the ckm angles a and b a/f2 g/f3 b/f1 introduction measuring b/f1

Richard KassRichard Kass 1

The CKM Angles and Introduction Theory overview Experiments at B-factoriesMeasuring Measuring Summary


The Cabibbo-Kobayashi-Maskawa Matrix

• The weak interaction can change the favor of quarks and lepton• Quarks couple across generation boundaries

• Mass eigenstates are not the weak eigenstates

• The CKM Matrix rotates the quarks from one basis to the other

Vcb Vub

d’ Vu

dVus

Vu

bd

s’ = Vcd Vcs Vcb sb’ Vtd Vtd Vtb b

u

d

t

c

bs

3 2

2

3

=sin(c)=0.22


Visualizing CKM information from Bd decays

The Unitarity TriangleThe CKM matrix Vij is unitary with 4 independent fundamental parameters

Unitarity constraint from 1st and 3rd columns: i V*

i3Vi1=0

Testing the Standard ModelMeasure angles, sides in as many ways possibleArea of triangle proportional to amount of CP violation

β

-i

-i

γ1 11 1 1

1 1

e

e

CKM phases (in Wolfenstein convention)

u

d

t

c

bs

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb


Three Types of CP Violation

In this talk we will be discussing type III) CP violation

0B CPf

I) Indirect CP violation/CP violation in mixingKKlexpected to be small (SM: 10-3) for B0’s

II) Direct CP violation: Prob(Bf) Prob(Bf) in KBr(B0) Br(B0)

III) Interference of mixing & decay: Prob(B(t)fCP) Prob(B(t)fCP) B0s (CKM angle )B0 (CKM angle )

0B Due to quantum numbers ofY(4S) and B meson we mustmeasure time dependant quantities to see this CP violation

Only CP violation possible forcharged B’s


)(cos)(sin

))(())(())(())((

)( 00

00

tmCtmS

ftBftB ftBftB

tA

ff

CP

CP Violation at the Y(4S)

0B

0B

CPf

mixing

tCPfA

CPfA

0t

q/p

CP violation from the interference between two paths, decay with and without mixing

f

ff A

Apq

2

2

2

||1Im2

||1||1

f

ff

f

ff

S

C

Sf and Cf depend on CKM angles

Direct CP Violation: C

|Af/Af|≠1→ direct CP violation

|q/p|≠1→ CP violation in mixing

Measure time dependent decay rates &m from B0B0 mixing

|BL>=p|B0>+q|B0>|BH>=p|B0>- q|B0>


The Y(4S) - a copious, clean source of B meson pairs1 of every 4 hadronic events is a BB pairNo other particles produced in Y(4S) decay Equal amounts of matter and anti-matter

28.0hadr

bb

BB T

hres

hold

Getting the Data SampleUse e+e- annihilations at Y(4S) to get a clean sample of B mesons

At Y(4S) produce B-/B+ (bu/bu) and B0B0 (bd/bd) mesonsmB

0 ~ mB- ~ 5.28 GeV


B Factories

Note: 1fb-1 ~ 1.1 million BB pairs BaBar has 352 fb-1 and Belle has 610fb-1 of data

To get the large data set necessary to measure CP-violation with B’s use B-factories SLAC and KEK Both factories have attained unprecedented high luminosities: >1034/cm/s2


Asymmetric e+e- Colliders

KEKII

KEK/SLAC are asymmetric e+e− colliders KEK: 8 GeV (e-)/3.5 GeV (e+) SLAC: 9 GeV (e-)/3.1 GeV (e+)B travels a measurable distance before decay: SLAC: =0.56 → c~260m KEK: =0.42 → c~193m

PEPII


Detectors at Asymmetric e+e- Colliders

Both detectors feature: Charged particle tracking (silicon+drift chambers + 1.5T B-field) Electromagnetic calorimetry (CsI) and electron ID /K/p separation up to the kinematic limit BABAR: dE/dx+DIRC Belle: dE/dx+aerogel+ToF Muon/KL identification

http://belle.kek.jp/belle/transparency/TP/detector2_org.html


Threshold kinematics: we know the initial energy of the Y(4S) system Therefore we know the energy and magnitude of momentum of each B

Key Analysis Techniques

2*2*BbeamES pEm **

beamB EEE

Background Background

(spherical)

(jet-structure)

Event topology

Signal Signal

Most analyses use an unbinned maximum likelihood fit to extract parameters of interest


t =0

How to Measure Time Dependent Decay Rates

We need to know the flavour of the B at a reference t=0.

B 0

(4S)

The two mesons oscillate coherently : at any given

time, if one is a B0 the other is necessarily a B0

In this example, the tag-side meson decays first.

It decays semi-leptonically and the charge of the

lepton gives the flavour of the tag-side meson :

l = B 0 l = B 0. Kaon tags also used.

tagB 0l (e-, -) =0.56

z = t c rec

sK

t picoseconds later, the B 0 (or

perhaps it is now a B 0) decays.

B 0

ll

d0B b

W

At t=0 we know this

meson is B0


The Many Ways to Measure sin2

)(/

/

,,)2(

/

000*0*

0

001

0

0

S

L

ScScS

S

KKKJ

KJ

KKKS

KJ

**0

*

,/

,

DDJ

DDDD

0

00

000000

00

)980(,

,,,

,,

SS

SSSS

S

KfK

KKKKK

KKKK

m)(charmoniu a) sccb

)charmonium (andcharm b) dccb

sssbsddb ,dominated-Penguin c)

Can use 3 different categories of B0 decays to measure :

golden mode


Precise Measurement of sin2 from B0charmonium K0

Theoretically very clean: ACP(t)=Sfsin(mt)-Cfcos(mt)The dominant penguin amplitude (suppressed by 2

Cab) has same phase as tree SM prediction: Cf=0 ACP(t)=Sfsin(mt)

confirmed by recent model-independent analyses [e.g. PRL 95 221804 (2005)] S=0.000±0.012

Experimentally very clean:Many accessible decay modes with (relatively) large BFs B→ψK0~8.5x10-4

B→ψ(2S)K0~6.2x10-4

B→χc1K0~4x10-4

B→ηcK0~1.2x10-3

CP odd CP even


Precise Measurement of sin2 from B0charmonium K0

(cc) KS (CP odd) modes J/ KL (CP even) mode

PRL94, 161803 (2005)227x106 BBsin2=0.7220.040±0.023

hep-ex/0507037386x106 BBsin2=0.6520.039±0.020(was 0.7280.056±0.023, Nov. 2004PR D71, 072003, 152x106 BB)


1 CKM fit2

World Average sin2[WA]=0.687±0.032

From external constraints sin2UTFit= 0.793±0.033 (sides) sin2UTFit=0.734±0.024 (all)

Great success for Standard ModelGreat success for all of us theorists, experimentalists, accelerator physicists

Brief history of sin2 from B0charmonium K0


Resolving the sin(2) Ambiguity

Belle: Use bcud [B 0DCP(Ks) h0] decays [A.Bondar, T.Gershon, P.Krokovny, PL B624 1 (2005)]

Theoretically clean (no penguins), Neglect DCS B0DCPh0 decayInterference of Dalitz amplitudes sensitive to cos

Dalitz model fitted in D*-tagged D0 decays

o rules out =68o @ 97% CL [Belle. hep-ex/0507065]

BABAR: B0J/K*0(K*0Ks0)Extract cos2 from interference of CP-even and CP-oddstates (L=0,1,2) in time-dependent transversity analysis cos<0 excluded at 86% C.L. [BABAR, PRD 71, 032005 (2005)]

sin(2) is the same for

222 |),(||| SS KKmmff

h0=,,


00 / :decays JBdccb

These decays suffer from potential penguin-pollution:

0 ,2sin CS BABAR: B0 J/0 updated measurements [hep-ex/0603012, submitted PRD-RC]:

Br(B0J0)=(1.94±0.22±0.17)x10-5

SJ/0=-0.68±0.30±0.04 CJ/0=-0.21±0.26±0.09

Consistent with previous Belle results: PRL93, 261801 (2004) SJ/0=-0.72±0.42±0.09 CJ/0=-0.01±0.29±0.03

bd penguin amplitudehas different weak & strongphases with respect to tree.


(*)(*)0 :decays DDBdccb

D*+D*-: [PRL 95, 151804 (2005)] VV decay: both CP-odd and CP-even components.CP-odd fraction extracted with transversity analysis:

fodd=0.125±0.044±0.070S+=-0.75±0.25±0.03

C+=+0.06±0.17±0.03

D(*)+D- [PRL 95, 131802 (2005)]: SDD =-0.29±0.63±0.06 CDD =+0.11±0.35±0.06 SD*+D-=-0.54±0.35±0.07 CD*

+D

-=+0.09±0.25±0.06 SD*-D+=-0.29±0.33±0.07 CD*-D+=+0.17±0.24±0.04

D*+D- D*-D+ D+D-


summary :decays dccb

All results consistent with SM expectation of tree dominance

SDD≡SDDsin~[Z-Z. Xing, PR D61 014010 (2000)]Still below current experimental sensitivity


Sin2eff in b → s Penguins

d d

SM NP

Golden example: B0→KS

No tree level contributions: theoretically cleanSM predicts: ACP(t) = sin2sin(mt)

Decays dominated by gluonic penguin diagrams

Impact of New Physics could be significantNew particles could participate in the loop → new CPV phases

Measure ACP in as many b→sqq penguins as possible! φK0, K+ K− KS, η′ KS, KS π0, KS KS KS, ω KS, f0(980) KS

BUT there are complications: Low branching fractions (10-5) non-penguin processes can pollute

u

su

d

b

dB


All “sin2” Results ComparedWill be discussed in O. Long’s talk “Rare decays and new physics studies”


(0,0) (0,1)

(,)

Vub Vud

Vcd Vcb

*

*

Vtd Vtb

Vcd Vcb

*

*

The Unitarity Triangle

[21.7 ± 1.3]o


The CKM angle

But we do not live in the ideal world. There are penguins...

B0→K+ large Br~2x10-5

~Pure Penguin

In an ideal world we could access from the interference of a b→u decay () with B0B0 mixing ():

d

d

0B

*tbV

tdV

b

b

0Bt

t

*tdV

tbV** // tdtbtdtb VVVVpq

B0B0 mixing

du

dd0B

ubV

*udV

b u

Tree decay

ubudVVA *

222 iii eeeAA

pq

http://www.devil-linux.org/


sin(2): Overcoming Penguin PollutionAccess to from the interference of a b→u decay () with B0B0 mixing () complicated by

Penguin diagram

du

dd0B

ubV

*udV

b u

Tree decay

ubudVVA *

)cos()sin()( tmCtmStA dd

sin

)2sin(1 2

C

CS eff

ii

iii

CP eePTeePTe

2

du

dd

0Bg

b

utcu ,,

Penguin decay

tbtdVVA *

Inc. penguin contribution

0)2sin(

CS

222 iiiCP eee

AA

pq

How can we obtain α from αeff ?Time-dep. asymmetry :

T = "tree" amplitude P = "penguin" amplitude =strong phase

d

d

0B

*tbV

tdV

b

b

0Bt

t

*tdV

tbV** // tdtbtdtb VVVVpq

B0B0 mixing


How to estimate |eff|: Isospin analysis

Use SU(2) to relate decay rates of different final states

Important point is that can have I=0 or 2 but gluonic penguins only contribute to I=0 (by I=1/2 rule) &EW penguins are negligible

Need to measure several B.F.s: eff

Gronau-London: PRL65, 3381 (1990)

00

000000

00

BB

BB

BB

BF(B+)=BF(B-) since is pure I=2, only tree amplitude

However, for this technique to workamplitudes must be very smallor very large!


B0→275×106 B pairs66643 signal events

227×106 B pairs46733 signalevents

Phys.Rev.Lett. 95 (2005) 101801 Phys.Rev.Lett. 95 (2005) 151803

0B

0B


B0→

S = −0.67±0.16±0.06C = −0.56±0.12±0.06

S = −0.30±0.17±0.03C = −0.09±0.15±0.04

So two comparable measurements of S = sin(2eff) Measurements of direct CP asymmetry less compatible

0B

0B 0B

0B


17.044.0 53.052.0

CPA 06.056.012.0 CPA

PRL

94, 1

8180

3(20

05) PRL 94, 181802 (2005)

0B 0B

B0→

22

22

||||||||

000000

000000

BB

BBCP AA

AAA

275 x 106 BB pairs 227 x 106 BB pairs


Using isospin in system

Precision measurement of not possible with current stats using

CL 90%at 35eff

PRL 94, 181802 (2005)


B → to the Rescue

Nature is KIND!B0~100% longitudinally polarized! Transverse component taken as 0 in analysis, essentially all CP evenLarge Branching Fraction! Br(B0)=(30±4±5)x10-6

Br(B0)~6xBr(B0)

helicity anglePRL 93 (2004) 231801

22

12

41

22

12

21

2

sinsin)1(coscoscoscos

LL ff

ddNd

Pseudoscalar→ Vector Vector3 possible ang. mom. states: S wave (L=0, CP even) P wave (L=1, CP odd) D wave (L=2, CP even)

bkg

signal


B0 → BaBar (227 x 106 BB)

09.018.003.0

24.033.0 08.0 14.0

C

S09.030.000.0

09.041.008.0

C

S

Belle (275 x 106 BB)PRL 95, 041805 (2005) PRL 96, 171801 (2006)


But How large is B0→ ?

In system the amount of neutral decays is small

Measure: B0→ events in 227 x 106 BB events

Br < 1.1 x 10-6 at 90% CL.

Phys.Rev.Lett. 94 (2005) 131801

1233 2220

eff

Isospin triangle for is flattened compared to

Penguin Pollution Defeated!

http://www.devil-linux.org/


B±→±

New result with 231 x 106 BB events

Previous BaBar/Belle HFAG average hep−ex/0603003

New result is better match to isospin model

09.014.010.005.004.096.0

10)8.25.22.17( 6

CP

L

AfBr

64.61.6 104.26

Br

Smaller uncertainty on |eff−comparedto mode

C.L. %68 @ 11eff

Moriond QCD 2006


B0 → AnalysisB0 → →− is not a CP eigenstate

– 6 decays to disentangle: – Tried by BaBar and Belle for just ±phase space– Did not set limits on – Can use a Dalitz plot analysis to get from decays Snyder & Quinn: Phys. Rev. D48, 2139 (1993)

0000 , BB

Convert to a square Dalitz plot

Mostly resonant decaysMove signal away from edges Simplifies analysis

MC

)12

22(cos1

00

01

mmmmm

mB

m0=invariant mass of charged tracks

0 0= helicty angle


B0 → ()0 Dalitz plot analysisDalitz plot analysis yields CP asymmetries and strong phases of decaysUsing 213 x 106 BB events hep-ex/0408099

05.011.034.004.014.010.0

CS1184±58 B→

Signal eventsBlue histos are different types of backgrounds

m’ and ’ are variables for a square Daltiz plot

)6113( 2717

Analysis provides a weak determination of :

However, useful forresolving ambiguities…..


Combined constraints on

(HFAG) 99 129WA

gives single best measurement resolves 2-fold ambiguity from

World Average:

Global CKM Fit (w/o ):51697 ms


(0,0) (0,1)

(,)

Vub Vud

Vcd Vcb

*

*

Vtd Vtb

Vcd Vcb

*

*

[21.7 ± 1.3]o

The Unitarity Triangle

[99 ± 11]o


Summary and OutlookBABAR & Belle measure sin2 in ccK0 modes to 5% precision

sin2charmonium=0.687±0.032Comparison with sin2eff in b s penguin modes could reveal new physics effects

BUT need to carefully evaluate SM contributionssin2eff measurements are statistically limited, can add new modes, beat 1/√L scaling

Extraction of depends crucially on penguin contributions B→ Theory experimental feedback is helpful

from

sin in penguins

Expected precision Vs time

reference (current 00 Br)

reference

reference

Luminosity (ab-1)


Putting it all together As of today the complex phase in the CKM matrix correctly

describes CP Violation in the B meson system!

More to come from BABAR/Belle, CDF/D0, and LHCbWill they find CKM violation????


Extra Slides


• size of possible discrepancies Δsin2β have been evaluated for some modes:

– estimates of deviations based on QCD-motivated specific models; some have difficulties to reconcile with measured B.R.

• Beneke at al, NPB675• Ciuchini at al, hep-ph/0407073• Cheng et al, hep-ph/0502235• Buras et al, NPB697• Charles et al, hep-ph/0406184

– model independent upper limits based on SU(3) flavor symmetry and measured b d,sqq B.R.

• [Grossman et al, PRD58; Grossman et al, PRD68; Gronau, Rosner, PLB564; Gronau et al, PLB579; Gronau et al, PLB596; Chiang et al, PRD70]

Adding Theoretical Uncertainties

2xΔs

in2β

‘naive’ upper limit based on final state quark content,CKM (λ2) and loop/tree (= 0.2-0.3) suppression factors

[Kirkby,Nir, PLB592; Hoecker, hep-ex/0410069]


There is a problem

KK

K

B0 +-

B0 K+-

B0+ 157 19 (4.7 0.6 0.2) x 10-6

B0K+ 589 30 (17.90.9 0.7) x 10-6

Penguin/Tree ~ 30%

q

q

the ckm angles a and b a/f2 g/f3 b/f1 introduction measuring b/f1

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