Sandrine LAPLACESandrine LAPLACELAL - OrsayLAL - Orsay

Seminar at theCentro de Física das Interacções Fundamentais

Lisbon, Portugal

November 26, 2002

Reference for updated plots: http://ckmfitter.in2p3.fr

Implications of the Most Recent Results Implications of the Most Recent Results on CP Violation and Rare Decay Searcheson CP Violation and Rare Decay Searches

in the B and K Meson Systemsin the B and K Meson Systems

CKM Quark Flavor MixingCKM Quark Flavor Mixing

, , i

i i iLL R Ri

L

uQ u d

d

Quarks: Masses ?

Scalar Higgs field

1

2

Yukawa couplingHiggs-quarks

01

2 v

, M2 2

u uij iji j u

Y L R ij

Y v Y vL Q u

Interaction quarks-W

(charged currents):

†u u u udiagM V M V

†u dCKMV V V

from flavour tomass eigenstates

33 unitary matrix

† = 2 2

i j i u d jcc L L L i j L

g gL u d W u V V d W

From the Higgs to the CKM Matrix

SpontaneousSymmetry breaking

2 3

2 2

3 2

1 / 2

1 / 2

1 1CKM

A i

V A

A i A

Wolfenstein Parameterization (expansion in ~ 0.2):

CKM

ud us ub

cd cs cb

td ts tb

V V V

V V V V

V V V

CPV phase

VCKM unitary and complex

4 real parameters . (3 angles and 1 phase)

2 6J A

* *Im 0ij k i kjJ V V V V * *Im 0ij k i kjJ V V V V

0 no CPV in SM

(phase invariant!)

Jarlskog 1985

Kobayashi, Maskawa 1973

“Explicit” CPV in SM, if: 3 ( )( )( ) / 0t c t u c u tF m m m m m m m 3' ( )( )( ) / 0b s b d s d bF m m m m m m m

non-degeneratemasses

Link between flavour and CP violation

The Cabibbo-Kobayashi-Maskawa Matrix

ubV

B sector: K sector:

3 3 3

0ud ub cd cb td tbV V V V V V

A A A

Expect large CP-violating

effects in B-System

2 5

0

ud us cd cs td tsV V V V V V

A

0,0 0,1

η,ρ

ρ

η

Tree processes

Loop processes (mixing, ...)

New Physics?

tdV

The Unitarity Triangle

J/2

B dγ

2(1 / 2)

Wolfenstein-Parameters:

= |Vus| 0.2200 0.0025

A = |Vcb| / 2 0.83 0.05

(,) not well known

“,”-plane

Can we describe all observables with one unique set of , A, , ?

2(1 / 2)

Many Ways Lead to the Unitarity Triangle

Experimental and Experimental and Theoretical Input to the Theoretical Input to the Standard CKM AnalysisStandard CKM Analysis

Experimental and Experimental and Theoretical Input to the Theoretical Input to the Standard CKM AnalysisStandard CKM Analysis

ObservablesCKM

ParametersExperimental

SourcesTheoretical

UncertaintiesQuality

|Vud|

|Vus|

nuclear decay

K+(0) +(0) e small

K (1–)–1 K0 +–, 00 BK, cc

‘/K K0 +–, 00 B6, B8 ?

Im2[V*ts Vtd ...] (2A)4 2 K0L 0 small (but: (2A)4 ) ()

|Vtd| (2A)4

((1–)2 + 2)K+ + charm loop (and: (2A)4) ()

The CKM Matrix: Impact of non-B physics

Studying CP Violation in the B System

Studying CP Violation in the B System

ATLAS

CLEO 3BELLE

?

1999 1999

2008

2001

A Worldwide Effort:

BTEV

The CKM Matrix: Impact of B Physics

ObservablesCKM

Parameters() Experimental SourcesTheoretical

UncertaintiesQuality

md (|Vtd|) (1–)2 + 2 BdBd f +f – + X, XRECOfBdBd

ms (|Vts|) A Bs f + + X = fBsBs/fBd

Bd

sin2 , Bd cc sd, ss sd small

sin2 , Bd +(+) – Strong phases, penguins

?

, B DK small

b u, Direct CPVStrong phases,

penguins?

|Vcb| A b cl (excl. / incl.) FD*(1) / OPE

|Vub| 2 + 2 b ul (excl. / incl.) Model / OPE

|Vtd| (1–)2 + 2 Bd Model (QCD FA) ?

|Vts| NPBd Xs (K()) ,

K() l+l– (FCNC)Model ?

|Vub|, fBd 2 + 2 B+ + fBd

() Observables may also depend on and A - not always explicitly noted

Linac

Fixed TargetExperiments

BABAR

SLD (& MARK II)

e–

e+

The Asymmetric B-Factory PEP-II:

(4 )e e S BB

9 GeV e on 3.1 GeV e+ :

coherent neutral B pair production and decay (p-wave)

boost of (4S) in lab frame : = 0.56

B0B0 Mixing: Principle

0 0

20 0i

B Bdi Mdt B B

00

00

L

H

B p B q B

B p B q B

Schrödinger equation governs time evolution of B0-B0 System:

with mass eigenstates:

Defining: 12

*12 12 12

2 | |

2Re / | |

B H L

B H L

m M M M

M M

mixing

(unmixed) (mixed)( ) cos

(unmixed) (mixed) B

N NA t m t

N N

One obtains for the time-dependent asymmetry:One obtains for the time-dependent asymmetry:

0 0

0 0

unmixed : ( ) ( )

mixed : ( ) ( )

e e B t B t

e e B t B t

where: and: mixing( 0) 1A t

B0B0 Mixing (Theory)

FCNC Processes:

whose oscillation frequencies md/s are computed by:

222 2 1

2 ( ) 0.5 ps (for )6 q q

Fq B W B t B q tq tb

Gm m m S x f B V V q d

Perturbative QCD

Non perturbative QCD (lattice)

CKM Matrix Elements

Important theoretical uncertainties:

d/s

B0 B0–

d/s

b– –

W Wt

t

–

b

[B=2] –

: ,with q s d

/

2rel /

2 2 2rel

36%

/ 10%

d s

s d

B d s

B s B d

f B

f B f B

Improved error from ms measurement:

B0B0 Mixing (Experiment)

z

0tagB

ee

K

0recB

B-Flavor Tagging: Btag

Exclusive B Recon-struction:

Brec

0SK

/J

0 0rec flavB B (flavor eigenstates) mixing analyses0 0rec CPB B (CP eigenstates) CP analysis

(4S)

t z/

c z 250m

Experimental Technique:Experimental Technique:

B0B0 Mixing using Flavour Eigenstates

1(stat) (syst)(0 516 0 016 0 010 )ps

dBΔm . . . 1(stat) (syst)(0 516 0 016 0 010 )ps

dBΔm . . . BABAR PRD 66 (2002) 032003

mixing

(unmixed) (mixed)( ') 1 2 cos( ) Res( , ')

(unmixed) (mixed) dB

N NA t ω Δm Δt Δt Δt

N N

|t| (ps)

Asy

mm

etry BABAR

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12

1 2

BABARUnmixed Events

Ev

en

ts/ 0

.4 p

s

t (ps)

Mixed Events0

100

200

300

400

0

100

200

300

400

-10 -5 0 5 10

/ dm

BBAABBARARBBAABBARAR

BBAABBARARBBAABBARAR

Mistag probability Detector Resolution

(simplified picture)

Bs0Bs

0 Mixing

ms not yet resolved

Amplitude spectrum: LEP/SLD/CDF

cos( )sP A m t

Prob. of mixing: 0 0s sB B

A=0 for ms(meas)< ms(true)A=1 for ms(meas)= ms(true)

Waiting for a ms

measurement at Tevatron...

2

tdV

Theoretical uncertainty

SM fit

Experimental error

> 5% CL

SM fit

Improvement from ms limit

> 5% CL

Constraints from md and ms

CPV if or CPV if or

2ie

2~ ie

Time-dependent CP Observables:

0 0

0 0

( ( ) ) ( ( ) )( )

( ( ) ) ( ( ) )

sin( ) cos( )

CP

CP CP

CP CPf

CP CP

f d f d

B t f B t fA t

B t f B t f

S m t C m t

0B

0B

CPfCPm

ixing

decay

CPfA

CPfA

CP

CP CP

CP

ff f

f

Aqp A

CP eigenvalue

amplitude ratio

2

2

1 | |

1 | |CP

CP

CP

ff

f

C

2

2 Im

1 | |CP

CP

CP

ff

f

S

1CP Im 0CP

1q

p 1CP

CP

f

f

A

ACPV in

mixingCPV in decay

CPV in interference between Decay with and without mixing

Time-dependent CP Asymmetry

The Golden Channel:

Single weak phase:

• clean extraction of CP phase

• no CPV in decay:

0 0, ,/ /( ) sin(2 ) sin( )

dS L S LBJ K J K

A t m t

0

,/1

S LJ K

* * *

* * *

2iβe

tb td cb cs cd cs

tb td cb cs cd cs

V V V V V Vq A

p A V V V V V V

*cbV

csVb

d

c

d

c

s

0 0,, / S LB B J K

b

cs

d d

ct,c,ug

Tree DiagramPenguin

* *u t c tus ub cs cbA V V P P V V T P P

4 2(negligible)

CP = –1

BABAR hep-ex/0207042

BBAABBARAR81.3 fb-1

BBAABBARAR81.3 fb-1

(stat) (syst)sin2 0 741 0 067 0 033β . . .

Time-dependent CP Asymmetry: sin2

sin2

WorldAverage

BABARBABARBABARBABAR

*,

1( ) ( ) ,S

b c

F Om

HQET

b,c = static color source: light degrees of freedom

insensitive to spin and flavor of the heavy quark

Heavy Quark Effective Theory

Heavy-quark symmetry

|Vcb| |Vub|

1/QCD

b

mb–1

Fermi motion

22d ( )

( )d

cb

B DF V

BelleBelleBelleBelle

* *B D Dv v where

Isgur-Wise function

In particular:* (1) 0.91 0.04F 1)1( (lattice)

3

35.6 1.7 (LEP)

(1) 10 42.2 2.2 (CLEO)

36.2 2.3 (Belle)cbF V

Extrapolation to =1of the d/d spectrum:

u is light: heavy-quark symmetry does not hold

+0.21 3 0.29

+0.40 3 0.59

| | 3.25 0.14 0.55 10 (CLEO)

| | 3.69 0.23 0.27 10 (BABAR)

ub

ub

V

V

Form factor from quenched lattice

Need unquenching to become model independant !

|Vcb| and |Vub| exclusive

BABARBABARBABARBABAR

2 mn2 5( ) ( )( )

n m3n m

C D192

F c u b b c ub c u QCDS

b b

G V m mf

m m

/ 0.1 1QCD bm ( ) / 1S bm HQE Heavy Quark

ExpansionTheoretical tool:

Measurement: semi-leptonic BXc (Xu) l

|Vcb| |Vub|

free quark decay nonperturbative corrections

Coef. 2 = mB* -mB, mc are known

theoretical unknowns

|Vcb|.103 = 40.81.0exp 2.5th Belle

= 40.71.0exp 2.2th LEP

CLEO: combined analysis to measure =(mB-mb) and 1

|Vcb|.103 = 40.40.9exp 1.3th CLEO

using mX spectrum moments and b s photon spectrum

( )~ 100

( )c

u

B XB X

Need to cut bc bkg

HQE breaks down

BABAR: spectral moments analysis

discrepancies with b s ?

|Vub|.103 = 4.080.34exp 0.53th CLEO

|Vub|.103 = 4.090.38exp 0.54th LEP

cut on El + b s :

sensitivity to whole phase space (?):

1 2

( ), , ,c

n mb

mC D f

m

|Vcb| and |Vub| inclusive

The Standard CKM AnalysisThe Standard CKM AnalysisThe Standard CKM AnalysisThe Standard CKM Analysis

Standard Inputs

|Vud| 0.97394 0.00089 neutron & nuclear decay|Vus| 0.2200 0.0025 K l|Vcd| 0.224 0.014 dimuon production: N (DIS)|Vcs| 0.969 0.058 W XcX (OPAL)|Vub| (4.09 0.61 0.42) 10–3 LEP inclusive|Vub| (4.08 0.56 0.40) 10–3 CLEO inclusive & moments bs|Vub| (3.25 0.29 0.55) 10–3 CLEO exclusive

product of likelihoods for |Vub|

|Vcb| (40.4 1.3 0.9) 10–3 Excl./Incl.+CLEO Moment Analysis K (2.271 0.017) 10–3 PDG 2000md (0.496 0.007) ps–1 BABAR,Belle,CDF,LEP,SLD (2002)ms Amplitude Spectrum’02 LEP, SLD, CDF (2002)sin2 0.734 0.054 WA, ICHEP 02mt(MS) (166 5) GeV/c2 CDF, D0, PDG 2000fBdBd (230 28 28) MeV Lattice 2000 1.16 0.03 0.05 Lattice 2000BK 0.87 0.06 0.13 Lattice 2000

|Vud| 0.97394 0.00089 neutron & nuclear decay|Vus| 0.2200 0.0025 K l|Vcd| 0.224 0.014 dimuon production: N (DIS)|Vcs| 0.969 0.058 W XcX (OPAL)|Vub| (4.09 0.61 0.42) 10–3 LEP inclusive|Vub| (4.08 0.56 0.40) 10–3 CLEO inclusive & moments bs|Vub| (3.25 0.29 0.55) 10–3 CLEO exclusive

product of likelihoods for |Vub|

|Vcb| (40.4 1.3 0.9) 10–3 Excl./Incl.+CLEO Moment Analysis K (2.271 0.017) 10–3 PDG 2000md (0.496 0.007) ps–1 BABAR,Belle,CDF,LEP,SLD (2002)ms Amplitude Spectrum’02 LEP, SLD, CDF (2002)sin2 0.734 0.054 WA, ICHEP 02mt(MS) (166 5) GeV/c2 CDF, D0, PDG 2000fBdBd (230 28 28) MeV Lattice 2000 1.16 0.03 0.05 Lattice 2000BK 0.87 0.06 0.13 Lattice 2000

Tre

e p

roc

es

s

n

o N

ew

Ph

ys

ics

Sta

nd

ard

CK

M f

it i

n

ha

nd

of

latt

ice

QC

D

+ other parameters with less relevant errors…

status: ICHEP’02

(,) plane

Region of > 5% CL Region of > 5% CL

Standard Constraints

(not including sin2)

Standard Constraints

(not including sin2)

status: ICHEP’02

(,) planeStandard Constraints

(not including sin2)

Standard Constraints

(not including sin2)A TRIUMPH FOR THE STANDARD MODEL AND THE KM PARADIGM !

A TRIUMPH FOR THE STANDARD MODEL AND THE KM PARADIGM !

KM mechanism most probably the dominant source of CPV at EW scale

KM mechanism most probably the dominant source of CPV at EW scale

status: ICHEP’02

sin2

Both decays dominated by single weak phaseBoth decays dominated by single weak phase

BABAR, hep-ex/0207070 0.52

0.50 syst

0syst

0 0.050.06syst

0.19 0.09 0.39 0.40

"sin2 " 0.73 0.64 0.18

' 0.76 0.64

s

s

s

K

K

K

Belle, hep-ex/0207098

b s

u,c, tg,Z,

tb tsV V

Penguin:

s

dd

s

cTree:

b

dd

+WcbV csV

0K

c /J

s0K

New CP Results from complemen-tary modes:

New CP Results from complemen-tary modes:

New Physics ?

status: ICHEP’02

(,) planeStandard Constraints

(including sin2)

Standard Constraints

(including sin2)

sin2 already provides the most precise and robust constraint

sin2 already provides the most precise and robust constraint

Need new and improved

constraints

...

status: ICHEP’02

New Constraints: New Constraints: Charmless Charmless BB Decays Decays

New Constraints: New Constraints: Charmless Charmless BB Decays Decays

[ Constraining ]

| | 1 must fit for direct CPIm () sin(2) need to relate asymmetry to

C = 0, S = sin(2)

2 ( ) 2i iff f

f

Aqe e

p A

C 0, S ~ sin(2eff)

For a single weak phase (tree): For additional phases:

Tree diagram:Tree diagram: Penguin diagram:Penguin diagram:

( ) sin( ) cos( )CP CPCPf df f dA t m t m tS C

C

C

C

CP

PP

P

ff

ff

q A

ApCP eigenvalue 2ie

ratio of amplitudes 2

2

2

1 | |

1 | |

2Im

1 | |

CP

CP

CP

CP

CP

CP

f

f

f

f

ff

C

S

ubV

tdV

dd

CP Violation in B0 + – Decays

Different Strategies:

Determination of P/T by virtue of flavour symmetries (mild theoretical assumptions, eg, PEW=0)

• SU(2): Gronau-London Isospin AnalysisGrossmann-Quinn bound (also Charles, Gronau et al.)

• SU(3): Fleischer-Buras, Charles (P ~ PK) Using theoretical predictions for P/T

• “naive” Factorization (|P/T|2 ~ BR(B+ +0) / BR(B+ +0) )

• |P/T| and phase from QCD Factorization (Beneke et al.) and pQCD (Li et al.)

2

2 2

2

12Im , C

1 1

/ /

ii

i

P TP T

S

ee

e

2

2 2

2

12Im , C

1 1

/ /

ii

i

P TP T

S

ee

e

Predictions for | – eff| from B0 + –

sin(2eff) & Isospin Analysis

Using the BRs : +–, ±0, 00 (limit)

and the CP asymmetries : ACP(±0) , S , C

and the amplitude relations:

00 0

0 0

/ 2 ,

and

A A A

A A A A

BABAR

S+ 0.02

0.34

C– 0.30

0.25

oef 51f

BABAR BABAR BABAR BABAR 2 – 2eff

status: ICHEP’02

Isospin analysis for present central values, but more statistics

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

What about More Statistics?

|P/T| and arg(P/T) predicted by QCD FA (BBNS’01)

BABAR BABAR

sin(2eff) & QCD FA

S

C

0.41 0.30 1.21

0.32 0.27 0.94

Belle: (Moriond’02)

Agreement with SM fit: 1%

S+ 0.02

0.34

C– 0.30

0.25

BABAR: (ICHEP’02)

2~ ie

Time-dependent CP Observables:

0 0

0 0

( ( ) ) ( ( ) )( )

( ( ) ) ( ( ) )

sin( ) cos( )d d

B t B tA t

B t B t

S m t C m t

0B

0B

A

A

q A

p A

A

A

q A

p A

Not a CP eigenstate:

0 0

0 0

( ( ) ) ( ( ) )( )

( ( ) ) ( ( ) )

sin( ) cos( )d d

B t B tA t

B t B t

S m t C m t

S S S C C C

N( ) N( )A

N( ) N( )CP

CPviolation

Asymmetrydue to non-CP

eigenstate

Other ways to : B0

C = 0.45 0.19 0.09 S = 0.16 0.25 0.07

ACP = -0.22 0.08 0.07 ACP

K = 0.19 0.14 0.11

C = 0.38 0.20 0.11 S = 0.15 0.26 0.05

B bkg

B + udsc

Total PDF

ICHEP’02

B0

BABAR

Systematics dominated by B background

CP analysis of B0 and B0K

2

/

/ i i

i

ii

i

ii

ee

e

P T

P T

2

/

/ i i

i

ii

i

ii

ee

e

P T

P T

As for B0, need to know P/T:

sin2Im ieff

Strategies similar to B0:

flavour symmetries• SU(2): full analysis needs B000 (limit), B+0+ (measured), B++0 (not measured) bound using B000

• SU(3): from B0K, K*

Using theoretical predictions for P/T:

not mature yet

Additional strategy: Dalitz plot analysis

B0+- , B0-+ , B000 interfere to give B0+-0

Using interferences provide enough observables to determine P/T

Experimentally very difficult because of backgrounds

Predictions for | – eff| from B0

CKM and New PhysicsCKM and New PhysicsCKM and New PhysicsCKM and New Physics

0 0 412

SL 40 012

( ) ( ) 1 | / |A Im

M 1 | / |( ) ( )

phys phys

phys phys

B t l X B t l X q p

q pB t l X B t l X

( 0.4 5.7 ) x 10-2

( 1.4 4.2 ) x 10-2

(-1.2 2.8 ) x 10-2

( 0.48 1.85) x 10-2

( 0.2 1.4 ) x 10-2

Measurements

OPALCLEO

ALEPHBABAR

WA

SM -1.4 <ASL(10-3)< -0.5 (>10% CL)

ASL not expected to constrain , but to exhibit / constrain New PhysicsThe present world average already constrains some models…

SM NP

|12/M12| O(mb2/mW

2)

arg(12/M12) O(mc2/mb

2) O(1)

ASL10-3 10-2

SL,Z.Ligeti,Y.Nir,G.Perezhep-ph/0202010

Testing New Physics:The Semi-leptonic Asymmetry

Without ASL Including ASL

General NP in mixing amplitude

22 SM12 12M r Mdi

d e

Minimal Flavour Violation model

2

0

| | and 2 0( )

( )tt

dt

Fr

S x

ASL not significantly enhanced

Conclusion

Measurement can discriminate betweenvarious NP models

<0 allowed

The Semi-leptonic Asymmetry

Where are we todayWhere are we todayWhat brings the future ?What brings the future ?

Where are we todayWhere are we todayWhat brings the future ?What brings the future ?

BABAR / Belle

Similar scenario

expected for Belle

3

PEP-II Luminosity Projections

Global CKM fit (CKMfitter) gives consistent picture of Standard Model

sin(2 ) now most accurate constraint

future consistencies:BABAR Belle ? J/ KS KS

ms : constraint on UT angle from LEP/SLD/CDF limit expect measurement from TEVATRON soon

Need more constraints on CKM phase:

Charmless B decays: Conventional isospin analysis in B0 potentially unfruitful to extract

sin(2 ) Significant theoretical input needed Pursue other ways to measure : B0

Summer ’06: (sin2WA) ~ 0.025 for 1000 fb–1

Many more results to come from the B-factories

Conclusions

Backup slides

Babar detector

xexp

Measurement Constraints on theoretical parameters

Theoretical predictions

Xtheo(ymodel= , yQCD)ytheo

ytheo =(A,,,,mt…)

“2” = –2 lnL(ymodel)

L(ymodel) = Lexp [ xexp – xtheo(ymodel)] Ltheo(yQCD) xexp

Uniform likelihoods: “allowed ranges”

Frequentist: Rfit Bayesian

Probabilities

Assumedto be

Gaussian

yQCD=(BK,fB,BBd, …)

« Guesstimates »

Extracting the CKM Parameters

AH, H. Lacker, S. Laplace, F. Le Diberder EPJ C21 (2001) 225, [hep-ph/0104062]

If CL(SM) good

Obtain limits on New Physics parameters

If CL(SM) bad

Hint for New Physics ?!

Test New PhysicsMetrology

Define: ymod = {a; µ}

= {, , A,,yQCD,...}

Set Confidence Levels in {a} space, irrespective of the µ values

Fit with respect to {µ} ²min; µ (a) = minµ {²(a, µ) }

²(a)=²min; µ(a)–²min;ymod

CL(a) = Prob(²(a), Ndof)

Probing the SMTest: “Goodness-of-fit”

2 2F d

Evaluate global minimum ²min;ymod

(ymod-opt)

Fake perfect agreement: xexp-opt = xtheo(ymod-opt)

generate xexp using Lexp

Perform many toy fits:

²min-toy(ymod-opt) F(²min-toy)

fit package

CL(SM)2 2

min;ymod

Three Step CKM Analysis Using Rfit

/ 1 Prob( ) Prob( )ffA A B f B f

( ) ( )sin sin

( ) ( )CP

B f B fA T P

B f B f

Time-integrated Observable:

Interfering contributions to the decay amplitude generate direct CPV:

Strong phase difference

Weak phase difference

For neutral B’s direct CPV competes with other CPV phenomena

2

2

( )

( )

T T P P

T T P P

i i i i

i i i i

B f T e e P e e

B f T e e P e e

=0 and =0 no direct CP Violation

“Direct” CP Violation in the Decay

Branching Fs. and ACP for B /K status: ICHEP’02

Agreement among experiments.

6( 10 )

Bounds on

0.13 0.110 0

( ) BR( )1.09

( ) BR( )B K

RB K

FM bound:FM bound:

NR bound:NR bound:0

0.20 0.180

BR( )2 1.40

BR( )c

KR

K

no constraint

Ratios of CP averaged branching fractions can lead to bounds on :

0.16 0.120 0

1 BR( )0.89

2 BR( )n

KR

K

BF bound:BF bound: no constraint

some constraint

Fleischer, Mannel PRD D57 (1998) 2752

Buras, Fleischer EPJ C11 (1998) 93

Neubert, Rosner PL B441 (1998) 403

< 1 ?

1 ?

1 ?

status: ICHEP’02

Neubert-Rosner Bound

a)a) b)b)

0

3 / 2 0

2 ( )/ tan (SU(3),BBNS) (0.221 0.028)

( )

Kth c th

f BRT P R R

f BR K

Penguin

Tree

a)a)

b)b) QCD FA: small relative strong phases

status: FPCP’02

S

C

Only predictive approach: QCD FA...it works...yet !

Using , from standard CKM fit

Predicting the Experimental Observables

Input: |P| from BR(K 0 +) Input: |P| from BR(K 0 +) Input: SU(2) + BR(K

+ –) Input: SU(2) + BR(K + –)

Need to make more assumptions ... achieve better constraints

BABAR BABAR BABAR BABAR

2 2 eff

oef 25f

sin(2eff) & SU(3) or “naive” FA