F. Mart í nez-Vidal IFIC – Universitat de Val è ncia-CSIC

F. Martínez-Vidal

IFIC – Universitat de València-CSIC

Measurement of the CKM-matrix angle (3)

(at B Factories)

OutlineIntroduction: CKM, UT and CPV observablesAccess to Experiments & analysis techniquesDalitz analysisConclusions and perspectives

International WE Heraeus Summer School on Flavor Physics and CP Violation

Technische Universität Dresden (Germany)September 2nd, 2005

Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle

2

Introduction


3

The Cabibbo-Kobayashi-Maskawa matrix

• In the Standard Model, the CKM matrix elements Vij describe the electroweak coupling strength of the W to quarks

• Complex phases in Vij are the origin of SM CP violation

– Observing SM CP violation access to CKM angles

CP The phase changes sign under CP

Transition amplitude violates CP if Vub ≠ Vub*, i.e. if Vub has a non-zero phase

1)1(

1

)(1

23

22

32

2

2

AiA

A

iA

VVV

VVV

VVV

V

tbtstd

cbcscd

ubusud

CKM

(in Wolfenstein convention)

Mixes the left-handed charge –1/3

quark mass eigenstates d,s,b to

give the weak eigenstates d’,s,b’.


4

Visualizing the phase – the “db” unitarity triangle

cbcd

ubudargVVVV

tbtd

cbcdargVV

VV

0*** tbtdcbcdubud VVVVVV

β

-i

-i

γ1 1

1 1 1

1 1

e

e

CKM phases (in Wolfenstein convention)

and are the two angles of the triangle ()

Surface proportional to amount of SM CPV

Phase of Vub (bu transition)

Vtd

Phase of Vtd (B0-B0 mixing)

Vtd


5

Observables in CPV: interfering amplitudes

• How do complex phase affect decay rates (the basic input for any CPV observable)?

– Decay rate |A|2 phase of sole amplitude does not affect rate

• Case: 2 amplitudes with same initial and final state

– Decay rate |A1 + A2|2

+ |A1|2 + |A2|2 +

2|A1||A2| cos(1-2)=

2

A1 = |A1|*exp(i) A2 = |A2|*exp(i2)

|A1|

1

|A2|

2+ A1+A2=


6

Observables in CPV: interfering amplitudes• Total interfering amplitude depends on phase difference

|A1|

1

|A2|

2+ = A1+A2

|A1|

1

|A2|

2+ = A1+A2

|A1|

1

|A2|

2+ =A1+A2

A1+A2

A1+A2

A1+A2

+ = +

CP

CP

CP

CP


7

Observables in CPV: interfering amplitudes• Dependence on phase difference scales with amplitude ratio

– Observation in practice requires amplitudes of comparable magnitude

|A1|

1

|A2|

2+ = A1+A2

|A1|

1

|A2|

2+ = A1+A2

|A1|

1

|A2|

2+ =A1+A2

+ = +

A1+A2

A1+A2

A1+A2

CP

CP

CP

CP


8

Observables in CPV: weak phase

)(exp||)( otherweakfB iAfBA

)(exp||)( otherweakfB iAfBA

CPhadro

niz

ati

on

hadro

niz

ati

on

• How disentangle weak phase from overall phase difference between amplitudes?

– Weak phase flips sign under CP transformation (CP-odd)

– Look at decay rates for B f and B f

CP

CP


9

Observables in CPV: asymmetries

• …obviously, CP asymmetries depend on the weak-phase

+

+Bf

BfA=a1+a2

A=a1+a2

=

=

+

a1

a2A

-a1

a2

A

CP 22

22

||||

||||

AA

AAACP

depends on weak

CP

CP

CP

CP


10

Observables in CPV: asymmetries

A

a1

a2

+weak

A

a1

a2

-weak

• …but also the CP-even (strong) phase

+Bf

A=a1+a2

A=a1+a2

=

=

CP 22

22

||||

||||

AA

AAACP

=0 need ≠0 !

+CP

CP

Bf


11

Access to


12

Access to : BD0K

0 0

0 0 Use interference between and decays

where the ( ) decay to a common final state B D K B D K

D D f

Vcb

Cabibbo & color favored

B

K

b c

D0

Vub

(Cabibbo & color)-suppressed

B

D0bu

K

Atot=A+A

A (D0K) 3

relative strong & weak phasesA (D0K) 3 ei(B-)

rB |A/A|~0.1-0.3

Size of CP asymmetry depdens on

CF[CS] ~(0.2-0.6) × )

Larger rB larger interference larger sensitivity to PLB557,198(2003)

~0.4


13

Access to BD0K

• Different incarnations of same principle (all theoretically clean)

• CP violation effects depend on– : weak phase difference between B decay amplitudes– B : strong phase difference between B decay amplitudes– rB : relative magnitude of B decay amplitudes– D : strong phase difference of D decay amplitudes– rD : relative magnitude of D decay amplitudes

• For multi-body D decays, last two described by Dalitz decay model

GLW

ADS

Dalitz (GGSZ)

Atwood, Dunietz, SoniUse BD0[K+]K and BD0[K+]K decays

Gronau, London, WylerUse BD0[CP±]Kdecays

Bondar (Belle), Giri, Grossman, Soffer, ZupanUse multibody D decays, eg. BD0[K0

S]K decays

PLB253, 483 (1991)PLB265, 172 (1991)

PRL78, 3257 (1997)PRD63, 036005 (2001)

PRD68, 054018 (2003)PRD70, 072003 (2004)


14

GLW method• Reconstruct BD(*)0K(*) with CP-even and CP-odd D0/D0 final states

• CP modes: quite small D0 branching ratio: e.g. Br(D0K+K)~4x10-3

• Many modes: •CP-even : K+K, + CP-odd : KS0, KS, KS, KS

• Observables

0 02

0

( ) ( )1 2 cos cos

2 ( )CP CP

CP B B B

B D K B D KR r r

B D K

0 0

0 0

( ) ( )2 sin sin

( ) ( )CP CP

CP B B CPCP CP

B D K B D KA r R

B D K B D K

3 independent measurements (ACP+ RCP+ = ACP- RCP-) vs 3 unknowns (rB, B, )8-fold ambiguity(rB,B) different for BD0K, BD*0K, BD0K*

Normalize to D0 decay into flavour state (eg. K+)


15

ADS method

ADSDBDBADS RrrKKDBKKDB

KKDBKKDBA /sin)sin(2)][()][(

)][()][()()(

)()(

cos)cos(2

)][(2)][()][( 22

DBDBDBADS rrrrKKDB

KKDBKKDBR

KDB 0

KDB0 KD

0

KD0favored

favoredsuppressed

suppressed

KK D][ KDB 0

KDB0 KD

0

KD0favored

favoredsuppressed

suppressed

KK D][

• Same idea as for GLW method, but different D0 final state: doubly-Cabibbo-suppressed decay, [K+]D , instead of CPES

• Small BFs (~10-6), but amplitudes of comparable size expect maximum CPV• Observables:

2 independent measurements vs 3 unknowns (rB, B, )The system can be solved with BD*0K decays

Diii

BD reeerKKBA DB )(

PLB592, 1 (PDG2004)

rD2 = (0.3650.021)%

D : D decay strong phase unknown (scan all values)

PRD70, 091503 (2004)

No DCS signal so far…


16

Dalitz method

Schematicview of the

interference

2 0 2

2 0 2 ( ) ( )

S

S

m M Km M K

2m2m

2m2m

0 D 0 D

• Reconstruct BD(*)0K(*) with Cabibbo-allowed D0/D0KS

• If D0/D0 Dalitz f(m+2,m

2) is known (included charm phase shift D):

),(),()(),( 2222022

mmfeermmfKDBAmmM ii

BB

),(),()(),( 2222022

mmfeermmfKDBAmmM ii

BB

B:B+:

|M|2 =)( Bi

Ber

No

D m

ixin

gN

o C

P v

iola

tion

in D

dec

ays

• Relatively large BFs: BF[(B D0K)(D0 K0 )]=(2.20.4)10-5

• Only charged tracks in final state high efficiency/low bkg ambiguity only 2-fold ( ↔ )


17

Dalitz method: sensitivity to

2m

2m

D0 KS

The highest the weight the more important the event for measurement

points : weight = 1

weight =

2

2

ln( )d L

d

22

2

1( ) ~

ln( )d Ld

rB=0.12

=70°

=180°

DCS D0 K*(892)+-

DCS D0 K0*(1430)+-

• Sensitivity varies strongly over Dalitz plane• Second derivative of the log(L) event-by-event weight the event


18

Access to 2+B0D(*)+

Favored b c transition

2 *2i i i iu cdbA e e e V er V

c0B

d

bu

d

*D

h

*cb udA V V

Doubly-Cabibbo suppressed b u transition

d

bc

d

0B

u

*D

h0B

u,c,t

u,c,t

V*ub

Vcd

Vcb

V*ud

)(

)((*)0

(*)0(*)

hDBA

hDBArB

Use interference between

~

~

Similarly:

golden mode at LHCb

0 0( )s s sB B D K

PLB427, 179 (1998)

~0.02 from moduli (small CP asymmetry, ~2%)

• Favored decay has “large” branching ratio (~0.3-0.8%)• …but need huge statistics partial and full reconstruction• rB

(*) must be obtained from external measurements + SU(3) (theory error 30%, under discussion among theorists)


19

Experiments &analysis techniques


20

Experiments: BaBar at PEP-II (SLAC)

“Storied Royal Elephant”DIRC PID)

144 quartz bars11000 PMs

1.5T solenoid

EMC6580 CsI(Tl) crystals

Drift Chamber40 stereo layers

Instrumented Flux Returniron / RPCs/LSTs (muon / neutral hadrons)

Silicon Vertex Tracker5 layers, double-sided sensors

e+ (3.1GeV)

e (8.9 GeV)


21

Experiments: Belle at KEK-B (KEK)


22

Analysis techniques

• Reconstruct D0/D*0 mesons in the various decay modes

• Combine with fast tracks K/ to make B candidates

KDDD 00* ,

Particle ID

Aerogel+ToF+dE/dx

Information combined into likelihoodsWide momentum coveragesCheck high momentum performance with D*D0samples

Primary K/ separation uses DIRC (C)Combine dE/dx from SVT and DCH


23

Analysis techniques • Veto significant/potentially dangerous B decay backgrounds

– E.g. B[]DK has background from B [K]D

• Suppress continuum e+eqq (q=u,d,s,c) background using– Angular distribution: B flight direction– Event shape variables:

• Signal: almost at rest• Background: “jetty”• Use multivariate variables

– Fisher discriminant– Neural Net

– Resonance masses, decay angles, helicity in PPV, VPP decays (eg. DKS, K*KS)


24

Analysis techniques• Characterize B candidates using

– Beam constrained mass:• B mesons produced almost at rest

• Resolution ~3 MeV dominated by beam energy spread– Energy difference:

• Energy of B candidate almost equal to half beam energy

• Resolution ~10-50 MeV depends on neutrals in final state

• Select best B candidates based on invariant masses of daughter particles

• Signal extracted using maximum likelihood fits to mES, , Fisher, PID, etc.

• Use sidebands and control samples to check backgrounds

*beam

* EEB cepB /V M300~*

•Global Maximum Likelihood fit:•Yields (signal + bkg)•CP parameters

•Cut based signal selection•Signal region maximum Likelihood fit:

•CP parameters


25

Example: exclusive reconstruction of BD0K*

K*B

+

KS +

0

00

*,

*,*,)(

cos

DKKsKs

DKKsKsDKKs

xxp

xxp

D0

=1 for signal events

+

KS+

B

+e-eY(4S)

B

X

-

0SK

0D

0DKs

0SK

*K

Ks


26

Dalitz analysis


27

D0 KS Dalitz model

• Dalitz method requires knowledge of

• |f(m+2,m

2)| can be extracted from tagged D0 rates from e+e continuum

– Tag using charge of soft pion from D*+ D0+ decays

• …but phase difference variation D(m+2,m

2) requires assumption of Dalitz model

• In the isobar model formalism a three-body D0 decay proceeds mostly via 2-body decays (1 resonance + 1 particle)

• With CP-tagged DKS decays the amplitude is

– Can use tagged D mesons from CLEO-c to measure directly cosD, removing (or largely reducing) the model dependence

),(2222 22

|),(|),( mmi Demmfmmf

D0 ABC decaying through a resonance r=[AB]

PRD63, 092001 (2001)PRL89, 251802 (2002)

),(),( 2222 mmfmmf


28

D0 KS Dalitz model: nominal

• The D0 amplitude fAD can be parameterized as a coherent sum of Breit-Wigner amplitudes (quasi 2-body terms) plus a constant term (non-resonant)

),(),( 131201312

0

ssAeaeassA ri

rr

iD

r

rJrrDr BWMFFA

)(

1)(

2ijrrrij

ijr

siMMssBW

Lorentz invariant amplitude for resonance r containing angular dependence

Relativistic Breit-Wigner with mass dependent width

Relative amplitudes and phases

Vertex form factors of the D0 meson and the resonance r(model underlying quark structure of the D0 and the resonance r)Usually, parameterized using Blatt-Weisskopf penetration factors

rD FF ,

J. Blatt and V. Weisskopf,Theoretical Nuclear Physics.

John Wiley & Sons (1952), New York

H. Pilkuhn, The interactions of hadrons,North-Holland (1967), Amsterdam

JrM Angular dependence

sij=[s12,s13,s23] depending on the resonance KS(m2), KS+(m+

2), +


29


•17 amplitudes: 13 distinct resonances + 3 DCS K* resonances + 1 non-resonant term

• Not so good for S-wave need controversial (500) and ’(1000) scalars to describe reasonably well the data

• Masses and widths fixed to PDG2004 values except for and ’ (fitted)

2/dof3824/3022=1.27

DCS K*(892)

CA K*(892)

(770)

hep-ex/0504039

82k tagged D0 events, 97% purity


30


2/dof2.30 (dof=1106)

DCS K*(892)

CA K*(892)

(770)

PRD70, 072003 (2004)hep-ex/0411049

• D0 decay model identical to BaBar

• 19 amplitudes: 13 distinct resonances + 5 DCS K* resonances [same as BaBar + DCS K*(1680) + DCS K*(1410)] + 1 non-resonant term

DCS K*(1680) and DCS K*(1410) excluded in BaBar model because:•number of expected events is very small•the K*(1680) and the DCS K*(1680) overlap in the same Dalitz region the fit returns ~ the same CA and DCS amplitudes


31


Sum of fit fractions : 123%Sum of fit fractions : 124%

• The relative amplitudes ar and phases r as obtained from the ML fit


32

D0 KS Dalitz model: no scalars

La ThuileG. Li, BES Collaboration BJ/ data

• scalar seems to be confirmed by BES Collaboration

• And Dalitz fit to tagged D0 KS sample is clearly much worse

2/dof4757/3022=1.57 vs 1.27


33

D0 KS Dalitz model: no scalars

• …but adding BW’s in the isobar model:• breaks the unitarity of the S (scattering) matrix• BW is only valid for single, isolated resonance

• For broad, overlapping and many channel resonances we need a more general approach K-matrix formalism

(Argand diagram)


34

D0 KS Dalitz model: K-matrix for S-wave

),( ),( 13120 ,0

2311312 ssAeasFssf rri

spinkspinrr

j

23-1

1j2323231 s si-1 jPsρKsF

• K-Matrix formalism overcomes the main limitation of the BW model to parameterize large and overlapping S-wave resonances– non trivial dynamics due to presence of broad, overlapping, and many channel resonances– avoid introduction ad hoc of not established scalars

• By construction unitarity is satisfied:– S : scattering operator– T : transition operator– : phase space matrix

• K-matrix D0 3-body amplitude

KiKT

iTS

SS

1)1(

21

1

S-wave amplitude

initial production vector (production)K-matrix (decay)


35


• Use V.V. Anisovich & A.V. Sarantev parameterization

2/

0.10.1 223

023

0

023

0

23223

mssss

s

ss

sf

sm

ggs A

A

Ascatt

scattscatt

ijr

jiij

K

scatt

scattprodj

jj

ss

sf

sm

g

023

01

232

0.1s

P

ig coupling constant of the K-matrix pole m to the ith channel:

1=, 2=KK, 3=multi-meson (4), 4=, 5=´

Adler zero term to accommodate singularities

scattscattij sf 0 , slow varying parameter of the K-matrix element (non-resonant), with

1 if 0 if scattij

Eur.Phys.Jour.A16, 229 (2003)


36


2/dof~unchanged)

(770)

S

-wav

e te

rm

Sum of fit fractions : 116%

• 9 distinct resonances + 3 DCS K* resonances + K-matrix S-wave

Unitarity guaranteed for S-wave component (by construction)


37

BD(*)0K(*) selection

16209Nsig 858Nsig 736Nsig

D0K D*0K D0K**[KS]

hep

-ex/0

411049

hep

-ex/0

504013

hep

-ex/0

504039

Hep

/ex-0

507101

275×

10

6

BB

227×

10

6

BB

20282Nsig 1190Nsig 844Nsig

D0K D*0(D00)K D*0(D0)K D0K*[KS]

842Nsig


38

BD(*)0K(*) Dalitz plot distributions

B+D0K+ BD0K

B+D0K+ BD0K

Differences between B+ and B signifies direct CP violation


39

Some peculiarities: BD*0Kstrong phase

Effective strong phase

shift of between D00

and D0 helps in the

determination of

• For BD*0K decays

• D*± decaying into CP eigenstates D00,D0

D* = D(-1)l=1 , l=1 for parity/angular momentum conservation

= -1⋅ D*

±→D0±0

D*±→D0

∓

PRD70, 091503 (2004)

Opposite CP eigenstate

BB

2B

20* cosr2r1aKDDB

BB

2B

2* cosr2r1aKDDB


40

Some peculiarities: BD0K*amplitude

cpicppS eAXDBA

0

iiuppS eeAXDBA up 0

13120 , ssAeAfDA D

if

f

12130 , ssAeAfDA Df

if

121313120 ,, ssAeAssAeAXfDBA D

iupD

icppS

upcp

p= B decay phase space pointA = real amplitudeXS=[KS] state

• The K* has an non-zero intrinsic width (~50 MeV) B Dalitz plot• Selection of B±→DK*[KS] decays results in the interference of B±→DK*± and B±→D[KS±]non-K*

• A general parameterization of the B±→D[KS±] decay amplitude can be found wich accounts by construction for the K* and non-K* contributions


41

Some peculiarities: BD0K*amplitude

2cp

2up

S0

S0

2S

A dp

A dp

XDBXDB

r

2up

2cp

iupcpi

A dpA dp

eAA dpe

p

S

SS i

SSi

SS erImy , erRex

*,,Im*,,Re2

,,

1213131212131312

2

121322

13120

ssAssAyssAssAx

ssArssAXKDB

DDSDDS

DSDSS

cpupp

• Let us introduce now the following notation:

• And the effective CP parameters

• The general decay rate is then:

• The effective CP parameters xS±, yS±, rS2 depend on the phase space selected

region without introducing any bias on the measurement

hep-ex/0211282

If K* intrinsic width ~ 0 (K case) =1, S=B, rS=rB


42

Fit results

violationCPdirect 0|sin|2 Brd

Determine x=rBcos(B), y=rBcos(B), for each decay mode from ML fit to B+ and B Dalitz distributions

D0K

D0K

D*0K

D*0K

D0K*

D0K*

B+

B

B+

B+

B+

B+

B+

B

B B

B B

dd

d d

d

d

y

xx xS

x x xS

y yS

y y yS

1- a

nd

2-

con

tou

rs f

or

=2

dof

l

nL

= 0

.5, 1

.921

)


43

From (x,y) to , B and rB

Measured CP parameters: (x,y) B decay mode 12-dimensional spaceExcellent Gaussian behavior

Perform ~1010 pseudo-experiments(Toy Monte Carlo)

Frequentist distillery(Neyman’s construction for confidence intervals)

(,B,rB) parameters:(rB,B) B decay mode and 7-dimensional spaceNon-Gaussian for low stat. samples & near physical boundary (rB>0)

rB rB rS

D0K D*0K D0K*(stat.+syst.

uncertainties)

2 fold (±) ambiguities for both and B

1- a

nd

2-

con

tou

rs f

or

=7

dof


44

, B and rB results

)el(mod11.)syst(13.)stat(2867

)2([email protected](50.0)KD(r

)el(mod03.0.)syst(03.0.)stat(10.017.0)KD(r

)el(mod04.0.)syst(03.0.)stat(08.012.0)KD(r

*0B

0*B

0B

)el(mod11.)syst(13.)stat(1568)KDKD(

*)Knon(8)el(mod11.)syst(9.)stat(35112)KD(

*)Knon(08.0)el(mod04.0.)syst(09.0.)stat(1825.0)KD(r

)el(mod04.0.)syst(02.0)stat.(12.0)KD(r

(model)04.0syst.)(03.0)stat.(08.021.0)KD(r

0*0

*0

*0B

16.011.0

0*B

0B

The importance of rB …

Significance of direct CPV2.32.4 …getting close to evidence

non-K* systematic error since non-K* contribution neglected in nominal fit

(min where CP is conserved, ie. rB=0 or =0)


45

Comments on systematic uncertainties

• Experimental systematic uncertainty accounts for:– PDF shapes of selection variables (mES, DE, Fisher, etc.)– Background fractions and Dalitz shapes– Efficiency variations across Dalitz plane (including tracking efficiency)– Invariant mass resolution– Biases from control samples

• Dalitz model systematic uncertainty includes:– No scalars

• By far, the dominant contribution: ~11o

• Using K-matrix S-wave model, the effect goes down to ~3o

– Not yet used in current measurement (conservative for now)– Other variations have much smaller effects (ie. fine tuning of model ~ little

effect on ):• fit uncertainty of the phases and amplitudes from D0 tagged sample fit• Vertex form factors FD=Fr=1• Constant BW width• Alternative lineshape for (Gounaris-Sakurai)


46

from DK (all methods)

151263meas

71357CKM

• Constraints on from WA D(*)K(*) decays

(GLW+ADS) and Dalitz methods compared to the predictions from the global CKM fit (excluding these measurements)

• Constraints in the () plane on from WA D(*)K(*) decays


47

Conclusions &perspectives


48

Conclusions and perspectives

• Measurement of at B Factories seemed an impossible mission few years ago !

– ...certainly is not an easy task (need lot of data, many methods and channels, a lot of brainstorming,...)

• 3 clean methods towards extraction of in place:

– ...all hindered by smallness of rB

– ...but ready for more precise measurements in the coming few years

– Other methods studied or under study (not shown here), but not yet useful

• First meaningful measurements already available

– Dalitz method is the currently “golden” channel for , but need all channels and strategies to improve errors and resolve ambiguities

• Old Dalitz plot technique is becoming the new paradigm for other measurements too

– Getting close to evidence of direct CP violation in DK (3)

• What’s next?

151263meas


49


13323 signal events

High background, difficult analysis (but possible). Not clear the gain in sensitivity

Exc

lude

KS0

eve

nts

Dalitz analysis from a tagged D0 sample

Expected ~90 BD(*)K events in 210 fb-1.Toy MC studies indicate small but not negligible gain on

• Improving statistical error:

– Larger data sample• Goal for B Factories is increase statistics 2x by ’06 and 4x by ~’08. On track...

– Add other D0 decay channels: KsK+K, 0, KS

hep

-ex/

0207

089

hep

-ex/

0505

084

227×106 BB


50


• Reduce Dalitz model dependence:– K-matrix for S-wave (KS channel)

– Use CP-tagged D mesons decaying to KS to measure directly the (cosine of)

phase difference variation (D)

• Overall, seems feasible an ultimate precision ~ 5o for 2 ab-1 (~2008)– Could be better or worse depending on ultimate value of rB (> or <0.1)

F. Mart í nez-Vidal IFIC – Universitat de Val è ncia-CSIC

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Transcript of F. Mart í nez-Vidal IFIC – Universitat de Val è ncia-CSIC