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

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

Jan Stark on behalf of Andreas HöckerLPNHE-Paris and Laboratoire de l”Acélérateur Linéaire-Orsay

France

Status of the CKM ParadigmStatus of the CKM Paradigm

Workshop WIN 2002

Christchurch, New ZealandJanuary 21-26, 2002

Quark Mass Mixing in the

Standard Model

The Unitarity Triangle

Constraining the CKM Matrix

statistical framework

standard constraints

charmless B decays

…and conclusion

Newest B and K Physics Results

OutlineOutline

CP Violation in the Standard Model Local SU(2) invariance of LSM with doublets (iL, liL), (uiL, diL), i=1..3

gives rise to charged weak currents

Mass terms: require scalar doublet (1, 2)

Spontaneous symmetry breaking leads to 3x3 quark mass matrices

Unitary rotation from mass to flavour eigenstates via

Modifies LSM for charged weak currents:

LRRLf ffffm

2g v

M u(d)u(d)

)m,m,diag(mUMU τ)t(b,μ)c(s,e)u(d,e)u(d,e)u(d, e)u(d,

d

UUV uCKM

Kobayashi-Maskawa 1973

Id)V(V CKMCKM

CKM MatrixCKM Matrix

1Ai1AA2/1

iA2/1V

23

22

32

CKM

Wolfenstein parametrization (expansion in ~ 0.2):

tbtstd

cbcscd

ubusud

CKM

VVVVVVVVV

V Complex matrix described by 4 independent real parameters

phase

ηλA 62J

0VVVV Im ** kjikijJ CP Violation:

SMin CPV no 0η

The Cabibbo-Kobayashi-Maskawa Matrix

(phase invariant!)Jarlskog 1985

The Unitarity Triangle(s)

γi22

cbcd

ubudu eηρ

VVVV

R

βi22

cbcd

tbtdt eη)ρ(1

VVVV

R

βγπα , argVγ *ub

0VVVV

VVVV

VVVV

cbcd

tbtd

cbcd

cbcd

cbcd

ubud

0VVVV

VVVV

VVVV

cscd

tstd

cscd

cscd

cscd

usud

B sector: K sector:

0λA λA 1

λA λA

3

3

3

3

Large CPV expected in the B system

0,0 0,1

RtRu

η,ρ

ρ

η

Constraining the Unitarity Triangle

Wolfenstein parameters:

and , A,

plane - and

:level 5% the At

:level 1% the At

|V||V|

06.083.0A/VA

V

0018.02205.0sinV

V

tdub

2cb

cb

cusus

What is the value of in our world ?

J/2

J

The Quest for CP Violation in the B System

ATLAS

BTEBTEVV

CLEO 3BBAABBARAR

Belle

2005 (???)

199919992000

2006

2001

Primary GoalPrimary GoalObtain precision measurements

in the domain of the charged weak interactions for testing the CKM sector of the Standard Model, andprobing the origin of the

CP violation phenomenon

CP Violation in InterferenceCP Violation in Interference

DecayMixing

B0 K0–

J/

d

b–

c–

c

s

d–W W

t

t–W

i2e~

Time-dependent CP Observable:

CP violation arises from interference between decays with and without mixing

t)sin( S t)cos(Δ C dfdf CPCP mm

)f(t)ob(BPr)f(t)Bob(Pr1λ CP0

CP0

fCP

0B

0B

CPfCP

mixing

decay

0t

tCPfA

CPfACP

CPCPCP

f

fff A

Apqηλ

CP eigenvalue i2e

amplitude ratio

2f

2f

f |λ|1|λ|1

CCP

CP

CP

2f

ff |λ|1

λ Im 2S

CP

CP

CP

cosine term sine term)sin(2α S π π B,B efff00 CP

2βsin S J/ψ B,B CPf0S

00 K

)f (t)Γ(B )f (t)BΓ()f (t)Γ(B )f (t)BΓ( (t)A

CP0CP0

CP0CP0fCP

0.79 0.10World average

sin2

sin2 per experiment: sin2eff (BABAR):

BABAR hep-ex/0110062

(submitted to PRD)

S+– = 0.03 ± 0.56

C+– = –0.25 ± 0.48

stat. and syst. errors aver-aged and symmetrized

Status: Lepton-Photon 2001

Rare B Decays and Rare B Decays and CP Violation in DecayCP Violation in Decay

f)Prob(B)fBProb(1/AA ff

φsin θsin AA)fBΓ(f)Γ(B)fBΓ(f)Γ(BA 21CP

Time-independent CP observable:

CPV in decay (“direct CPV”) arises from: Interference between various contributions to the decay amplitude

CP violation in decay amplitude

requires 2 decay amplitudes A1 and A2

Strong phase difference

Weak phase difference

For neutral modes, direct CP violation competes with other types of CP violation

partial decay rate asymmetry

1A Re

Im φ φ

θ

2A

CPVdirect no 0 Δθor 0 Δφ

fB fB

Teλ P A γi2Kπ

Also: CP-averaged BFs together with direct CPV can beused to obtain non-trivial constraints on CP angle

Fleischer, Mannel (98)Gronau, Rosner, London (94, 98)Neubert, Rosner (98)Buras, Fleischer (98)Beneke, Buchalla, Neubert, Sachrajda (01)Ciuchini et al. (01)

Theoretical analysis deals with:

SU(3) breaking Rescattering (FSI) W Annihilation EW penguins

B K and the Determination of Contributions from interfering tree and penguin amplitudes

Potential for significant direct CP asymmetries

Experimental tests: overall consistency of BF and direct CPV predictions

000

0

0

0

πKBπKBπKBππB

KKBπKBππB

0

0

0

%)90 (9.12.12.17

5.03.45.24.1

6.14.1

4.23.3

9.51.5

6.40.4

4.13.1

0.37.2

6.14

6.12.18

6.11

%)90(7.12

%)90 (5.2

3.16.17.167.00.11.4

2.12.8

0.22.18

0.18.10

8.07.5

1.37.2

3.30.3

1.29.1

0.28.1

%)90 (7.23.19

4.06.55.16.0

4.32.3

3.20.2

5.27.2

2.79.5

9.18.1

7.58.4

6.18.1

5.33.3

0.16

7.13

3.16

%)90(4.13

CLEO9.1 fb – 1

BABAR20.7 fb–1

BELLE10.5 fb – 1)10(BF 6

47.130.1

89.086.0

37.17

44.4

66.266.2

60.251.2

70.167.1

73.10

41.17

13.12

WorldAverage

B / K Branching Fractions, Summary

Compatibility among experiments. Most rare 2-body modes discovered!

Status: Lepton-Photon 2001

18.021.0)π(KA18.000.0)π(KA10.019.0)π(KA

0SCP

0CP

CP

BABAR

43.034.0

0SCP

22.020.0

0CP

19.017.0CP

10.0)π(KA

06.0)π(KA

04.0)π(KA

BABAR hep-ex/0105061

BELLE hep-ex/0106095BELLE

K

0K

πK0S

CLEO

BABAR

BELLE

24.018.0)π(KA23.029.0)π(KA16.004.0)π(KA

0SCP

0CP

CP

CLEO PRL 85 (2000) 525CLEO

Direct CP Asymmetries in K modes

Compatibility among experiments. No significant deviation from zero

Rare Kaon DecaysRare Kaon Decays

Rare Kaon Decays: K+ +–

2

τμ,e,ttd* tsNLcd* cs

422us

02 xXVVXVV

θsin 2π VνeπKB α νν π K BW

Semileptonic FCNC transition governed mainly by td coupling:

E787 (BNL-68713) hep-ex/0111091

Two decays detected so far at BNL (E787), yielding:

B(K+ +) = (1.57 +1.75 –0.82)10 –10

Theory:

Experiment:

Theoretical uncertainty domin. by charm exchange in box, in particular, mc

Consequences for the Consequences for the CKM Picture ? CKM Picture ?

http://www.slac.stanford.edu/~laplace/ckmfitter.html

Present Constraints

Parameter Observable Measurement Accuracy of constraint

Theoretical Uncertainties Quality

|Vud|

|Vus|

nuclear decayK+(0) +(0) e ~1% -

A |Vcb|Excl. B D*l Incl. b lXc

~5%FD*(1)

Model

2 + 2 |Vub|Excl. B0 ()l

Incl. b lXu

~17% ModelModel

(1–)–1 K CPV (K0) ~20% BK, cc, fK

’/K Direct CPV (K0) ? B6, B8 ?

(1–)2 + 2 md Mixing (Bd) 15% fBd, Bd

fBd2Bd ms Mixing (Bs) Lower limit

, sin2 CPV (bccs) 13% - , sin2 CPV (b uud) >100% Strong phases ?

, b uud,uus ? Strong Phases ?

(1–)2 + 2 |Vtd| K+ + ~50% charm loop ()

How can we Deal with Dominant Theoretical Uncertainties

Definition of the Fit Problem:

²(ymod) = – 2 ln L(ymod) (ymod = , A, , , ..., yQCD)

L(ymod) = Lexp(xexp – xtheo(ymod)) Ltheo(yQCD)

The experimental likelihood can be assumed to be Gaussian

Two main ways of approaching the theoretical likelihood:

Theoretical uncertainties arise from “Educated guesswork” (Hadronic Models, quenched approx., SU(3)-break., ...)

Critical piece of information from mind of physicistsCritical piece of information from mind of physicists

“Uniform likelihoods: ranges”

Frequentist Bayesian

“Probabilities”

If CL(SM) good

Obtain limits on New Physics parameters

If CL(SM) bad

Hint for New Physics: stop working and buy ticket to

Stockholm

Frequentist CKM Analysis using Rfit:

Three main analysis steps:

Test New PhysicsMetrologyProbing the SM

2

χχ

2 dχ)F(χCL(SM)2

modymin;2

Define: ymod = {a; µ} = {, , yQCD, ...}

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

Fit with respect to {µ} CL(a) = maxµ { CL(a, µ) }

Calculate confidence level: ²(a) = ²min; µ (a) – ²min;ymod

CL(a) = Prob(²min(a), Ndof)

Eval. global minimum: ²min;ymod

(ymod-opt)

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

generate xexp using Lexp

Re-perform many fits:

²min-toy(ymod-opt) F(²min-toy)

the package

Höcker, Lacker, Laplace, Le Diberder EPJ C21 (2001) 225, [hep-ph/0104062]

errorsrelevant less with parametersother Nierste) & (Herrlich 0.53 1.38 ) 2000 (Lattice 0.13 0.06 0.87 B) 2000 Lattice ( 0.05 0.03 1.16

) 2000 Lattice (GeV 0.028) 0.028 (0.230 Bf

2000)PDG (CDF/D0, GeV 5)(166 )(

rescaled)not 2001,Summer (WA, 0.102 0.793 sin22001) SLD, LEP, (CDF, Spectrum plitude Amm

) 2001 SLD, LEP, CDF, Belle, (BABAR, ps 0.008)(0.489 m

) 2000PDG ( 100.017)(2.271

(CLEO) lysisMoment Ana /Incl.Excl. 100.9) 1.3 (40.4 V

)Excl.(CLEOIncl.(LEP) 100.55)0.243.49 ( V

(OPAL) 0.058 0.969 V

)( :production dimuon 0.014 0.224 V

K 0.0025 0.2200 V

decay-nuclear neutron 0.00089 0.97394 V

cc

K

dB

s

1-d

3-K

3-cb

3-ub

cs

cd

us

ud

d

MSm

XXW

DISN

t

c

CLEO lepton-endpointmeasurement usingbs not yet included

Fit Inputs (Status: LP 2001)

B(K+ +) and charmless B decays not yet included

3-3Bs

1

cb

3-

3-cb

10)),1/M0.8(

exp):,0.9(1.0(40.4(CLEO) analysismoment |:V|

102) 2(41 :CLEO

102.0)0.5(40.7 :LEP

inclusive : |V|

semi-lep(B) quite safeB->D* at zero recoilmore vulnerable (1/mc)

)ph/9907270hep Bigi, I.I.(

08.089.0)0()Book Physics (

042.0913.0)0(

DB

DB

FBABAR

F

Status of |Vcb|

Bigi, N. Uraltsev: “A Vademecum on Quark-Hadron Duality”

hep-ex/0106346

CLEO

Belle

|Vcb| exclusive:LEP, CLEO, Belle

22

2

121

22

1ln2

21

212

211

1

AAs

AA

A

CL

A

AAmL

AErfcErfc

AErfcA

A

At present, we do not use the likelihood ratio. A rigorous proof that it provides a proper CL, for the present data set, must be given by means of a realistic Monte Carlo simulation.

CERN CKM Workshop (February’02)

Treatment of ms:

Lepton-Photon’01

Lepton-Photon’01

Probing the SM

Confidence Level of Standard Model: CL(SM) = 70%

²min;ymod = 2.3

Metrology (I)

LP’01 constraints

not including sin2

The standard constraints

5% CL bounds

Theoretical uncertainties

Metrology (I)

Compatible with sin2WA

Note: 4-fold ambiguity for

sin2

Metrology (I)

Zoom:

Metrology (I)LP’01 constraints including sin2Amplitude method

for ms limitLikelihood

ratio for ms

Metrology (II)

One-dimensional constraints:

Status: LP’01

Metrology (II)

One-dimensional constraint on sin2:

SM constraint without sin2

Differences among statistical approaches matter !

Metrology (III)

Constraints in the sin2 - sin2 plane:

LP’01 constraints not including sin2

Be aware of ambiguities !

Metrology (IV)

Constraints in the sin2 - plane:

Metrology (V)

Constraints from B(K+ +) [BNL-E787]:

At present dominated by experimental errors.

However: theoretical uncertainties will become important for constraints in the - plane

Metrology (VI)

Selected numerical results

Parameter 95% CL region

0.2221 ± 0.0041

A 0.763 – 0.905

0.07 – 0.37

0.26 – 0.49

J (2.2 – 3.7) 105

sin2 – 0.90 – 0.51

sin2 0.59 – 0.88

75º – 122º

18.1º – 30.8º

37º – 80º

mt (95 – 405) GeV/c2

Observable 95% CL region

BR(KL0) (1.6 – 4.4) 1011

BR(K++) (4.8 – 9.4) 1011

BR(B++) (5.6 – 23.8) 105

BR(B++) (2.2 – 9.4) 107

improves to 46º – 77º when using likelihood ratio for ms

Charmless B Decays Charmless B Decays

into two Pseudoscalarsinto two Pseudoscalars

HERE: FITS TO BBNS

BBNS: QCD FACTORISATION APPROACH:M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda

"QCD Factorization in B -> pK, pp Decays and Extraction of Wolfenstein Parameters", Nucl.Phys.B606 (2001) 245

PERTURBATIVE QCD APPROACH Y. -Y. Keum, H-n. Li and A.I. Sanda

“Penguin enhancement and B ->pK decays in perturbative QCD", hep-ph/0004173

M. Ciuchini, E. Franco, G. Martinelli, M. Pierini and L. Silvestrini,

“Charming Penguins strike back", Phys.Lett. B515 (2001) 33; “Two body B

Decays, Factorization and QCD / mB corrections”, hep-ph/0110022 S. J. Brodsky and S. Gardner,

“Evading the CKM Hierarchy”, hep-ph/0108121

F1F2

Endpoint Singularities ?

W Annihilation ?

b ( c c ) d ?

Sudakov ?

?

b W c d ?

C R I T I C I S M

W E A K N E S S E S ?

…and many more papers !

We follow…

ijji

jjii

udubF

eff

udbuO

udbuO

OCOCVVGH

21

21

21

21

24

552

551

2211*

From Naive Factorization…

b uu u

du

u

buu

ud

W

W

–

–

–

–

–

–

to the QCD Factorization Approach (BBNS, …)Color transparency:

energy release large qq pair in emitted meson is collinear soft gluons do not interact with small color dipole non-factorizable contributions calculable in pQCD

No problem for: mb However: mb finite (QCD/mb) corrections occur

B M1

M2

Non-perturbative physics:formation of M2 and B M1

Vertex corrections and penguinsHard spectator interactions

0ππB

Tree, strong and EW penguin Wilson coefficients are calculatedStrong phases are calculated and found to be small in general

direct CP asymmetries are smallthis is not in agreement with pQCD approach by Li, Keum, Sanda

Annihilation diagrams are not rigorously calculated but estimatedassumed to be small

Soft physics contribution in the spectator interaction is parametrizedassumed to be small

…in CKMfitter

Full BBNS calculation is implemented in CkmFitter Wilson Coefficients are calculated in each fit step incl. scale dependence Theoretical uncertainties are scanned within given ranges

Implementation of BBNS Model…

Fit to BR’s and ACP’s Within BBNS

BBNS5% CL

32%

90%

Compared to standard CKM fit Theoretical

uncertainties:

ms, mc, B, RK

Renorm. scale Gegenbauer mom.:a1(K), a2(K), a2()

F(B), fB

XH, XA

²min;ymod = 2.0

Prediction of BR’s for Unobserved Modes

Example: B0 00

Note: theoretical prediction uses BR of B+ +0 which is not known with sufficient accuracy at present !

Confidence Level

Branching Fraction

Large values of B0 00 correspond to 180º

γsin 0.181.06 )KBR(π)πBR(K

)τ(B)τ(B R 2

00

Fleischer-Mannel, Neubert-Rosner & BBNS

FM bound:

NR bound + additional theoretical input: 0.140.71 )KBR(π)πBR(K R 0

0*

0.034)(0.223BBNS)(SU(3),R )KBR(π )πBR(π 2

fftanθR ε T/P a) th0

0

π

Kcth3/2

small phases strong :FA(BBNS) b)Outlook to Summer 2002

Constraints if no penguins are present:

Sin2a = 0.31 4 ambiguities:

/2 – +

3/2 –

CL

0 1 2-1

0

-1

1

Time-Dependent CP Asymmetry in B+–

Use BABAR result: S = 0.03 +/– 0.56

& BBNS(Theoretical errors small compared to experiment)ππππ

iγππππ

iγ2iβ

ππ

2ππ

ππππ

/TPe/TPeeλ

λ12ImλS

constraint: sin2 & sin2

constraint: sin2 constraint: sin2

Global CKM fit gives consistent picture of Standard Model (CKMfitter) sin2 is competitive with the other (theoretically limited) constraints

consistency: BABAR Belle ?

ms : constraint on UT angle crucially depends on stat. interpretationfortunately: expect measurement from TEVATRON soon

More statistics needed for rare K decays

Need more constraints on CKM phase:

Charmless B decays and CP violation: best fits (in BBNS) around 80º

Other approaches intended to be implemented into CKMfittercollaboration with theorists much appreciated: please contact us !

Further discussion of theoretical uncertainties needed

ConclusionsConclusions

Summer ’02: (sin2) < 0.06 for 200 fb–1

http://www.slac.stanford.edu/~laplace/ckmfitter.html

More statistics to come from B-factories: interesting times ahead