1

Theoretical review on sin2 from b → s penguins

Chun-Khiang ChuaChung Yuan Christian University

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:

Cf=0, Sf=fsin2

0B

LSKJf ,/Oscillation, eim t

(Vtb*Vtd)2

=|Vtb*Vtd|2 e-i 2

)( 0 fBAA

)( 0 fBAA

fi

ff

ff

f

ff

ff

f

eAA

pqSC

mtSmtCftBftBftBftBa

2

22

2

00

00

,||1

Im2 ,

||1||1

,sincos ))(())(())(())((

Bigi, Sanda 81

Quantum Interference

Direct CPA Mixing-induced CPAf = 1

3

The CKM phase is dominating The CKM picture in the

SM is essentially correct:

WA sin2=0.681±0.025 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 on

e 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 proposed b

y 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 Most data: S<0

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, LD CS tree, 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 effects (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

csudcdusfufubus

cfcbcs

cfcbcd

ufubud

ud

usf r

VVVVrAVVAVVAVVAVV

VVr

1

)/()(ˆ

**

**

b→s

b→d

intrinsic un.: O(2)

12

S<0.22

An example

|r’Ks|≡

icA ic|A|: conservative, less modes better bound

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)(ˆ39.0|)(|

|)(|31.0)(ˆ02.1)(ˆ

29.0|)(|23.0)(ˆ10.008.0)'(ˆ

22.0|)'(|17.0)'(ˆ

00

SS

SSS

S

SSS

S

S

SS

KSKrKKKSKKKS

KKKrKKKr

KSKrKr

KSKr

Gronau, Grossman,Rosner (04)Engelhard, (Nir), Raz (05,05)

|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 Martin Beneke] pQCD: Keum, Li, Sanda [se

e talk by Cai-Dai Lu] SCET: Bauer, Fleming, Pirjol, Rothstein, Stewart

[see talk by Ira Z. Rothstein]

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

Signs and sizes of S?

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

pQCD: Mishima-Li SCET: Williamson-Zupan

(two solutions)

Some “hints” of deviations, e.g. 0KS

16

Dominant Penguin Contributions (PP,PV)

Dominant contributions: (similar sizes, common origin) (V-A)(V-A): a4, (S+P)(S-P): rM2 a6 (: M1=V) Constructive Interference: a4+rM2a6 M2M1=PP,VP Destructive Interference: a4rPa6, M2M1=PV Interferences between q=s and q=d amp. (in KS’, KS)

V=(V-A)/2+(V+A)/2

17

KS

No CS tree, unsuppressed P S small (~0.03) and positive

Beneke, 05

18

KS, KS

KS: C(a2) + suppressed P S large Opposite signs come from signs in wave functions.

KS: C(a2) + unsuppressed P S small, signs different from (KS), due to a6 terms

)(2

1 dduu

Ratio of F.F. fM not shown

00 ,

,

00 ,

,

19

KS, ’KS

Contructive interference in P(’KS) both in a4,6 and in q=d,s S>0 and small Destructive interference in P(KS) in q=d,s S>0, large (unstable)

)( '

)( '

)( '

)(3

1~

),2(6

1~'

ssdduu

ssdduu

Ps>PdP flip sign

)2/1(tan3.39 1

20

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

21

FSI effect on S

SmallS for ’Ks, Ks. Tree pollutions are diluted for non pure penguin

modes: KS, 0KS

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

22

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

Use rates to fix FSI parameters: F.F. FSI contributions dominated by DsDbar final states The dominant FSI contributions are of charming penguin like.

Do not bring in any additional weak phase.

Other sources of LD contributions? A(K) and 00 rate may hint at larger and complex CS tree

… SU(3): Chiang, Gronau, Rosner, Luo, Suprun Zhou; Charng, Li, … Implications on S?

See Cheng Wei’s talk

23

S from RGI parametrizations aaa

Ciuchini et al.; taken from 0801.1833

at UL=0.5S are still small:

A(K-0)

24

A(K)S?

C from exchange-type rescattering of T (enhance A, B(00)) Similar results for S:

CKC,Hou,Yang 2003; CKC 2007

QE FSI:TC

25

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

LD effects have not been considered.

26

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

Penguin-dominated KSKSKS: CP-even eigenstate. K+K-KS: CP-even dominated,

CP-even fraction: f+0.9 Three body modes Most theoretical works are based on flavor symmetr

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

See Hai-Yang’s talk for more details

27

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

K

K

28

CP-odd K+K-KS decay spectrum

Low mKK: KS+NR (Non-Resonance).. High mKK: bu transition contribution. Experimental data: KS only bu is highly constrained.

b→s b→u

See Hai-Yang’s talk

29

CP-even K+K-KS decay spectrum

Low mKK: f0(980)KS+NR (Non-Resonance). High mKK: bu transition contribution. b s and bu do not interfere

b→s

b→u

peak at mKK 1.5 GeV due to X0(1550) See Hai-Yang’s talk

30

S for K+K-KS, KSKSKS and others S are small.

For KsKsKs: - no b→u transition.

For K+K-KS: - b→u prefers large m

(K+K-), not seen - b→s prefers small m

(K+K-), - interference reduced small S

sin2=0.6810.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)

theory expt

S(K+K-KS) =0.040+0.028-0.033

0.05±0.11

S(KSKSKS) =0.038+0.027-0.032 -0.10±0.20

S(KS00) =0.048+0.027-0.032 -1.200.41

S(KS+-) =0.037+0.031-0.032

Stheory < O(0.1)Cheng,CKC,Soni, 2007

See Hai-Yang’s talk

31

Conclusion The CKM picture is established. However, NP is expected (m, DM, nB/n). In most calculations: the deviations of sin2eff from sin2 = 0.6810.025 are

At most O(0.1) in B0 KS, ’KS, 0KS, f0KS, a0KS, K*00, KSKSKS…

Larger |S|: B0 KS, 0KS, KS… The color-allowed tree contribution to S in B0→KKKS is constrained by d

ata to be small. In existing theoretical claculations:

S in B0→’KS, KS and B0→KSKSKS modes are tiny. Not affected by LD effects explored so far. Need more works to handle hadronic effects. More measurements [SU(3)].

The pattern of S is also a SM prediction. Most S>0. A global analysis is helpful. Measurements of sin2eff in penguin modes are still good places to look fo

r new phase(s) SuperB →0.1.

32

Back up

33

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

4711431211144)(%)( )(%)( )(%) (

BKB

ExptAcpFSIAcpFSInoAcp

Cheng, CKC, Soni, 04Different , FF…

34

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).

35

FSI effects on direct CP violation

Large CP violation in the K, K mode.

36

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

74.52.12.6

)48.0()(88.1)(45.5)(

2.14.1233.7)10()10(state Final

L

S

LSS

SSS

K

CPS

CPS

S

KKKff

KKKff

KKKinputKKK

CPKKKKKKKKK

BB

S

37

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.

05.000.007.003.0

04.001.005.001.0

40.153.010.154.0excluded

47.152.001.155.0

40.153.010.154.0excluded

008.0000.0019.0000.0

008.0000.0019.0000.0

009.0001.0020.0001.0excluded

008.0007.0019.0004.0

009.0001.0020.0001.0excluded

eff

77.0 1514 69.0 8763.4)(

86.4)(8763.4)(

Expt.(%)(%)718.0

20.058.0719.010.073.0728.0)(

726.0)(10.073.0721.0)(

Expt.2sinState Final

LSS

SSS

KL

CPS

KS

f

LSS

SSS

KL

CPS

KS

KKKKKK

KKKKKK

KKKA

KKKKKK

KKKKKK

KKK

L

S

L

S

sin2=0.6800.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)

38

b→sqq tCPV measurements

2-body: HYC,Chua,Soni;Beneke

3-body: CCS

Naïve b→s penguin average: 0.68±0.04, 0.56±0.05 (if f0K0 excluded), 0.0.12.2, 2.6 deviation from b→ccs average

Sf= ± sin2efffrom b→ccs

39

A closer look on S signs and sizes

)(2

1 dduu

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

small

large

small (’Ks)large (Ks)

small

large

Beneke, 05

0 ][

][][~)]([

][)]([~)'(

0 ][

][][~)]([

][)]([~)(

0 ][

][][~][

][][~)(

0 ][

][][~][

][][~)(

0 ][][~

)]([)]([

~)(

0] Re[ ,Re]cos[||

64

264)(

64

2640

46

2460

46

246

64

64

2

2

SPCP

araaara

KAA

SPCP

araaara

KAA

SPCP

aaraaar

KAA

SPCP

aaraaar

KAA

SPP

araara

KAA

AArS

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

)(3

1~ ),2(6

1~' ssdduussdduu

B→V

40

A closer look on S signs (in QCDF)

M1M2: (B→M1)(0→M2)

,Re

c

u

AAS

41

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,

HAiHA

BHA em

ydyX

b

d

sq

q

42

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

43

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)

44

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.

_

_

_

_

45

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

_

46

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

47

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

Tree

Penguin

48

Factorized into transition and creation parts

Tree

Penguin