j. albert caltech october 7, 2004

J. AlbertCaltech

October 7, 2004

(or φ3 and 2φ1+φ3)

http://chep.knu.ac.kr/fpcp2004/index.html

The Angle The Angle of the Unitarity Triangle of the Unitarity Triangle

We expect to be approximately (57±9)º, if the Standard Model is consistent.

But how to directly measure it…

FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 2

We have several ways of directly measuring . No single one of them is a “silver

bullet”:1) D(*)0

CPK(*)+ (Gronau-London-Wyler)

2) D0(Kπ)h+ (Atwood-Dunietz-Soni)

3) D(*)0(D03-body)K+ (Dalitz, GGSZ)

4) sin(2β+) from D(*)π/D(*)ρ

4a) assisted by Ds(*)π/Ds

(*)ρ

5) sin(2β+) from D(*)0K(*)0

6) The dark horse: D(s)(*)D(*) combined fit (D-L-A)

Measurement of Measurement of from Direct CPV from Direct CPV ( (i.e.i.e. GLW, ADS, GLW, ADS, GGSZ/Dalitz)GGSZ/Dalitz)

The D0K and D0K amplitudes have a relative weak phase of . But need 2 more pieces of information!:

Relative magnitude

Strong phase difference δB


cbV

*usV

ubV

*csV

Secret to Success: interference between color-allowed D0K and color-suppressed D0K amplitudes.Decay-time-independent!

( )

( )B

A b ur

A b c

The bigger the better!Larger rB larger interference term better constraints on .

From B D0K GLW analysis:

rB < 0.22 (90% CL) hep-ex/0402024

rB = 0.26+0.10±0.03±0.04 hep-ex/0406067-0.14

V ub

V cb

V us

V cs

*

*

How to Reconstruct a How to Reconstruct a BB00 DK DK EventEvent

DK/Dπ separation obtained via ΔE and from particle ID (e.g. BaBar DIRC)


Topological variables combined in a Fisher discriminant or a Neural Net

2*2*BbeamES pEm

ΔE

= E

*B -E*b

eam

Continuum e+e- q+q- rejection obtained via event topology.

ΔE (GeV)

The Gronau-London-Wyler MethodThe Gronau-London-Wyler Method

B- D0CPK(*)-, where D0

CP is a CP-eigenstate decay (CP+:

D0 π+π-, K+K- CP-: D0 Ksπ0)

We have the following observables:

4 observables (RCP+, RCP-,ACP+, ACP-) determine 3 unknowns (rB,δB,)


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

Normalized to flavor state

BF(B DK) ~ 10 -4, BF(D fCP) ~ 10 -2

Small… strongly statistics limited

BF(B DK) ~ 10 -4, BF(D fCP) ~ 10 -2

Small… strongly statistics limited

BB-- DD00CPCPKK(*)-(*)- yields from yields from


D0 background

B+ CP+ B- CP+ B- CP-B+ CP-

NBB=214 106

NBB=227 106

75 13

18 7

K K

0 76 13SK

15.1 5.8CP 34.4 6.9CP

Adding KS, KS

D0CP K -D0

CP K - CP+ (+-,K+K-) CP- (KS0)

D0CP K* - (K* - KS-)D0

CP K* - (K* - KS-)

BB-- DD(*)0(*)0CPCPKK-- yields from yields from


B+ D1*0 K+ B+ D1

*0π+

B+ D2*0 K+ B+ D2

*0π+

B+ D10 K+

B+ D20 K+

GGronauronau-L-Londonondon-W-Wyleryler Method Results: Method Results:


CP

CP

- 0.80 0.14 0.08

0.21 0.17

0.87 0.14 0.06

0.40 0.15 08

0

0

.

.

07C

C

P

P

R

R

A

A

D0CP K -D0

CP K -D0

CP K* - (K*- KS-)D0CP K* - (K*- KS-)

0.040.1CP- 4

CP

0.33 ( 1.15 0.0.34 0.1 )0 12 ( )

0.76 0.29 0.0

1.77 0.37 0.12

0.09 0.20 0.0

6

6

CP CP CP

CP

A AA

R

A

R

Additional systematic erroron ACP- ( CP even background)

More CP eigenstate final states still to be added… More statistics needed to constrain More statistics needed to constrain

Loose bound on rB22(1 )CP CP BR R r

From DCPK*2 0.23 0.24Br

0.100.081.09 0.26

0.02 0.24 0.05CP

CP

R

A

D*0 (D0CP0)K -D*0 (D0

CP0)K -

NBB=214 106 NBB=227 106

NBB=123 106

GGronauronau-L-Londonondon-W-Wyleryler Method Results: Method Results:


B+ D*02 K+ statistical

significance 4.5 σ

B+ D1*0K+ statistical

significance 5.6 σ

Acp=-0.27±0.25 ±0.04

Acp=0.26±0.26±0.03

06.028.043.1

*

*

*1

*1

1

DB

KDBDB

KDB

R

06.028.094.0

*

*

*2

*2

2

DB

KDBDB

KDB

R

Acp=0.07±0.14±0.06

Acp=-0.11±0.14 ±0.05

08.016.029.1

0

0

02

02

2

DB

KDB

DBKDB

R

10.018.098.0

0

0

01

01

1

DB

KDBDB

KDB

R

250 fb-1

The Atwood-Dunietz-Soni MethodThe Atwood-Dunietz-Soni Method


0

0

| ( ) |0.060 0.003

| ( ) |D

A D K

A Dr

K

Input:

Count B candidates with opposite sign kaons Count B candidates with opposite sign kaons

2 2([ ] ) ([ ] )2 cos( )cos

([ ] ) ([ ] )ADS D B B D D B

Br K K Br K KR r r r r

Br K K Br K K

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

([ ] ) ([ ] )ADS B D D B ADS

Br K K Br K KA r r R

Br K K Br K K

D decay into flavor stateD decay into flavor state

Phys.Rev.Lett.91:171801,2003

B D

D decay strong phase D unknown

BB-- DD(*)0(*)0ADSADS((KK++ππ--)) KK-- at at


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

1.30.8

2.

4.0.

1.4

2

1

3

*( )

*( )

([

([ ] )

] ) 0.2

([

.

)

7

] 1.2

4D

D D

D D

N K K

N

N

K

K

K

K

NBB=227 106

No significant signal in current datasetNo significant signal in current dataset

D

D*(Dπ)

D*(D)

BB-- DD(*)0(*)0ADSADS((KK++ππ--)) KK-- at at


30.7 ± 8.8 10178 ± 104Yields from ΔE fits

Yields from ΔE fits17.8 ± 7.1 535.0 ± 25.9

17.8-3.1 = 14.7±7.6 events (3.1 evts. peaking B background)

K

K

K

ADS Constraints onADS Constraints on r rBB from and from and


RADS

0.030 (90%CL)ADSR

0.23 (90% )Br CL

1

48 73

D

D

o o

any

r

any D0K

However, not easy to directly determine

However, not easy to directly determine

RADS can be translated to rB < 0.28 (90% CL)

RADS

3106

00 101π x)DD(R **

ADS

31913

0 1011γ x)DD(R **

ADS

The The DD(*)0(*)0((DD003-body)3-body)KK++ Dalitz Method Dalitz Method


If both D0 and D0 decay into the same final state, B+ D0K+ and B+ D0K+

amplitudes interfere. Mixed state is produced:

Phase θ is a sum of strong and weak phases: for B± D0K±

3*1 ~~ AVVM uscb

3φ32 η i

cs*

ub e~)i(ρ~AλV~VM

000~ DreDD i

δγθ

Use 3-body final state, identical for D0 and D0: Ksπ+π-.

Dalitz plot density:22222 ||),(

sKsKsKsKdmdmMmmd

22222222 |),(),(||),(|

ssssss KK

i

KKKKmmfremmfmmM

(r, , δ) can be obtained with simultaneous fit of B+ and B- data.

Sens

itiv

ity

to

Only two-fold ambiguity in extraction

Isobar model for f(m2+ ,m2

- )can fix phase variationδD across Dalitz plot.

γ32 ηρλ i

cs*

ub e~)i(A~VV~M

DD00(K(Kssππππ))KK++ Dalitz Fit fromDalitz Fit from


Plot of mpipi(770)

CA K*(892)

DCS K*(892)

2m

2m2m

Assumes no D-mixing, no CP violation in D decays!Belle’s is similar:

DD(*)0(*)0(K(Kssππππ))KK++ yields from and yields from and


83 11

40 8

D0K

D*0(D00)K

D*0(D0)K

Mbc (GeV)

Mbc (GeV)

261 19

Fit the D0 Dalitz plots using unbinned

maximum likelihood fit. D0 model fixed.

Free parameters (r, φ3, δ)

209 16

58 8

Dalitz Method Constraints on Dalitz Method Constraints on from from


0.18 (90% )Br CL

D0K-

68% 95%

D0K-

180

0

0.3

(130 45 8 10)oB

rB

-1800.30.

A posteriori rB with uniform a priori:

As for the D* modes: There is a phase shift between D* D0π and D* D0 γ as noted in hep-ph/0409281.The error on decreases significantly when this is accounted for!

As for the D* modes: There is a phase shift between D* D0π and D* D0 γ as noted in hep-ph/0409281.The error on decreases significantly when this is accounted for!

D0 modes alone = (73±45±10±10)º



Errors using toy MC experiments and frequentist approach

Sin(2Sin(2ββ++) from ) from DD(*)(*)π/Dπ/D(*)(*)ρρ


Time dependent analysisTime dependent analysis

favored bc amplitude suppressed bu amplitude

|||| *1 udcbVVA

time-dependent CP violation arises from interference of mixing and decay:

0B0

B

(*)D

iicdub eeVVA |||| *

2

2

b u

dc

dd0

B

*DubV

*cdVu

d

dd0B *D

*cbV

udV

b c

Exclusive reconstruction of D-+, D*-+,D-+

Partial reconstruction of D*-+

D*Combinatoric BBPeaking BB Continuum

Lepton tag

*0 DBsoftD

0

X

Asymmetry

parameters 2 sin(2 )cos

2 cos(2 )sinlep

a r

c r

~ ~

Lepton tag Kaon tag

D*Combinatoric BBPeaking BB Continuum

DD(*)(*)ππ sin(2 sin(2ββ++) results from) results from


• Two experimental methods: o exclusive reconstruction of D-+ and D*-+

o partial reconstruction of D*-+

- higher signal purity, lower efficiency

- high efficiency, more background

• results with exclusive reco.:

• constraints on sin(2+) (partial reco):

*0 DBsoftD

0

X

• |sin(2)| > 0.75 at 68% CL

• |sin(2)| > 0.58 at 90% CL

020003100320δγβ22 ...cos)sin(r

020003100490δγβ22 ...cos)sin(r **

010001600410δγβ22 ...cos)sin(r **

pairs BB 610110

• results with partial reco.: [hep-ex/0408038]

[hep-ex/0408059]

019003600150δγβ22 ...sin)cos(r **

033005500590δγβ22 ...sin)cos(r

033005400440δγβ22 ...sin)cos(r ** pairs BB 610178



Lepton tagPartial reconstruction results:

Assuming δ = 0 or π (factorisation), Belle obtains :

013.0028.0031.0)2sin(2 31* D

R

sin(2φ1 + φ3) from B0 D*-π+

010001600410δγβ22 ...cos)sin(r ** 019003600150δγβ22 ...sin)cos(r **

full reconstruction results:

018003700620δγβ22 ...cos)sin(r

017004000600δγβ22 ...cos)sin(r ** 018003700250δγβ22 ...sin)cos(r

019004000490δγβ22 ...sin)cos(r **

pairs BB 610152

pairs BB 610152

[PRL 93 (2004) 031802, erratum: ibid 93 (2004) 059901]

[hep-ex/0408106]

DD(*)0(*)0KK(*)0(*)0 results from results from


(*)0 00

00 (*)0

( )

( )

B D Kr

B D K

Sensitivity given by

0 *00 ( )B D K K

Search for b u transition(self tagging mode)

Eventually TD analysis…

NBB=124 106

0 0 *0 5( ) 4.110 90% . .BR B D K at C L

DD(*)0(*)0KK(*)0(*)0 results from results from


B < 1.9 x 10-5 90% CLB < 0.4 x 10-5 90% CL

3.3 events+7.5-2.1

0.4 events+3.6

-3.1

r <0.39D0K*0

(equvalent to rB but for neutral B)

B0 D0K*0 & B0 D*0K*0

upper limits (Vub

suppressed):

B(B0 D0K0)=(3.72±0.65±0.37)x1

0-5

B(B0 D0K*0)=(3.08±0.56±0.31)x1

0-5

19.2 events 3.2 σ+6.4

-5.8

12.3 events 2.1 σ+7.5

-5.8

B =( 3.18 ±0.32) x10-5+1.25

-1.12

B < 4.8 x 10-5 90% CL

NEW!solution for

(in V-V and P-P modes)

A Different ApproachA Different Approach:: Using B Using B D D(s)(s)(*)(*)DD(*)(*)


where:

3 observables, 5 unknowns: Use information from 2 other

sources: β from charmonium sin2β

DsD decays for Act amplitude!

A slightly more complex solution for the vector-pseudoscalar modes!

from penguins!!

Datta and London present a method for extracting gamma from measurements of D(s)

(*)D(*), using a combination of branching fraction and CP asymmetry information. hep-ph/0310252 (Phys.Lett.B 584 81 (2004))

The CP asymmetry from the tree amplitude measures sin2β, so where does come in?

comes from the u- and t-penguin terms:

Constraints on gamma from Constraints on gamma from DD(s)(s)(*)(*)DD(*)(*)


One can determine constraints on from fits to already-published data on D(s)

(*)D(*).

See J.A., Datta, & London, hep-ph/0410015(submitted to Phys. Lett. B)

Input measurements from…

Constraints will improve greatly with upcoming data!…

Constraints from vector-vector modes:

Constraints from vector-pseudoscalar modes: (weak)

Combined constraints:

ConclusionsConclusions


“In the world there are many different roads but the destination is the same. There are a hundred deliberations but the result is one.”

--- --- Confucianism,Confucianism, I ChingI Ching

Many paths to …

68 %C.L.

95 % C.L.

Many different approaches to measuring . Information from GLW, ADS, Dalitz, sin(2β+) measurements, and D(s)

(*)D(*) decays are all useful (and the future may hold new approaches…).

Incredible progress in analysis and technique development from both Belle and BaBar.

Statistics are the Statistics are the only thing holding only thing holding us back!us back!

BaBar GLW+ADS+D0K Dalitzφ3 (°) φ3 (°)

r δ

Belle D0K Dalitz

Combined BaBar+Belle D(s)

(*)D(*)

Backup Slides

DD00(K(Kssππππ))KK++ Dalitz Fit fromDalitz Fit from


)(GeV22sK

M

M

(

GeV

2 )

Ksπ

–2

ResonanceOur fit

Amplitude Phase, ° Fit

fraction

σ1 Ks1.66±0.11 218.0±3.8 11%

ρ(770) KS1 0 21%

ω Ks(3.30±1.13)·10-2 114.3±2.3 0.4%

f0(980) Ks0.405±0.008 212.9±2.3 4.8%

σ2 Ks0.31±0.05 236±11 0.9%

f2(1270) Ks1.36±0.06 352±3 1.5%

f0(1370) Ks0.82±0.10 308±8 0.9%

K* (892)-π+ 1.656±0.012 137.6±0.6 60%

K*(892)+π - 0.149±0.007 325.2±2.2 0.5%

K*0(1430) -π+ 1.96±0.04 357.3±1.5 5.8%

K*0(1430)+π - 0.30±0.05 128±8 0.1%

K*2(1430) -π+ 1.32±0.03 313.5±1.8 2.8%

K*2(1430) +π - 0.21±0.03 281.5±9 0.07%

K*(1680) +π - 2.56±0.22 70±6 0.4%

K*(1680) -π + 1.02±0.22 102±11 0.07%

Non resonant 6.1±0.3 146±3 24%

Assumes no D-mixing, no CP violation in D decays

DD00(K(Kssππππ))KK++ yields from and yields from and


83 11

40 8

D0K

D*0(D00)K

D*0(D0)K

Mbc (GeV)

Mbc (GeV)

261 19

K*(892) bands

73 events 73 events

)(GeV22sK

M )(GeV22sK

M

20 events 19 events

)(GeV22sK

M )(GeV22sK

M

B+ D0K+

B+ D*0K+ B- D*0K-

B- D0K-

Fit the D0 Dalitz plots using unbinned

maximum likelihood fit. D0 model fixed.

Free parameters (r, φ3, δ)



r=0.26 ± 0.03(syst) ± 0.04(model), φ3=86±23°±13°(syst) ±11°(model), δ=168±23°±11°(syst) ±21°(model)CP violation significance: 97%

+0.10-0.14

φ3 (°) φ3 (°)

r

δ (°

)

Combined: φ3=77 ± 13°(syst) ± 11° (model), rB = 0.26± ± 0.03(syst) ± 0.04(model), 95% CL interval: 26°<φ3<126° (incl. systematic error) CP violation significance: 95%

+17°-19°

B+ D0K+: B+ D*0K+:

Errors using toy MCexperiments and frequentist approach

r=0.20 ± 0.02(syst) ± 0.04(model), φ3=51±46°±12°(syst) ±11°(model), δ=302±46°±11°(syst) ±21°(model)CP violation significance: 23%

+0.19-0.17

(φ3, δ) and

(φ3+π, δ+π)ambiguity

1115



Lepton tag

S+ = 0.035 ± 0.041 ± 0.018S- = 0.026 ± 0.040 ± 0.018

Fit result

To extract S+ and S- we fix τB andΔm at their world average values, after constrainnig wrong tag fraction w± obtained from previous fit..

Assuming δ = 0 or π (factorisation), Belle obtains :

013.0028.0031.0)2sin(2 31* D

R

sin(2φ1 + φ3) from B0 D*-π+ partial reconstruction

A Different ApproachA Different Approach:: Using B Using B D D(s)(s)(*)(*)DD(*)(*)


Datta and London present a method for extracting gamma from measurements of D(s)

(*)D(*), using a combination of branching fraction and CP asymmetry information. hep-ph/0310252 (Phys.Lett.B 584 81 (2004))

The CP asymmetry from the tree amplitude

measures sin2β, so where does come in?

comes from the u- and t-penguin terms:

How can How can DD(s)(s)(*)(*)DD(*)(*) decays measure decays measure gammagamma??


For a given B D(*)D(*) decay, there are 3 observables: a branching fraction, a direct CP asymmetry, and a time-dependent CP asymmetry (3 of each – one for each helicity state – in the case of D*+D*-):

This is 3 equations in 5 unknowns. More information required…

The additional information can be obtained by inputting two things:

1) beta, as determined from charmonium decays, and

2) branching fractions of B Ds(*)D(*) decays.

SU(3)-breaking in the relation between D(*)D(*) and Ds(*)D(*) can be

parameterized by the ratio of decay constants Δ = fDs(*)/fD(*)

Extracting gamma from Extracting gamma from DD(s)(s)(*)(*)DD(*)(*) decaysdecays


The 3 equations in 3 unknowns can be solved into a single equation for :

For D*D (vector-pseudoscalar), things are a little more complicated. Six coupled equations to solve:

where:

j. albert caltech october 7, 2004

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