Interpreting CP asymmetries in Lydia ROOSLydia ROOSLPNHE LPNHE –– Paris Paris

On behalf of the CKMfitter group

Durham CKM Workshop

April 7, 2003

Interpreting CP Asymmetries in Interpreting CP Asymmetries in BB00 ++--

DecaysDecays

B CP asymmetries

2

2 2

2

0

12Im , C

1 1

/ /

/ /

( )

ic ui

ic u

iu cB

S

e R Re

e R

P T

P TR

A R e RT T

2

2 2

2

0

12Im , C

1 1

/ /

/ /

( )

ic ui

ic u

iu cB

S

e R Re

e R

P T

P TR

A R e RT T

Tree diagram:Tree diagram:

ubV d

Penguin diagram:Penguin diagram:

tdV

d

need |P/T| and =arg(P/T) 0,0 0,1

Rt /Rc

η,ρ

ρ

η

Ru /Rc

0 0

0 0

ππ ππ

( ) ( )( )

( ) ( )

sin( ) cos(C )S d d

B Bt

B B

t tm m

A

Theoretical frameworks1. strong isospin symmetry SU(2)

(GL)

• CP-averaged Br(B) only (00 not seen yet)

• EW penguins neglected

2. 1 + SU(3) flavour symmetry

(BF,Ch)

• OZI-suppressed annihilation

penguins neglected

• No correction of SU(3) breaking

3. 1 + |P| from K0- (GR,BBNS)

• Rth from QCD factorisation

• Neglect annihilation diagram in

K0-

remains unconstrained

4. QCD factorisation (BBNS) • Use the prediction of both |P/T|

and • Non-factorisable 1/mb

contributions fixed to default value

00 0

0 0

/ 2 ,

and

A A A

A A A A

use Br(B0K+-) and |P| = |PK|

|P|R1

ff|P| 0

0

K

thK

GL: Gronau, London, Phys.Rev.LettD65:3381,1990 BF: Buras,Fleisher, Phys.Lett.B360:138,1995 Ch: Charles, Phys.Rev.D59:054007,1999

GR: Gronau, Rosner, Phys.Rev.D65:013004,2002BBNS: Beneke et al., Nucl.Phys.B606:245-321,2001

Experimental inputs

ICHEP’02 Branching fractions (x10-6)WA = BaBar + Belle + CLEO

Global CKM fit using standardconstraints

(referred as standard CKM fit in this talk)BaBar Belle

S+ 0.02

0.34– 1.23

0.42

C– 0.30

0.25– 0.77

0.28

-0.10 0.024sign convention changed!

not seen

CKMFitter: Hoecker et al., Eur.Phys.J.C21,225,2001 and http://ckmfitter.in2p3.fr

ICHEP02 Aspen03

32 CL range: .12-.31 .29-.40

BABAR BABAR Belle Belle

Constraints in the () plane from isospin analysis

BABAR BABAR

2 2 eff

Belle Belle

00 0

2

1 2 /cos(2 2 )

1eff

B B

C

Grossman-Quinn 98; Charles 99; Gronau-London-Sinha-Sinha 01

no significant constraints

2

2

1 2 /cos(2 2 )

1K

eff

B B

C

Constraints in the () plane: SU(3)

BABAR BABAR Belle Belle

Charles 99

no significant constraints

Constraints in the () plane: |P+–| from K0-

BABAR BABAR Belle Belle

BABAR BABAR Belle Belle

Constraints in the () plane:QCD Factorisation

Negative C and small positive negative

BABAR BABAR Belle Belle

What about ?

BABAR BABAR Belle Belle

At present, significant theoretical input needed to extract

QCD Factorisation:uncertainty from hard spectator interaction

and annihilation diagramBABAR BABAR Belle Belle

no zoom

Non-factorisable power-suppressed contribution parameters free

Constraints/predictions on |P/T| and (C,S ) and ( ,)from standard CKM fit

• non-factorisable contributions free• theoretical parameters varied within a given range• uncertainty from ( ,)

non-factorisable contributions fixed

Predicting C and S using , from standard CKM fit

Only predictive approach: QCD Factorisation.poor knowledge of sin2 large uncertainty in S

Constraint on Br(B 00)

Inputs = C, Br(B +-), Br(B +0)

Moriond’02 Belle measurements !!

0 0 00 0 0

2

1 1(1 ) (1 )

2 2

1

B B B B By y

B B B B B

y C

Gronau-London-Sinha-Sinha 01

S

C

0.41 0.30 1.21

0.32 0.27 0.94

How about More Statistics?

Isospin analysis for present central values, but 500 fb–1

(BaBar C,,S and WA branching fractions)

and even more...

The only hope for BaBar and Belle is not to observe B0 00

Various strategies to interpret time-dependent asymmetry measurements C, S studied:

– Significant constraints on from QCD Factorisation but still need validation from data

– Qualitative information when constraining the penguin amplitude using Br(B-K0-)

– Mild assumption frameworks based on SU(2) and SU(3) do not lead to significant constraints

If central value of BR(00) stays large, isospin analysis probably cannot be performed by first generation B factories

Conclusion