP (weak) phase in A:

A=±A

Cf=0, Sf=±sin2

0B

LSKJf ,/Oscillation, eim t

(Vtb*Vtd)2

=|Vtb*Vtd|2 e-i 2

)( 0 fBAA

)( 0 fBAA

A

AeSC

mtSmtC

ftBftB

ftBftBa

if

f

ff

f

ff

ff

f

2

22

2

00

00

,||1

Im2 ,

||1

||1

,sincos

))(())((

))(())((

Quantum Interference

Direct CPA Mixing-induced CPA

Time-dependent CP asymmetries

30

)(

)(

2*

**

***0

ib

uf

cfcbcs

cfcbcs

ufubus

ttbts

ccbcs

uubus

eRAAVV

AVVAVV

FVVFVVFVVfBA

Expressions of S & C

)/arg( ,/ where

,sinsin||2

,cossin2cos||2

cf

uff

cfc

ufuf

fff

fff

AAAAr

rC

rS

Sources of S: u-penguin, color-suppressed tree for two-body modes

color-allowed tree for three-body modes (e.g. K+K-K0)

or LD u-penguin and color-allowed tree induced from FSI

0.42

(=0.22)

Hence, (Gronau 89)

*usubVV

b u

d d

charmonium allSSS fff

for b→sqq

31

b→s tCPV measurements

Naïve b→s penguin average: 0.53±0.05, 2.6 deviation from b→ccs average

All Sf<0

It is expected in SM that Sf is at most O(0.1) in B0 KS, KS, 0K

S, ’KS, 0KS, f0KS, K+K-

KS, KSKSKS

[London,Soni; Grossman, Gronau, Ligeti, Nir, Rosner, Quinn,…]

32

G. Kane (and others): The 2.7-3.7 anomaly seen in b→s penguin modes is the strongest hint of New Physics that has been searched in past many many years…

It is extremely important to examine how much of the deviation is allowed in the SM and estimate the theoretical uncertainties as best as we can.

A current hot topic

33

17.026.0 030.0077.0 053.0 04.0 0.06

21.035.0 165.0034.0 07.0 0.07

07.007.0 008.0019.0 00.0 0.01 '

24.048.0 187.0 04.0 .090

24.020.0 0.153 01.0 512.0

18.030.0 03.0 02.0

Expt SCET pQCD FSIQCDF QCDF Mode

02.003.0

02.003.0

02.004.0

0

02.005.0

02.004.0

00.004.0

00.004.0

10.006.0

12.015.0

0.0307.0

0.0307.0

03.004.0

05.006.0

01.003.0

00.004.0

S

S

S

S

S

S

K

K

K

K

K

K

Two-body modes

QCDF: HYC, Chua, Soni; Beneke

pQCD: Li, Mishima

SCET: Willamson, Zupan

34

theory expt

sin2(K+K-KS) =0.050+0.028-0.033

-0.098+018-0.16

sin2(KSKSKS) =0.041+0.027-0.032 -0.098±0.20

sin2(KS00) =0.051+0.027-0.032 -1.3980.71

sin2(KS+-) =0.040+0.031-0.032

sin2 < O(10%)

Three-body modes (HYC, Chua, Soni):