1#

CKM Unitarity anglesa (f2) and g (f3)

(Recent results from the B factories.)

Hassan JawaheryUniv. of Maryland

Lepton-Photon SymposiumFermi National Accelerator Laboratory

August 12, 2003

Outline• Introduction & definitions• Experimental observables related to a and g• Experimental results, some discussion of

implications for SM & constraints on a and g

2#

||VVcdcb

VtdVub*

**tdtbcdcbVVVV**udubcdcbVVVV

0VVVVVV *tbtd

*cbcd

*ubud

=++

( )

( ) ˜˜˜

¯

ˆ

ÁÁÁ

Ë

Ê

---

--

--

ª

11

2/1

2/1

23

22

32

lhrl

lll

hrlll

AiA

A

iA

VCKM

The Unitarity Test

CPDefinitions

)arg(

)arg(

)arg(

*

*

*

*

*

*

cdcb

cdub

tdtb

cdcb

udub

tdtb

VV

VV

VV

VV

VV

VV

-=

-=

-=

g

b

a

Both involve Vub

f1=b f2=a f3=g

3#

Constraints from the CKM fit |Vub|, |Vcb|, eK, Dmd , Dms

oo

o

o

o

o

8037

12277

5.264.19

<<

<<

<<

g

a

b

At 95% C.L.

ÿ Unitarity Tests : Search for deviation from SM

ÿUsing direct measurements of angles check: a + g + b=p

ÿ Check if B Decays are consistent with the range of angles from theCKM fit?

Indirect infoon angles

A. Hoeoecker et al, Eur. Phys. Jour.

C21 (2001) 225, [hep-ph/0104062]

4#

b uu

sd ,

W

B‡p p: (p+ p-, p+ p0, p0 p0 )

B‡rp, B‡ r r, a1p,….

Tree diagrams are not alone:

b uu

sd ,

W

B‡Kp: (K+ p- , K0 p+ , K0 p0 , ..) CKM suppressed

Penguins (gluonic & E.W) can alsolead to the same decays:

W

t

b sd ,

u

u

g

Main source of info on a and g: Decays involving b‡u transitions

Data indicate gluonic penguins arelarge & complicate extraction of a

I- Charmless B Decays

Interference of T & P results in Direct CPviolation & sensitivity to g

d

s

5#

b uW

sc

+

-- >- KDB 0

-- >- KDB 0

B- ‡ DCPK-

II- Decays involving interference of b‡u W- & b‡c W- Processes

(Penguin Free)

bW

s

cu

Involves arg(Vub)=g

B‡DK:

g dependence of rate anddirect asymmetry

B0‡D- p+:

c0B

d

b ud

*D-

p+

()

d

bc

d

p+0Bu

*D-()

0B

d

+

Direct CP asymmetrysensitive to sin(2b+g) arg(Vub)=g

Same finalstate via B0

mixing & b‡u

6#

Experimental Observables

With Tree and Penguins both in action:

ãä |T

P|cpA

|T

P|ãä |

T

P|Br

)iä|P|eiã(|T|eA)iä|P|eiã(|T|eA

sinsin2

2coscos21

-=

++µ

+--=+-=

To constrain g requires estimates of:

| Ppp/Tpp| & relative strong phase d

ÿBranching fractions for various non-charm B decays

ÿTime Integrated (Direct) CP asymmerties

)fÂÃf)ÂÃ

f)ÂÃ)fÂÃAcp

Æ(+Æ(

Æ(-Æ(=

7#

More observables: Time – Dependent CP Asymmetries

)==== ahl a 2sin(&02**

**

SCeVVVV

VVVV i

udubtdtb

udubtdtb

With Tree alone

2

2

1

1

||

||

l

l

+

-=fC

21

2

||

)Im(

ll

+=fS

ÿ Time evolution of tagged B0 decays, e.g. in the case of B0 Æ p+p-

)]tmcos(C)tmsin(S1[4

e)t(f dfdf

)/t(

DDDD±t

=DtD-

± m

CPV due to mixing and decay interference

Direct CPV in Decay)(

)(

p

q0

0

fBA

fBA

Æ

Æ=l

iãeiäe|T

P|1

iãeiäe|T

P|1

2ieë-+

+= a

With Penguin and TreeS=sin2aeff

Da=aeff –a

C ≠ 0

Belle: Af = - Cf (BaBar)

8#

A few comments on the already established pattern fromcharmless 2-body decays

Connected via Isospin symmetry(Gronau &London) (Isospin engineering)

( ) ( )00 ∂∂∂∂~ ++-- Æ=Æ BABA

( )-+Æ ∂∂~

2

10BA

( )-+Æ ∂∂2

10BA

( )000 ∂∂ÆBA

( )000 ∂∂~

ÆBA∂∂kDa

With Tree alone,expect:

%5ªÆB

Æ

pppKB

4ªÆB

Æ

pppKB

Measurements:

ËPenguins are significant players

P’ & use SU(3)connections to estimate P

(P’ & T’)

(P’)

(P & T)(P & T)

(T)

(P’ & T’)(P’ & T’)

Control rescattering effects

Constructing these triangles is amajor goal of the experiments

9#

Goals and Issues on the Measurement Side

ÿThe reality (Considering the presences of large Penguin effects)

ÿNo single measurement is expected to lead to determination of a & g

ÿNeed info from many decay modes and the emerging pattern & connectionsvia symmetries, [isospin, SU(3) ], and eventually more predictive theories[perhaps QCD factorization or perturbative QCD- when verified ] to constrainvarious components of the problem.

ÿSearch for CP violation: Direct (C≠ 0) & Indirect (S≠0) deviating from(sin2b): [i.e. indirect CPV outside of mixing phase.]

ÿMeasure/Constrain a & g using many different modes and exploit theredundancy to resolve the ambiguities.

Keep finding the pieces of the charmless puzzle a & gThe job description Eventually

10#

Experiments and Data

Belle at KEK-B Machine140 fb-1 on U(4s) (158 fb-1 total)

152x106 B B events

BaBar at SLAC PEP-II Machine113 fb-1 on U(4s) ( 126 fb-1 total)

124x106 B B events

CLEO at the CESR Machine – Some results on Br & direct Asymmetries.

The pioneer of the field and the first source of information on B decays,

Including observation of charmless decays. [~13 fb-1 on peak]

Asymmetric e+e- B Factories:Physics coverage : Bd & Bu Decays

The B physics reach of hadronmachines & current status coveredby Kevin Pitts . Next Talk

The focus of this talk

11#

Analysis Issues for Rare B Charmless decays

-Looking for modes with Br~10-6 to 10-5

-Continuum qq(bar) background at 103 larger than the signal BKG Suppression using event shape & topology, kinematics, particle ID,..

Kinematic variables:

DE=Ebeam-EB

provides separationof KK, Kp, pp decays

22Bbeam pEMes -=

Signal Monte Carlo

p+p-

Other info into analysis:

ÿ Dt=Dz/<cgb>

ÿFlavor tag of other side

ÿParticle ID, event shape,..

12#

The road to a: Measurement of CPV in B‡p+ p-

p+p-

Kp

BaBar: 81 fb-1 Belle 78 fb-1

p+p- Kp

Isolation of Signals

~200 B‡p+ p-

Per experiment

Kp

p+p-

13#

Time Dependent CPV in B‡p+ p-

(BaBar)

Asy

mm

etry

E

vent

s/1p

s

(Belle)

5-5 0

5-5 0

B0 tag

B0 tag

Fits to: )]tmcos(C)tmsin(S1[4

e)t(f dfdf

)/t(

DDDD±t

=DtD-

± m

81 fb-1 78 fb-1

04.025.030.0

05.034.002.0

±±-=

±±=

pp

pp

C

S

)(08.027.077.0

41.023.1 08.007.0

pppp

pp

AC

S

-±±-=

±-= +-

Dt(ps) Dt(ps)

14#

New Results:BaBar Update of CPV measurementswith full data sample (Run 1+2+3): 113 fb-1 on Peak data

013.0041.0107.0

05.019.019.0

03.022.040.0

±±-=

±±-=

±±-=

p

pp

pp

KA

C

S

4.105.12

5.373.873

0.249.265

±=

±=

±=

KK

K

N

N

N

p

pp

ÿReprocessed Run1+2 (82 fb-1 )

ÿAdded Run 3 ((31 fb-1 )

New CPV Results

Run1+2(reprocessed)

S=-0.252±0.27 C=-0.166 ±0.22

Run 3

S=-0.67±0.35 C=-0.33 ±0.34

B0 tag

B0 tag

15#

Summary of CPV in B‡p+ p-:

Current world average (with BaBar new results)

S=-0.58±0.20 C=-0.38 ±0.16

Too early to claim observation of CPV in B‡p+ p- :Direct (in decay) or Indirect(mixing & decay)

Belle’s update with their full data set awaited

S & C not enough to measure a:

Need Da=aeff – a, which requires the otherpieces of the isospin analysis.

)eff

á2sin(2C1S&0C -=≠

Ignoring thelarge c2 ~6.3(~2 s)

16#

BaBar: The decay B‡p0 p0

21431346)( ++

--00 =ppN 60 103.06.01.2)( -00 ¥±±=Æ ppBB

Significance: 4.2 s

ÿUsed their full data set (113 fb-1 )

ÿ Measured Br(B‡r+p0) [Br(B‡r+p0 ) =(11±2.7)x10-6 ]

Control over a major background source. Br about half of previous assumed value

r+p0

qq bkgd

Fischer Discriminant

signal

ËObservation

17#

Belle: The decay B‡p0 p0

3.94.86.25)( +

-00 =ppN

Analyzed full data set of 140 fb-1

From a fit to 2-dimensionaldistribution of Mes and DE

Find:

Significance:3.4 s

60 103.06.07.1)( -00 ¥±±=Æ ppBB

ËEvidence

18#

Branching ratios (x10-6)

1.97 ±0.472.1 ±0.6 ±0.31.7±0.6 ±0.3<4.4p0p0

5.2 0.85.5 0.65.3 1.3 0.54.6p+ p0

4.6 0.44.7 0.6 0.24.4 0.6 0.34.5p+ p-

AverageBaBarBelle CLEOMode

± ± ± ±±

± ± ± ±

4121

.

.± 5040

.

.±

8161

.

.± 7060

.

.± 0190

..±

What about Da: All but one piece is in place

For a full Isospin analysis need: Cp0p0 (direct CPV)

&

Still some constraint can be set using the measuredaverage Branching fraction:

)B(B 000 ppÆ)BB( 000 ppÆ

(Quinn- Grossman),

With WA Br(B‡ p0 p0 )

|a-aeff |<48o at 90% c.l.

Not much improvement on QG bound

( ) ( )00 ∂∂∂∂~ ++-- Æ=Æ BABA

( )-+Æ ∂∂~

2

10BA

( )-+Æ ∂∂2

10BA

( )000 ∂∂ÆBA

( )000 ∂∂~

ÆBA∂∂kDa

Not a very useful limit & don’t expectmore than ~10o improvement in future.

)Æ

)Æ£D

±± 0

0002

(

(sin

pppp

aBB

BB

19#

Summary of measurements of B‡pp & Kp Decays

See John Fry’s talk this morning for more detail &comparison with Theory

Thanks to Heavy flavor averaging group(HFAG):Rare decays: J. Smith (colorado), J.Alexander(Cornell), P.Chang (KEK)

03.009.0

)(02.016.004.0

)(012.0041.0107.0

)(014.0035.0086.0

±-=

±±-=

±±-=

±±-=

Average

CLEO

BaBar

BelleAKp

Evidence Direct CPV ?

20#

What did we learn about a & g?

Is this all consistent with

Standard Model?

Does it accommodate the range of UTangles from the global CKM fit?

21#

Cpp vs Spp :

Allowed range & comparison with SM ( CKM fit)

Data consistent with SM (CKM fit)

Gronau and Rosner approach

(PRD 093012)|Ppp / Tpp | estimated usingB->K0p+ & B‡pln , B‡ p0p+

(with use of SU(3) & factorization)

Here calculate S & C for |P/T|~0.3Unconstrained strong phase d

iãeiäe|TP

|1

iãeiäe|TP

|12ieë

-+

+= a

21

2

||

)Im(

ll

+=fS

2

2

1

1

||

||

l

l

+

-=fC

BaBar

Physical boundary

Belle

BaBar

My Average

22#

A more optimal use of information using the CKMfitter tools with variousassumptions (LAL 02-103: Authors Hoecker, Lacker, Pivak, Roos).

In all scenarios data canaccommodate the range of afrom the SM CKM fit

SU(3) & some use of QCDFactorization to estimate SU(3)breaking effects

23#

Useful ratios of branching fractions and ps-asymmetries with sensitivity to g:

˙˚

˘ÍÎ

È

Æ+Æ

ƱÆ=

˛˝¸

ÓÌÏ +--+

)()(

)()(000000

00

0 2

1

pppp

KBBrKBBr

KBBrKBBr

A

Rnn

˙˚

˘ÍÎ

È

Æ+Æ

ƱÆ=

˛˝¸

ÓÌÏ

--++

--++

)()(

)()(

pp

pp00

00

0

2KBBrKBBr

KBBrKBBr

A

Rcc

gd

gdg

sinsin2

)cos21(cos)(cos21

,,,

0

2,

2,,,

ncncnc

ncncncnc

rA

rqqqrR

=

+-+--=

000

00

0 B

B

t

t

KBBrKBBr

KBBrKBBr

A

R +--++

+--+

˙˚

˘ÍÎ

È

Æ+Æ

ƱÆ=

˛˝¸

ÓÌÏ

)()(

)()(

pppp

Constraints on g: Connecting the B‡Kp data via symmetries

Ratios using HFAG averages:

R0=0.99±0.09 A0= - 0.09 ±0.03

Rc=1.30±0.15 Ac=0.0 ± 0.06

Rn=0.8 ±0.11 An=-0.07 ± 0.03

Rosner, Gronau,Neubert, Fleischer,Mannel, ..

All shown to accommodaterange of g from CKM fit

(Fleischer), (Gronau, Rosner),…

Size of EW penguins|T/P|

24#

1 s range of R0

60 < g <120 at 1 s level

No useful limit at 2 s level

Consistent with CKMrange: oo 8037 <<g

g

R0

A0=-0.06(A0+1s)

A0=-0.12(A0-1s)

Gronau & Rosnermethod hep/ph-0307095

(R0 vs g) for fixed A0

R0

25#

Other channels of reaching a:

B‡ (ppp): CPV studies require isolation of states with specificCP parity: e.g. B‡ (r+p- + r-p+) using Dalitz plot analysis.

Interference between (r+p- + r-p+) can be used to determine a even in thepresence of penguins [Quinn-Snyder]

ÿBaBar has presented CPV results based on quasi 2-bodydecays B0‡”r+ “p-, B0‡”r-”p+ -- updated for thisconference with their full data sample.

ÿ1st Belle results on CPV with these modes expected soon.

ÿComponents of the Isospin analysis (pentagon) are alsobeing measured. (J. Fry’s talk today)

B‡(pppp): e.g. B‡rr has been measured and shown to bedominated by the CP even component – good news for CPVstudies.

26#

CPV Studies with the decay B0‡rp

Not a CP eigenstate & involves more observables:

Summing over the r charge:

Direct CP violation: Crp

Indirect CP (mixing and decay): Srp

Charge Asymmetry:

[ ][ ])cos()()sin()(1())(1()(

)cos()()sin()(1())(1()(

/||

/||

0

0

tmCCtmSSehAtf

tmCCtmSSehAtf

hhhht

CPh

B

hhhht

CPh

B

DDD±-DDD±-±=D

DDD±-DDD±+±=D

D-

D-

±

±

rrrrtr

rrrrtr

r

rm

m

)()(

)()(+--+

+--+

+

-=

hNhN

hNhNA h

CP rrrrr

Dilution (Non CP parameters): DCrp & DSrp

)cos()sin()/( tmCtmSBBA DD-DDª rprprp

00

27#

BaBar results on CPV in B‡rp: 113 fb-1

804.2 ±49.2

N(rp)260.4 ±31.4

N(rK)0.18 ± 0.12 ± 0.08

-0.11±0.06 ±0.03

0.33 ±0.18 ±0.03

-0.13±0.18 ±0.04

0.20 ±0.13 ±0.05

0.35 ±0.13

±0.05

ACP(rK)ACP(rp)DSSDCC

rK

rp

rKrp

)cos()sin()/( tmCtmSBBA DD-DDª rprprp

00

28#

2.5 s (2.7s if stat. only)

99%

90%

98.6%

Define two asymmetries:

CAC

CACABNBNA

CAC

CACABNBNA

CP

CPCP

CP

CPCP

⋅+D+

D⋅++=

S

Æ-Æ=

⋅-D-

D⋅--=

S

Æ-Æ=

-++-

-+

+--+

+-

rp

rprp

rp

rprp

prpr

prpr

1

)()(

1

)()(

00

00

05.018.0 ,07.052.013.0

13.0

19.0

17.0 ±-=±-=-

+-+-

++- AA

New Results

04.011.0 ,06.062.017.0

16.0

28.0

24.0 ±-=±-=-

+-+-

++- AA

PRL

2.3s (Stat. only)

Test Of Direct CPV

29#

Quinn-Grossman bound applied to the longitudenalpolarization component of the rates:

oeff

LLeff lcBfBf

19||

...%90@10.0)/()(sin 2

<-

<¥¥(£)- 0+0+0000

aa

aa rrrrrrrr

The Channel to watch in Future

The components of B‡rr areidentifeid: B0‡r+r- (BaBar),B+‡r+r0 (Belle & BaBar)

Decays nealy 100% longitudinallypolarized [CP-even]

Limit has been set on B0‡r0r0.

See John Fry’s talk this morning for more detail

>2 times more restrictive than B‡pp system

A promising channel:the B‡rr system

30#

Reaching g

via

(b‡u(cs) & b‡c(us) interference:

B‡DK DecaysMethod and observables suggested by Gronau,Wyler,Atwood,Dunietz, Soni,Quinn, Sanda

31#

B‡DK Modes- No penguins

b uW

sc

)( *uscbVV

gd ii eeAKDBA 2||)( 10 =>- --

bW

s

cu

12

0 dieAKDBA ||)( =>- --

)( *uscbVV

In B- ‡ DCPK- , the diagrams interfere & provide the sensitivity to g :

[DCP=(1/÷2)(D0± D0 ) ] -+-+= KKD evenCP ,pp ,.., fp ssoddCP KKD 0=

)()(

)()(

+Æ+Æ

+Æ+Æ=

+-+

+--

KDBBKDBB

KDBBKDBBR cpcp

cp 00

00

)()(

)()(

+Æ+Æ

+Æ-Æ=

-

-

KDBBKDBB

KDBBKDBBA

cpcp

cpcpcp 00

00

gd coscos DKDKDK rr 21 2 ±+=

gd

gd

coscos

sinsin

DKDKDK

DKDK

rr

r

21

22 ±+

±=

rDK (~0.1 –0.2)& dDK

Also unknown

Experimenters are very active in constructing the DK puzzle

Observables

DK triangle

32#

cosqhel

fromP→PVMK*-

D0 _ Kp, Kppp,Kpp 0D0 _ Kp, Kppp,Kpp 0

B-_DCP K*-

13.1±4.34.3s

D1=K+K-, p+p-D1=K+K-, p+p-

D2=Ksp0, Ksf, Ksw

D2=Ksp0, Ksf, Ksw

7.2±3.62.4s

B- _ D*0 K*-

B _ D*0 K*-

ALLD*0 _ D0p 0 D*0 _ D0g

B0 _ D K0

33#

Average

-0.19 ±0.17 ±0.051.41 ±0.27 ±0.150.06 ±0.19 ±0.041.21 ±0.25 ±0.14Belle

0.17 ±0.23 ±0.081.06 ±0.26 ±0.17BaBar

A2 (CP=-1)R2(CP=-1)A1 (CP=+1)R1(CP=+1)B‡DoK-

Average

6.1 ±1.6 ±1.7CLEO

0.19 ±0.50 ±0.04-0.06 ±0.33 ±0.075.2 ±0.5 ±0.6Belle

6.3 ±0.7 ±0.4BaBar

A2 (CP=-1)R2(CP=-1)A1 (CP=+1)R1(CP=+1)Br(x10-4)B‡DoK*-

=Æ -- )KDB(**0B

(8.3 ± 1.1(stat) ± 1.0(sys)) x 10-4 & GL/G=0.86 ±0.06 ±0.03 (BaBar)

(7.7 ± 2.2(stat) ± 2.6(sys)) x 10-4 CLEO

3.4 ±1.3 ±0.65.0 ±1.3 ±0.6B0‡DoK0

3.0 ±1.3 ±0.64.8 ±1.1 ±0.5B0‡DoK*0

Br(x10-5)

Average

Br(x10-5)

BaBar

Br(x10-5)

Belle

Mode

B0‡D*oK*0

B0‡DoK*0

B0‡D*oK*0

B0‡D*oK0

<4.0 (90% c.l.)

<1.8 (90% c.l.)

<6.9 (90% c.l.)

<6.6 (90% c.l.)

The B‡DKpuzzle underconstruction

Vub

Vub

34#

What about g: Current errors are still toolarge to allow for simultaneous extraction of g &ratio of (b‡c) and (b‡u) amplitudes (rdk) andthe strong phase. Need many fold more data.(dg~20 may be possible with 500 fb-1)

With assumptions on (rdk): mild limits can beextracted. e.g M. Gronau (hep-ph/0306308): g>72o at1 sigma level.

35#

Reaching sin(2b+g)

via

(b‡u(cd) & b‡c(ud) interference

(& B0 mixing)

B0‡D(*+) p-

Method and observables first suggested by Sachs,Dunietz

36#

B0‡D(*+)p- Modes

c0B

d

b ud

*D-

p+

()

Dominant diagramb ‡ c transition

d

bc

d

p+0Bu

*D-()Suppressed diagramb ‡ u transition

0B

b

d

*||)( udcbi VVeADBA 2

10 dp µÆ -+ gdp i

ubcdi eVVeADBA ||||)( *

20 2µÆ -+

)}sin()cos(1{),(

)}sin()cos(1{),(|0

|0

tmStmCNetDBP

tmStmCNetDBP

ddt

ddt

DD-DD=DÆ

DD+DD±=DÆD|G-±

D|G-±

mm

mm

mp

p

Time evolution:

)±++

=± dgb2sin(1

22r

rS

22111rCr-=+ª

02.0)(

)(0

0

ªÆ

Æ=

+-

+-

pp

DBA

DBAr Small asymmetry expected

37#

BaBar

II - Fully reconstructed

B0‡D(*+)p- Decays

Lepton tags kaons tags

()()0000tagtagtagtagBBCPBBNNNN-=+A

Belle Fully reconstructed B0‡D(*+)p- Decays

)±±±=-+

)±±±=++

)±±±=-+

)±±±=++

ndgb

ndgb

ndgb

ndgb

pp

pp

pp

pp

lDr

lDr

lDr

lDr

DD

DD

DD

DD

*(036.0013.0056.0022.0)2sin(2

*(036.0013.0059.0094.0)2sin(2

*(036.0016.0056.0033.0)2sin(2

*(036.0016.0059.0092.0)2sin(2

**

**

**

I- Partially reconstructed B0‡D*+p- Decays: (number of events)

035.0068.0025.0sin)2cos(2

021.0038.0022.0cos)2sin(2

035.0070.0031.0sin)2cos(2

021.0038.0068.0cos)2sin(2

**

**

±±-=+

±±-=+

±±-=+

±±-=+

pp

pp

pp

pp

dgb

dgb

dgb

dgb

DD

DD

DD

DD

r

r

r

r

017.0025.0064.0cos)2sin(2 ** ±±-=+ pp dgb DDr

2b+g

38#

(*)(*)0(*)(*)0(*)()()SscdDcsDfBrBDVrBrBDVfpp+--+ƪÆ

Use measurements of B0‡D(*+)sp+ to

estimate r(*) (Factorization & SU3correction )

0.004*0.0050.0050.007()0.021()0.017rDrDpp++--==

sin(2)0.89 @ 68.3% C.L.sin(2)0.76 @ 90% C.L.bgbg+>+>

Interpretation:BaBar’s attempt

Favors the CKMfavored solutionto sin2b

39#

Summary & Conclusionsÿ Major progress made in probing the charmless sector of B decays for

information on unitarity angles a & g:ÿ New updated measurements of CPV in B‡ p+p- still show no

significant evidence for CP violation in this mode.ÿ Observation of B‡p0 p0 – a missing component of Tree/Penguin disentanglement plan.ÿ CPV studies in B‡rp shows hints of direct CP violation.ÿ The decay B‡rr is now measured and looks promising for CPV

studies and constraining a. Indications that penguins are smaller.ÿ Indication of direct CPV in B‡K-p+ (WA: Belle, BaBar, CLEO) No indication for large direct CP yet.ÿ The emerging constraints on the angles from the pattern of data are

consistent with the favored range from the CKM picture in theStandard Model.

ÿ Penguin free modes (B‡DK & D*p) are beginning to contribute toconstraints on CKM parameters & many new B‡DK modes identified.

ÿ Much more data & major progress in theoretical understanding ofhadronic B decays needed to complete the picture and conclusivelyperform the CKM unitarity test.