F. Martínez-VidalIFIC – Universitat de València-CSIC(on behalf of the BaBar Collaboration)

from B±D(*)0[KS]K(*)±in BaBar

Outlinefrom BD0[KS ]K

Dalitz modelSelection criteria and data sampleExtended ML fit and (x±,y±) resultsExperimental and Dalitz model systematic errorsStatistical interpretationSummary & Outlook

CKM’06 Workshop, WG5 SessionDecember 12nd, 2006

hep-ex/0607104hep-ex/0507101PRL95, 121802 (2005)

from B-D0[KS]K-

*DCS (892)K

• Interference between bcus and bucs decay processes

• The interference (sensitivity) is a function of the Dalitz plot position

Cabibbo & color favored (Cabibbo & color)-suppressed

cbV

*usV

ubV*

csVB 0D

K

B

K

0D

2 2 2 2 2 2

2 2 2 2 2 2

( , ) ( , ) ( , )

( , ) ( , ) ( , )

B

B

i iD B D

i iD B D

A m m A m m r e e A m m

A m m A m m r e e A m m

2 2 0( )Sm m K

0 *

0 *

Interference of [ ]

(suppressed) witA

h [ ]DS like

B D K K

B D K K

2m

2m

2m

0 *0 (1430) DCS D K

0 0 0SD K

rB=0.12

=70°

B=180°

0 0 0

0 0 0

Interference of [ ]

with [GLW ke

]li

S

S

B D K K

B D K K

0 *(892) DCS D K

2m

2

2

ln( )d Ld

weight =

D0D0

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 3

Dalitz model: reference BW model• extracted from high statistics (390k) and high purity (97.7%) tagged D0 data,

obtained from D*+D decays from continuum• Use as reference isobar model with coherent sum of Breit-Wigner amplitudes

– 3-body D0 decays proceed mostly via 2-body decays

– BaBar model: 16 resonances (3 DCS) + 1 NR, with all parameters from PDG except:• K*

0(1430), taken from E791 experiment (E791 uses isobar model while PDG quotes LASS parameterization)

• “Ad hoc” (500),’(1000) resonances (required to describe the S-wave), extracted from D*+D fit

2 2( , )DA m m

Kopp et al., PRD63, 092001 (2001)

2 2 2 2( , ) ( , )riiD NR r r

r

A m m a e a e A m m 2 2( , ) J

r D r r rA m m F F M BW

2

1( )( )r

r r r

BW ss M iM s

Angular dependence of the amplitude depends on the spin J of the resonance r. Includes FD and Fr form factors (Blatt-Weisskopf penetration factors)

Relativistic Breit-Wigner with mass dependent width r

depending on the resonance KS, KS , . Mr is the mass of the resonance 2 2 2{ , , }s m m m

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 4

Dalitz model: reference BW model

K*(892)

K* DCS

(770)

0D

S

-wav

eN

on-r

eson

ant

CA

K*

DC

SK

*

P,D

-w

aves

2/dof1.2 Total fit fraction: 120%

m2(GeV2/c4)

m2 (G

eV2 /c

4 )

m2(GeV2/c4)

m2(GeV2/c4) m2

(GeV2/c4)

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 5

Dalitz model: S-wave K-matrix model

S

-wav

eC

A K

*D

CS

K*

P

,D-

wav

es

Total fit fraction: 111%

2/dof 1.2 unchanged, since dominated by K P-wave

• Main limitation of the BW model: significant violation of unitarity due to large and overlapping scalar resonances

• Use K-matrix formalism to overcome the problemAnisovich & Sarantev, Eur. Phys. Jour. A16, 229 (2003)

2 2 2 2 21

0, 0

( , ) ( , )riD r r

r spin K spin

A m m F m a e A m m

1

1 1 jj

j

F s I i s s P s

K K-matrix

Phase space matrix Used to assign S-wave systematic error

Initial production vector

m2(GeV2/c4)

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 6

Selection criteriaD0K D*0K (D00) D*0K (D0) D0K*

|cos T| <0.8 <0.8 <0.8 <0.8 |mass(D0)-PDG| <12 MeV <12 MeV <12 MeV <12 MeV |mass(KS)-PDG| <9 MeV <9 MeV <9 MeV <9 MeV E() ----- >30 MeV >100 MeV ----- |mass(0)-PDG| ----- <15 MeV ----- ----- Kaon Tight Selector Yes Yes Yes ----- |m-PDG| ----- <2.5 MeV <10.0 MeV ----- cos Ks >0.99 >0.99 >0.99 >0.99 |mass(K*)-PDG| ----- ----- ----- <55 MeV |cosH| ----- ----- ----- >0.35 |E| <30 MeV <30 MeV <30 MeV <25 MeV

Efficiency 15% 7% 9% 11% cos Ks suppresses fake KS

|cos T| suppress jet-like eventsKaon Tight Selector and |E| suppress D(*) events

<5% of signal (D0)K from (D00)K cross-feed. Common events assigned to (D00)K sample

For each D(*)0K(*) channel we also reconstruct its own control sample: D0, D*0(D00), D*0(D0), D0a1

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 7

B- D(*)0K-, D0K*- data sample• Selected candidates and Dalitz distributions

D0K398±23

D*0K, D*0 D0

97±13

hep-ex/0607104 347x106 B

hep-ex/0507101 227x106 B

B-DK- B+ DK+

D*0K, D*0D093±12

SignalDBBqq

D0K*42±8

Differences between B+ and B- signifies CPV

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 8

Extended ML fit

comb 2 2 comb 2 2 0 0qq

2 2 2 2 2 2 2 2 2

2 2 2

2Sig,Dπ

BB

2 2 2 2 0qq BB( , ) ( , ) | ( , ) | D Dalitz model

( , ), ( , ) Fake Da

( , ) | ( , )

litz shapes (from MC

| | ( ,

an

) ( |

d

, )Bi iD B

D

D

P m

P m m A m m A m

P m m P m m A

m e e A m m

m P D

m

r

m

m m D

0

0 0q

0ESqq,BB

q,BB

True fractions (from MC and m sideb

# Charge-flavor correlation (from MC) #

and data)

sideband da

#

ta)

RS B D KRB D

R D

K B D K

qq

BB

RWron

qq

S

gSig Wron

c

Sig

Dπ

qRS RSqq qq

RS R

ig

ombqq

c SBB B

qq qq

BB

q

BB

Sig

Dπ

ombBB BB

S g

B

g

B

i

B

(1 ) (1 )

(1 ) (1 )

P P

P P

PDF

R

R

R

R

N

R

N

N

N

N

R

R

P

P

P

P

R

R

S RSNegligibleWronBB Bg ig BS(1 ) RP P

*0 2Fisher | cos |,| cos |, ,T BF L L

2 2( , , ) ( , )j j ES jP P m E F P m m

CKM’06 Workshop, WG5, 12th December

• General signal decay rate:

• Generalized CP cartesian coordinates

– Account for natural width of XS system, for generic B D0Xs

• Cases

– B D(*)0K: Null width

– BD*0[D00]K, D*0[D0]K :

– B D0K : Don’t know Fit for

2 2 2 2 2 2 * *| ( , ) | | | | | 2 Re[ ] Im[ ]D s D s D D s D DA m m A r A x A A y A A

02 2 0( , ) ( / )D D SA A m m A D D K

Re , Ims si is s s sx r e y r e

2 2 2 2 ,

0 1s s sx y r

Gronau, PLB 557, 198 (2003)

Extended ML fit: signal parameterization

2( , , )s s sx y r

2 2 2 21, , , s s s Bx x y y r r x y

0 0 0

0 0 0

[ ] [ ]

, [ ] , [ ]B BD D

x y D x y D

Bondar, Gershon, PRD 70, 091503 (2004)

2 2

Bp

s

icb ubi

cb ub

A A e dpe

A dp A dp

22

2

ubs

cb

A dpr

A dp

CKM’06 Workshop, WG5, 12th December

Extended ML fit: (x±,y±) results

D0K D*0K D0K*

2

rB-

rB+

d

2 | sin | 0 direct CPVBd r

B-

B+

B-

B+

All results are preliminary !

• Perform simultaneous ML fit to B± decay rates vs 2 2( , )m m

Dalitz model systematic error

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 11

Experimental systematic errors

Experimental systematics Dalitz model systematics≳Statistical error >>

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 12

Dalitz model systematic error• S-wave:

– Use K-matrix S-wave model instead of the nominal BW model• P-wave

– Change (770) parameters according to PDG– Replace Gounaris-Sakurai by regular BW

• D-wave– Zemach Tensor instead of Helicity formalism as spin factor

• K S-wave– Allow K*

0(1430) mass and width to be determined from D*+D0+ fit– Use LASS parameterization with parameters from D*+D0+ fit

• K P-wave– Use BJ/KS+ data as control sample for K*+(892) parameters– Allow K*+(892) mass and with to be determined from D*+D0+ fit

• K D-wave– Zemach Tensor instead of Helicity formalism as spin factor

• BW running width: consider a fixed value • Blatt-Weiskopf penetration factor • Remove K2

*(1430), K*(1680), K*(1410), (1450) • Dalitz plot normalization

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 13

• Residual for the (x, y+) coordinates wrt the nominal CP fit

• Yellow band is the nominal fit statistical error (100 data statistics)

• Assign as (conservative) systematic uncertainty the quadratic sum of all models

Dalitz model systematic error: (x±,y±) biases for alternative models

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 14

Statistical interpretation• Use frequentist method with Neyman confidence intervals construction for

interpretation of CP cartesian parameters (12 for 3 modes) in terms of fundamental parameters (rB, , B)

* *

0.142 0.198

0.016 0.206 0.282B B

B B

r r

r r

21

BD(*)0K combined 5D-confidence regions projections

mod 180 (92 41 11 12)No 2 constraint on

*No 1 limit on ( alone)DK

0.50 ( 0.75)S Sr r

Dalitz model error

BD0K* 3D-confidence region projection

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 15

Summary and Outlook• For now (preliminary):

• Good precision on the measurement of (x±,,y±) but the improvement on error of (for both, stat. and syst. errors) also depends on the value of the rB parameter– Our current values significantly smaller than Belle

• Critical to constraint better rB and improveis– More data– To combine with GLW and ADS– Help from Nature…

• Updating with full Run1-Run5 for all modes– Combination with D0K*

• Expect ~ 85 signal events– Trying to include D0KSK+Kin combined fit

• Dominated by CP component help on x± coordinates (like GLW)

Dalitz model error prediction

rB = 0.1

(92 41 11 12)

0.1Br

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 16

Backup

17

Dalitz model: S-wave K-matrix model

2 2 2 2 21

0, 0

( , ) ( , )riD r r

r spin K spin

A m m F m a e A m m

1

1 1 jj

j

F s I i s s P s

K

• Main limitation of the BW model: significant violation of unitarity due to large and overlapping scalar resonances

• Use K-matrix formalism to overcome the problemAnisovich & Sarantev, Eur. Phys. Jour. A16, 229 (2003)

0 20

2 0 0

1.01.0 / 2scatt

Ai j scattij ij Ascatt

A

sg g ss f s s m

m s s s s s

K

012

0

1.0 ( )scatt

j prodj j scatt

g ss fm s s s

P

Initial production vectorK-matrix

Phase space matrix

21, 2,( )

( ) 1 i iab ab

m ms

s

Adler zero, to accommodate singularitiesCoupling constant of pole to ith channel

Slowly varying term 0 if 1 scatt

ijf i

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 18

Dalitz model systematic error: D wave• Zemach Tensor vs Helicity formalism

– Enforces transversity of the mesons (M2ABM2

r in angular dependence)

– In DS the NR term is much smaller (5%) in Zemach Tensor than in Helicity model (25%)

Monte Carlo simulation using f2(1270)

MCZemach

MCHelicity Data

Data Ds

Affects seriously spin 2 resonances

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 19

Dalitz model systematic error: K*(892), K*0(1430)

• K*(892)– PDG parameters are from

1970’s (low statistics, ~5000 events), we have ~200k

– If we allow mass and width to float, observe ~+1 MeV (5 MeV) shift on mass (width) with respect to PDG

• Same behavior from partial wave analysis of BJ/K control sample (no S-wave, very clean)

– By far, this gives the largest contribution to the 2/ndof

• K*0(1430)

– If we allow mass and width to float, results are consistent with E791 experiment

Improved !

Improved !

K*(892) K*0(1430)

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 20

(D0)K-(D00)K cross-feed• Overlapping in data among different modes only appears between (D00)K and

(D0)K samples• Confirmed from Monte Carlo simulation: the cross-feed between the samples is

due to events of (D00)K where we loose a soft and we reconstruct it as a (D0)K • Since the cross-feed goes in one direction, (D00)K (D0)K, we assign common

events to the (D00)K signal sample• After all the cuts and after this correction applied we expect <5% of signal (D0)K

from cross-feed• A systematic effect to the cross-feed has been assigned adding a signal component

according to the (D00)K Dalitz PDF and performing the CP fit• The systematic bias of the fit with and without (D00)K has been quoted as

systematic error• Negligible with respect to the other systematic error sources

CKM’06 Workshop, WG5, 12th December

F. Martínez-Vidal , from B±D0[KS]K(*) in BaBar 21

BaBar vs Belle results: HFAG

• BaBar has better precision on (x±,y±), but Belle has larger separation between the blows

– Need more data to better constraint rB !

Dalitz,BaBar

15Dalitz,Belle 18

(92 41 11 12)

(53 3 9)

[plots do not include Dalitz model errors]

PRD 73, 112009 (2006)