1

SM expectations on sin2 from b → s penguins

Chun-Khiang ChuaAcademia Sinica

FPCP 2006 9 April 2006, Vancouver

2

Mixing induced CP Asymmetry

)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

))(())((

))(())((

Bigi, Sanda 81

Quantum Interference

Direct CPA Mixing-induced CPA

3

The CKM phase is dominating The CKM picture in the

SM is essentially correct:

WA sin2=0.687±0.032 Thanks to BaBar, Belle and

others…

0

||

||

***

)(

)(

1

3

tdtbcdcbudub

itdtd

iubub

VVVVVV

eVV

eVV

4

New CP-odd phase is expected… New Physics is expected

Neutrino Oscillations are observed Present particles only consist few % of t

he universe density What is Dark matter? Dark energy? Baryogenesis nB/n~10-10 (SM 10-20)

It is unlikely that we have only one

CP phase in Nature

NASA/WMAP

5

The Basic Idea A generic b→sqq decay amplitude:

For pure penguin modes, such as KS, the penguin amplitude does not have weak phase [similar to the J/KS amp.]

Proposed by Grossman, Worah [97]

A good way to search for new CP phase (sensitive to NP).

ttbts

ccbcs

uubus FVVFVVFVVfBA ***0 )(

0// SSsss KJKJKKK SSS

6

The Basic Idea (more penguin modes) In addition to KS, (’KS, 0KS, 0KS, KS, KS) were propose

d by London, Soni [97] (after the CLEO observation of the large ’K rate)

For penguin dominated CP mode with f=fCP=M0M’0, cannot have color allowed tree (W± cannot produce M0 or M’0) In general Fu should not be much larger than Fc or Ft

More modes are added to the list: f0KS, K+K-KS, KSKSKS Gershon, Hazumi [04], …

ttbts

ccbcs

uubus FVVFVVFVVfBA ***0 )(

0// SS KJKJfff SSS

7

sin2eff

To search for NP, it is important to measure the deviation of sin2eff in charmonium and penguin modes

Deviation NP

How robust is the argument?

What is the expected correction?

8

Sources of S:

Three basic sources of S: VtbV*ts = -VcbV*cs-VubV*us

=-A2 +A(1-)4-iA4+O(6) (also applies to pure penguin modes)

u-penguin (radiative correction): VubV*us (also applies to pure penguin modes)

color-suppressed tree Other sources?

LD u-penguin, CA tree?

*usubVV

b u

d d

9

Corrections on S Since VcbV*cs is real, a better expression is to use the unit

ary relation t=-u-c (define Au≡Fu-Ft, Ac≡Fc-Ft;; Au,Ac: same order for a penguin dominated mode):

Corrections can now be expressed as (Gronau 89)

To know Cf and Sf, both rf and f are needed.

ttbts

ccbcs

uubus FVVFVVFVVfBA ***0 )(

)()( 2***0 ib

uccbcs

ccbcs

uubus eRAAVVAVVAVVfBA

)/arg( ,/

,sinsin||2 ,cossin2cos||2cf

uff

cfc

ufuf

ffffff

AAAAr

rCrS

~0.4 2

10

Several approaches for S

SU(3) approach (Grossman, Ligeti, Nir, Quinn; Gronau, Rosner…) Constraining |Au/Ac| through related modes in a model independe

nt way

Factorization approach SD (QCDF, pQCD, SCET)

FSI approach (Cheng, CKC, Soni)

Others

)/arg( ,/

,sinsin||2

,cossin2cos||2

cf

uff

cfc

ufuf

fff

fff

AAAAr

rC

rS

11

SU(3) approach for S Take Grossman, Ligeti, Nir, Quinn [03] as an example

Constrain |rf|=|uAu/cAc| through SU(3) related modes

cfcbcd

ufubud

cfcbcs

ufubus

BVVBVVfBA

AVVAVVfBA

'*

'*0

**0

)'(

)(

)'(

:)3(

0

'

'**

'

)('

')(

fBACAVVAVV

BCASU

f

ff

cfcbcd

ufubud

f

cuf

ff

cuf

f

csudcdusf

ufubus

cfcbcs

cfcbcd

ufubud

ud

usf r

VVVVr

AVVAVV

AVVAVV

V

Vr

1

)/()(ˆ

**

**

b→s

b→d

O(2)

12

S<0.22

An example

|r’Ks|≡

13

More SU(3) bounds (Grossman, Ligeti, Nir, Quinn; Gronau, Grossman, Rosner) Usually if charged modes a

re used (with |C/P|<|T/P|), better bounds can be obtained. (K- first considered by Grossman, Isidori, Worah [98] using -, K*0

K-) In the 3K mode U-spin sym.

is applied. Fit C/P in the topological a

mplitude approach

⇒S

19.0|)(|15.0)(ˆ

18.0|~)(|14.0~)(ˆ

29.0|)(|23.0)(ˆ

10.008.0)'(ˆ

22.0|)'(|17.0)'(ˆ

00

SS

SS

S

SS

KSKr

KKKSKKKr

KSKr

Kr

KSKr

Gronau, Grossman, Rosner (04)

|Sf|<1.26 |rf||Cf|<1.73 |rf|

Gronau, Rosner (Chiang, Luo, Suprun)

14

S from factorization approaches There are three QCD-based factorization app

roaches: QCDF: Beneke, Buchalla, Neurbert, Sachrajda [se

e talk by Alex Williamson] pQCD: Keum, Li, Sanda [se

e talk by Satoshi Mishima] SCET: Bauer, Fleming, Pirjol, Rothstein, Stewart

[see talk by Christian Bauer]

15

S)SD calculated from QCDF,pQCD,SCET

Most |S| are of order 2, except KS, 0KS (opposite sign)

Most theoretical predictions on S are similar, but signs are opposite to data in most cases

Perturbative phase is small S>0

QCDF: Beneke [results consistent with Cheng-CKC-Soni]

pQCD: Mishima-Li SCET: Williamson-Zupan

(two solutions)

16

A closer look on S signs and sizes

0 ][

][][~

)]([

][)]([~)'(

0 ][

][][~

)]([

][)]([~)(

0 ][

][][~

][

][][~)(

0 ][

][][~

][

][][~)(

0 ][

][~

)]([

)]([~)(

0] Re[ ,Re]cos[||

64

264)(

64

2640

46

2460

46

246

64

64

2

2

SP

CP

ara

aaraK

A

A

SP

CP

ara

aaraK

A

A

SP

CP

aar

aaarK

A

A

SP

CP

aar

aaarK

A

A

SP

P

ara

araK

A

A

A

ArS

c

u

cMc

uuMu

Sc

u

c

u

cKc

uuKu

Sc

u

c

u

ccK

uuuK

Sc

u

c

u

ccK

uuuK

Sc

u

c

u

cc

uu

Sc

u

c

u

)(2

1dduu

constructive (destructive)Interference in P of ’Ks (Ks)

)(3

1~ ),2(

6

1~' ssdduussdduu

small

large

small (’Ks)large (Ks)

small

large

Beneke, 05

B→V

17

723 5.6 2437

1.7 6.0 48

517 4.5 211

7.133.13

0

1.02.0

5.111.03.12.07.111.06.11.0

1415

0

7.85.02.21.15.96.05.21.1

0

B

B

KB

Expt(%) QCDF PQCD

Direct CP Violations in Charmless modes

With FSI ⇒ strong phases ⇒ sizable DCPV

FSI is important in B decays What is the impact on S

1314

0

13

0

4711431

211144

)(%)( )(%)( )(%) (

B

KB

ExptAcpFSIAcpFSInoAcp

Cheng, CKC, Soni, 04Different , FF…

18

FSI effects on sin2eff (Cheng, CKC, Soni 05) FSI can bring in additional

weak phase B→K*, K contain tree V

ub Vus*=|Vub Vus|e-i

Long distance u-penguin and color suppressed tree

19

FSI effects in rates

FSIs enhance rates through rescattering of charmful intermediate states [expt. rates are used to fix cutoffs (=m + r QCD, r~1)].

Constructive (destructive) interference in ’K0 (K0).

20

FSI effects on direct CP violation

Large CP violation in the K, K mode.

21

FSI effect on S

Theoretically and experimentally cleanest modes: ’Ks (Ks) Tree pollutions are diluted for non pure penguin modes: KS, 0KS

22

FSI effects in mixing induced CP violation of penguin modes are small The reason for the smallness of the deviations:

The dominant FSI contributions are of charming penguin like. Do not bring in any additional weak phase.

The source amplitudes (K*,K) are small (Br~10-6) compare with Ds*D (Br~10-2,-3)

The sources with the additional weak phase are even smaller (tree small, penguin dominate)

If we somehow enhance K*,Kcontributions ⇒ large direct CP violation (AKs). Not supported by data

23

Results in S for scalar modes (QCDF) (Cheng-CKC-Yang, 05) S are tiny (0.02 or less):

LD effects have not been considered.

Do not expect large deviation.

24

K+K-KS(L) and KSKSKS(L) modes

Penguin-dominated KSKSKS: CP-even eigenstate.

K+K-KS: CP-even dominated,

CP-even fraction: f+=0.91±0.07 Three body modes Most theoretical works are based on flavor symmetr

y. (Gronau et al, …) We (Cheng-CKC-Soni) use a factorization approach

25

K+K-KS and KSKSKS decay rates KS KS KS (total) rat

e is used as an input to fix a NR amp. (sensitive).

Rates (SD) agree with data within errors. Central values sli

ghtly smaller. Still have room fo

r LD contribution.00.004.006.000.008.016.0

expttheory

00.004.006.003.040.116.0

expttheory

02.024.202.603.040.188.0

03.054.098.203.022.040.0excluded

04.083.008.304.046.043.0

05.048.129.506.013.165.0

70.031.238.810.059.108.1

expt6

theory6

92.0

07.091.092.0

74.5

2.12.6

)48.0()(

88.1)(

45.5)(

2.14.1233.7

)10()10(state Final

L

S

LSS

SSS

K

CPS

CPS

S

KKK

ff

KKK

ff

KKK

inputKKK

CP

KKK

KKK

KKK

BB

S

26

It has a color-allowed b→u amp, but…

The first diagram (b→s transition) prefers small m(K+

K-) The second diagram (b→u transition) prefers small m

(K+K0) [large m(K+K-)], not a CP eigenstate Interference between b→u and b→s is suppressed.

b→s b→u

27

CP-odd K+K-KS decay spectrum

Low mKK: KS+NR (Non-Resonance)..

High mKK: (NR) transition contribution..SKKB 0

b→s b→u

28

CP-even K+K-KS decay spectrum

Low mKK: f0(980)KS+NR (Non-Resonance).

High mKK: (NR) transition contribution. SKKB 0

b→s

b→u

29

K+K-KS and KSKSKS CP asymmetries

Could have O(0.1) deviation of sin2 in K+K-KS It originates from c

olor-allowed tree contribution.

Its contributions should be reduced. BaBar 05

S, ACP are small In K+K-Ks: b→u pr

efers large m(K+K-) b→s prefers small m(K+K-), interference reduced small asymmetries

In KsKsKs: no b→u transition.

06.008.012.007.011.028.0

05.000.002.006.001.006.0

01.029.095.002.032.011.0excluded

01.016.073.001.027.000.0

01.029.095.002.032.011.0excluded

007.0000.0001.0018.0000.0001.0

007.0000.0000.0018.0000.0000.0

004.0024.0080.0015.0011.0013.0excluded

002.0040.0113.0013.0023.0031.0

18.017.0

014.0024.0080.0015.0011.0013.0excluded

eff

77.0

214174.0

214116.0)(

09.0)(

10916.0)(

Expt.(%)

024.0

25.065.0024.0

34.009.0025.0)(

0460)(

57.00250)(

Expt.2sinState Final

LSS

SSS

KL

CPS

KS

f

LSS

SSS

KL

CPS

KS

KKK

KKK

KKK

KKK

KKK

A

KKK

KKK

KKK

.KKK

.KKK

L

S

L

S

30

Conclusion The CKM picture is established. However, NP is expected

(m, DM, nB/n). The deviations of sin2eff from sin2 = 0.6870.032 are at

most O(0.1) in

B0 KS, KS, 0KS, ’KS, 0KS, f0KS, a0KS, K*00, KSKSKS. The O(0.1) S in B0→KKKS due to the color-allowed tree co

ntribution should be reduced. A Dalitz plot analysis will be very useful.

The B0→’KS, KS and B0→KSKSKS modes are very clean. The pattern of S is also a SM prediction. A global analysis

is helpful. Measurements of sin2eff in penguin modes are still good pl

aces to look for new phase(s) SuperB →0.1.

31

Back up

32

A closer look on S signs (in QCDF)

M1M2: (B→M1)(0→M2)

,Re

c

u

A

AS

33

Perturbative strong phases:

penguin (BSS) vertex corrections (BBNS) annihilation (pQCD)

Because of endpoint divergences, QCD/mb power corrections in QCDF due to annihilation and twist-3 spectator interactions can only be modelled

with unknown parameters A, H, A, H, can be determined (or constrained) from rates and Acp.

Annihilation amp is calculable in pQCD, but cannot have b→uqq in the annihilation diagram in b→s penguin.

)1(ln ,

,

0

,HAi

HAB

HA em

y

dyX

b

d

sq

q

34

Scalar Modes

The calculation of SP is similar to VP in QCDF All calculations in QCDF start from the following projection:

In particular

All existing (Beneke-Neubert 2001) calculation for VP can be brought to SP with some simple replacements (Cheng-CKC-Yang, 2005).

SVPhxMdxezqzqph hzkzki ,, ),(0|)'()(|)( ||

1

0

)'( 21

35

FSI as rescattering of intermediate two-body state 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

• Form factor or cutoff must be introduced as exchanged particle is

off-shell and final states are necessarily hard

Alternative: Regge trajectory, Quasi-elastic rescattering …

(Cheng, CKC, Soni 04)

36

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 -0.020.03

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

-0.01 -0.110.02

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

-0.04 0.040.04

B0 6.0 9.0+2.3-1.5

11.51.0 -0.04 0.022+0.008-0.012 -0.090.14

For simplicity only LD uncertainties are shown here

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

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

by 3.4SD effects?Fleischer et al, Nagashima Hou Soddu, H n Li et al.]

Final state interaction is important.

_

_

_

_

37

BR

SD

(10-6)

BR

with FSI

(10-6)

BR

Expt

(10-6)

DCPV

SD

DCPV

with FSI

DCPV

Expt

B0+ 8.3 8.7+0.4-0.2 10.12.0 -0.01 -0.430.11 -0.47+0.13

-0.14

B0+ 18.0 18.4+0.3-0.2 13.92.1 -0.02 -0.250.06 -0.150.09

B000 0.44 1.1+0.4-0.3 1.80.6 -0.005 0.530.01 -0.49+0.70

-0.83

B0 12.3 13.3+0.7-0.5 12.02.0 -0.04 0.370.10 0.010.11

B 6.9 7.6+0.6-0.4

9.11.3 0.06 -0.580.15 -0.07+0.12-0.13

Sign and magnitude for A(+-) are nicely predicted !

DCPVs are sensitive to FSIs, but BRs are not (rD=1.6)

For 00, 1.40.7 BaBar

Br(10-6)= 3.11.1 Belle

1.6+2.2-1.6 CLEO Discrepancy between BaBar and Belle should be clarified.

﹣

__

B B B

_

38

Factorization Approach SD contribution should be studied first. Che

ng, CKC, Soni 05 Some LD effects are included (through BW).

We use a factorization approach (FA) to study the KKK decays.

FA seems to work in three-body (DKK) decays CKC-Hou-Shiau-Tsai, 03.

Color-allowed Color-suppressed

39

K+K-KS and KSKSKS (pure-penguin) decay amplitudes

Tree

Penguin

40

Factorized into transition and creation parts

Tree

Penguin

41

sin2eff in a restricted phase space of the K+K-KS decay

The corresponding sin2eff, with mKK integrated up to mKK

max. Could be useful for experiment.

CP-even

Full, excluding KS