Measurements of the
CKM angle g at BaBar
Fernando Martínez-Vidal,
On behalf of the BaBar Collaboration
CKM angle g
• Apex of the CKM Unitary Triangle (UT)
over constrained
CP violation measurements give angles
Semileptonic decay rates (and other
methods) give sides
• Precise measurement of SM parameters
• Search for NP in discrepancies of
redundant measurements
• Still have some work to do on g: less
precisely known UT angle (most difficult to
measure)
See also UTfit analysis at
http://www.utfit.org/
Very impressive
consistency
ICHEP 2010, Paris
Fernando Martinez Vidal
1
CKM angle g
• Apex of the CKM Unitary Triangle (UT)
over constrained
CP violation measurements give angles
Semileptonic decay rates (and other
methods) give sides
• Precise measurement of SM parameters
• Search for NP in discrepancies of
redundant measurements
• Still have some work to do on g: less
precisely known UT angle (most difficult to
measure)
This talk
Experiments providing most of analyses today
• Important to measure g since, together
with |Vub|, selects r-h value independently
of most types of NP
SM candle type of measurement
3.1 GeV e+
9 GeV e–
468M BB pairs
ICHEP 2010, Paris
3.5 GeV e+
8 GeV e–
657M BB pairs ~10-15o
• The constraint on g come from tree-level
B→DK decays
Fernando Martinez Vidal
1
γ from B→DK decays
B
*
Measure interference between tree amplitudes b→u and b→c
• Use final state accessible from both D and D
• Largely unaffected by New Physics
• Clear theoretical interpretation of observables in terms of γ
• Difficult because BFs are small due to CKM suppresion (10
0
*
0
-5-
10-7, so not many events) and rB=|Aub|/|Acb| is small due to
further CKM and color suppressions (small interference)
B
All measurements are statistics limited
ICHEP 2010, Paris
Fernando Martinez Vidal
2
γ from B→DK decays
Neutral B→D(*)0K*0
rB~0.3
Charged B→D(*)0K(*)
rB~0.1
B
GLW
CP-odd
CP-even
f=
*
f=
K- K+
π+ π-
K0s π0
K0s ω
ADS
K+ πK+
π-π0
K+ π- π+ π-
Dalitz plot
π0
π+
Dalitz plot
K0s π+ π-
π-
K0s π+ π-
ADS
K0s K+ K-
K+π-π0
K+πK+π-π+ π-
CP-conj
CP-conj
K0s Φ
CP-conj
CP-conj
• Complementary methods applied on same B decay
*
modes share the same hadronic parameters (rB, dB) and g
• Strategy: many decay chains are analyzed and then
B
combined to improve the overall sensitivity to γ
•
In this talk
Atwood, Dunietz, Soni, PRL 78, 3357 (1997)
Gronau,
London,
Wyler,
PLB 253, 483 (1991); PLB 265, 172 (1991)
ICHEP
2010,
Paris
we present new
or recent results
3
γ from B→DK decays
Decay amplitude
s
D  K S 
0

0

D  K S   
s




 
A( B  [ K S   ]K )  
D0 decay strong phase variation



Hadronic parameters
 rB e
b→c
rB=|A(b→u)|/|A(b→c)|
dB (strong phase difference
between A(b→u) and A(b→c))
Dalitz plot method
2

s

m
(
K

)

S
No D-mixing nor CPV







ig  id B
s
s
b→u 
Hadronic parameters
0
s
D  K S   




 

A( B  [ K S   ]K )  



s
D 0  K S   







determined experimentally
from data
Giri, Grossman, Soffer, Zupan, PRD 68, 054018 (2003);
Bondar, unpublished.
ICHEP 2010, Paris
 rB e ig id B
s
b→c 
Fernando Martinez Vidal
b→u
s
4
γ from B→DK decays
Decay amplitude
No D-mixing nor CPV
D  K S 
0

y  rB sin( d B  g )
0





 
A( B  [ K S   ]K )  

Interference terms in decay 

rates proportional to
D  K S   
 rB e
b→c
x  rB cos(d B  g )
Dalitz plot method







ig  id B
Relative weak phase g
changes sign
0
b→u
D 0  K S   
D  K S   
Fit for x± and y± for each B
decay mode




 

A( B  [ K S   ]K )  



 rB e ig id B
b→c
ICHEP 2010, Paris







Fernando Martinez Vidal
b→u
5
γ from B→DK decays
D  K S 
Large interference in some
regions of the Dalitz plot, e.g.
D0→KSr
D0→K*-+ vs D0→K*+-




 

A( B  [ K S   ]K )  



0

D  K S   
 rB e
b→c
b→u
D  K S   
D 0  K S   
0
CF K*(892)+π-
 rB e ig id B
b→c
ICHEP 2010, Paris
ig  id B
CF K*(892)+π-




 
A( B  [ K S   ]K )  



No D-mixing nor CPV
DCS K*(892)+π-
Decay amplitude

0
Dalitz plot method
Fernando Martinez Vidal
DCS K*(892)+π-














b→u
6
Experimental techniques
• Exclusive reconstruction of multiple B decays:
B±→DK±, B±→D* [D0]K± , B±→D* [Dg]K±, B±→DK*±
• Exploit kinematic constraints from beam energies.
mES=√E*2beam -|pB*|2
ΔE=EB*-E*beam
• The main source of background : e e
+ -
with q=u,d,s,c
→ qq,
ΔE
• Event shape variables combined into a linear
signal
region
(Fisher) or non linear (Neural Network)
combination. Tagging information sometimes used
sidebands
BB
Dπ spherical
e+
qq
e-
e+
jet-like
e-
mES
• Signal is separated from background through unbinned maximum likelihood fits to B
±
data using mES, DE and Fisher (or Neural Network) discriminant
• Use large B
±
→ D(*) K(*)±
→ D(*) ± data control samples (rB~0.01, x10 smaller than for DK)
ICHEP 2010, Paris
Fernando Martinez Vidal
7
γ from D Dalitz plot method
• BaBar analysis based on complete data sample (468 M BB pairs)
• Reconstruct B →DK , B →D [D ]K
arXiv:1005.1096.
Sub. to Phys. Rev. Lett.
, B±→D* [Dg]K±, and B±→DK*± final states with
D→KSπ+π-, KSK+K- (eight different final states for each B charge)
±
±
±
Only BaBar
*
0
±
B±→DK±
All components
Continuum + BB BG
Continuum + BB + D BG
• Efficiencies
improved substantially (20% to 40% relative) with respect to previous BaBar
measurement (383 M BB) PRD78, 034023 (2008)
• Reprocessed data set with improved track reconstruction
• Improved particle identification
• Revised K selection criteria: negligible background from D→  h h and B→Da (1260)
+ - + -
S
ICHEP 2010, Paris
Fernando Martinez Vidal
1
8
D→KS+-,KSK+K- amplitude analysis
arXiv:1004.5053. Accepted by Phys. Rev. Lett.
• Extract D amplitude from an independent analysis of flavor tagged D mesons (D →D π )
• Experimental analysis using complete data sample benefits from synergy with D-mixing analysis
0
0
Model determined without (reference) and with D-mixing
*+
0
+
See Matt Bellis talk in this
session for more details
• Fit for amplitudes relative to CP eigenstates [K r(770) and K a (980)] and assume no direct CPV
S
Wave
ππ S-wave
Parameterization
K-matrix Main differences
with Belle
Kπ S-wave
ππ P-wave
K-matrix (LASS-like)
S 0
Wave
K±Ks S-wave
K+K-
S-wave
BW: ω(782), G.S ρ(770)
BW: CA and DCS K*(892),
K+K- D-wave
CA K*(1680)
ππ D-wave
Kπ D-wave
ICHEP 2010, Paris
BW: CA and DCS a0(980),
CA a0(1450)
K+K- P-wave
Kπ P-wave
Parameterization
Flatte a0 (980),
BW a0(1450) and f0(1370)
BW Φ(1020)
BW f2(1270)0
BW f2(1270)0
BW CA and DCS K2*(1430)
Good fit quality (c2/ndof) taking into account statistical,
experimental and model uncertainties
Fernando Martinez Vidal
9
γ from D Dalitz plot method
• CP violation parameters are extracted from simultaneous unbinned maximum likelihood fit to B
±
→ D(*) K(*)± data using mES, DE, Fisher and the Dalitz plot distributions (s+,s-)
B-→DK-
x  rB cos(d B  g )
y  rB sin( d B  g )
g
arXiv:1005.1096.
Sub. to Phys. Rev. Lett.
B-→D*K-
g
dB
B+→DK+
B+→DK+
B-→DK-
Differences between B+ and B- gives
information on g
ICHEP 2010, Paris
B+→D*K+
Fernando Martinez Vidal
B-→DK*B+→DK*+
10
γ from D Dalitz plot method
• Use frequentist method to obtain the (common) weak phase g and the hadronic parameters r ,
B
dB (different for each B decay channel) from 12 (x,y) observables
arXiv:1005.1096.
Sub. to Phys. Rev. Lett.
rB ( DK )  0.096  0.029
042
rB* ( D* K )  0.13300..039
066
crS ( DK * )  0.14900..062
d B ( DK )  (119 19
20 )
d B* ( D* K )  (82  21)
d S ( DK * )  (111  32)
g (mod 180)  ( 68  14  4  3 )
stat
syst
model
Our previous result:
g (mod 180)  ( 76  22  5  5 )
3.5s significance of CPV
[Error on g scales roughly as 1/rB]
• Smaller stat error due to additional data + improved reconstruction + slightly higher r (DK)
• Model error benefited from overlap with D-mixing analysis (e.g. reduction of experimental
B
uncertainties inherent to the model uncertainty)
10.8
g (mod 180)  ( 78.4 11
.6  3.6  8.9 )
ICHEP 2010, Paris
rB ( DK )  0.16000..040
038
Fernando Martinez Vidal
11
γ from ADS method
arXiv:1006.4241.
Sub. to Phys. Rev. D
• Update with final data sample (468 M BB pairs). Previous analysis used 232 M BB pairs
• Reconstruct B →DK , B →D [D ]K
±
±
±
*
0
±
,
and B±→D* [Dg]K±, with
+±
D→K π (“same sign”)
+
D→K-± (“opposite sign”)
•
•
CP asymmetry since “equalizes”
the magnitudes of the interfering amplitudes
“opposite sign”
PRD72, 032004 (2005)
“Maximizes”
B±→DK±
First sign of an ADS signal in
B± → DK± (2.1s)
and
B± → D* K± (2.2s)
ICHEP 2010, Paris
2.1s
Fernando Martinez Vidal
12
γ from ADS method
• Fit directly observables R
±
ADS and B “same sign” yields
reconstruct the ADS asymmetry
RADS
AADS
( B   [ K   ]D K  )
Good sensitivity to rB
1 
 ( R  R  )  rB2  rD2  2rB rD cos(d B  d D ) cos g
2
R  R
 
 2rB rD sin( d B  d D ) sin g / RADS

R R
B+→DK+
R

 


(
B

[
K

]
K
)

D
R 
 ( B   [ K   ] D K  )
AADS ( DK )  0.86  0.47 00..12
16
([ D ]K )  0.018  0.009  0.004
0
*
RADS
([ Dg ]K )  0.013  0.014  0.008
ICHEP 2010, Paris
to
B-→DK-
RADS ( DK )  0.011  0.006  0.002
*
ADS
arXiv:1006.4241.
Sub. to Phys. Rev. D
*
AADS
([ D 0 ]K )  0.77  0.35  0.12
*
25
AADS
([ Dg ]K )  0.36  0.94 00..41
Fernando Martinez Vidal
13
γ from ADS method
arXiv:1006.4241.
Sub. to Phys. Rev. D
• Use frequentist interpretation (similar to Dalitz plot method) to obtain weak phase g and
hadronic parameters rB, dB from RADS(*) and AADS(*) observables
Inputs:
rD =
δD = arg
[
|A(D0→ K-π+)|
(HFAG)
K-π+)|
|A(D0→
A(D0→ K-π+)
A(D0→ K-π+)
rD = (5.78 ± 0.08)%
]
(CLEOc)
δD = (201.9 +11.4
-12.4
)ᵒ
(HFAG, CLEOc)
rB ( DK )  0.09500..051
041
035
rB* ( D* K )  0.09600..051
[54o ,83o ]
[0.067,0.125]
[0.094,0.175]
BaBar Dalitz plot method
ICHEP 2010, Paris
Fernando Martinez Vidal
14
γ from GLW method
arXiv:1007.0504.
Sub. to Phys. Rev. D
• Update with final data sample (468 M BB pairs). Previous analysis used 383 M BB pairs
PRD77, 111102 (2008)
• Reconstruct B →DK
final states with D→K+K-,π+π- (CP even) and D→KS0,KSw,KSf (CP
odd) (five different final states for each B charge)
±
±
B-→DK-
All components
Continuum + BB BG
Continuum + BB + D BG
• Efficiencies improved substantially (40% to 60% relative) with respect to previous measurement
• Reprocessed data set with improved track reconstruction
• Improved particle identification
• Introduce Fisher discriminant in the fit rather than apply cut on event shape variables
ICHEP 2010, Paris
Fernando Martinez Vidal
15
γ from GLW method
• Extract signal yields fitting directly to observables R
RK / 



( B  DCP  K )  ( B  DCP  K )

( B   DCP   )  ( B   DCP   )

ACP 



±
K/
arXiv:1007.0504.
Sub. to Phys. Rev. D
, RK/, and ACP±
RK /  


0
( B  D K )  ( B  D K  )
0
( B  D  )   ( B  D   )

0

( B  DCP  K )  ( B  DCP  K )

( B   DCP  K  )  ( B   DCP  K  )

0
RCP 


RK / 

RK / 
3.6s significance of CPV in B±→DK± from ACP+
ACP   0.25  0.06  0.02
ACP   0.09  0.07  0.02
RCP   1.18  0.09  0.05
RCP   1.07  0.08  0.04
ICHEP 2010, Paris
Fernando Martinez Vidal
16
γ from GLW method
• Extract signal yields fitting directly to observables R
RK / 



( B  DCP  K )  ( B  DCP  K )

( B   DCP   )  ( B   DCP   )

ACP 



±
K/
arXiv:1007.0504.
Sub. to Phys. Rev. D
, RK/, and ACP±
RK /  


0
( B  D K )  ( B  D K  )
0
( B  D  )   ( B  D   )

0

( B  DCP  K )  ( B  DCP  K )

( B   DCP  K  )  ( B   DCP  K  )

0
RCP 


RK / 

RK / 
3.6s significance of CPV in B±→DK± from ACP+
ACP   0.25  0.06  0.02
x  0.057  0.039  0.015
ACP   0.09  0.07  0.02
RCP   1.18  0.09  0.05
RCP   1.07  0.08  0.04
1
x  RCP  (1  ACP  )  RCP  (1  ACP  )
4
x  0.132  0.042  0.018
Consistent with and of similar
precision to Dalitz results
x  0.103  0.037  0.006  0.007
x  0.060  0.039  0.007  0.006
[Dalitz results]
ICHEP 2010, Paris
Fernando Martinez Vidal
16
γ from GLW method
• Extract signal yields fitting directly to observables R
RK / 



( B  DCP  K )  ( B  DCP  K )

( B   DCP   )  ( B   DCP   )

ACP 



±
K/
arXiv:1007.0504.
Sub. to Phys. Rev. D
, RK/, and ACP±
RK /  

0
( B  D  )   ( B  D   )

0
RCP 
3.6s significance of CPV in B±→DK± from ACP+

0
( B  D K )  ( B  D K  )

( B  DCP  K )  ( B  DCP  K )

( B   DCP  K  )  ( B   DCP  K  )

0


RK / 

RK / 
Dalitz
ACP   0.25  0.06  0.02
ACP   0.09  0.07  0.02
RCP   1.18  0.09  0.05
RCP   1.07  0.08  0.04
ICHEP 2010, Paris
1
x  RCP  (1  ACP  )  RCP  (1  ACP  )
4
x  x (Dalitz)  0.163  0.055
(3.0s )
x  x (GLW)  0.189  0.062
(3.1s )
Fernando Martinez Vidal
16
γ from GLW method
• Extract signal yields fitting directly to observables R
RK / 



( B  DCP  K )  ( B  DCP  K )

( B   DCP   )  ( B   DCP   )

ACP 



±
K/
arXiv:1007.0504.
Sub. to Phys. Rev. D
, RK/, and ACP±
RK /  

0
( B  D  )   ( B  D   )

0
RCP 
3.6s significance of CPV in B±→DK± from ACP+

0
( B  D K )  ( B  D K  )

( B  DCP  K )  ( B  DCP  K )

( B   DCP  K  )  ( B   DCP  K  )

0


RK / 

RK / 
Dalitz+GLW
ACP   0.25  0.06  0.02
ACP   0.09  0.07  0.02
RCP   1.18  0.09  0.05
RCP   1.07  0.08  0.04
1
x  RCP  (1  ACP  )  RCP  (1  ACP  )
4
4.4s significance of CPV in B±→DK±
ICHEP 2010, Paris
x  x (Dalitz  GLW)  0.175  0.040
Fernando Martinez Vidal
16
γ from GLW method
arXiv:1007.0504.
Sub. to Phys. Rev. D
• Use frequentist interpretation (similar to Dalitz plot method) to obtain weak phase g and
hadronic parameters rB, dB from RCP± and ACP± observables
RCP   1  rB2  2rB cos d B cos g
Weak sensitivity to rB
ACP 
 2rB sin d B sin g

1  rB2  2rB cos d B cos g
[54o ,83o ]
[0.067,0.125]
BaBar Dalitz plot method
ICHEP 2010, Paris
Fernando Martinez Vidal
176
Summary and outlook
• Recent progress on g, the hardest UT angle to
measure
• BaBar Dalitz plot method approach drives the
measurement and benefited from synergy with Dmixing analysis (e.g. reduction of experimental
uncertainties inherent to the model uncertainty)
(see Matt Bellis talk later in this session)
• First sign of an ADS signal in B
±
→ DK± and
B± → D* K±
• Compelling evidence of direct CPV in
B± → D(*)K(*)± decays
g (mod 180)  ( 68  14  4  3 )
stat
syst
model
3.5s significance of CPV, B± → D(*)K(*)±
combined, Dalitz only
3.6s significance of CPV, B± → DK± only,
GLW only
ICHEP 2010, Paris
Fernando Martinez Vidal
18
Summary and outlook
• Recent progress on g, the hardest UT angle to
measure
• BaBar Dalitz plot method approach drives the
measurement and benefited from synergy with Dmixing analysis (e.g. reduction of experimental
uncertainties inherent to the model uncertainty)
(see Matt Bellis talk later in this session)
• First sign of an ADS signal in B
±
→ DK± and
B± → D* K±
• Compelling evidence of direct CPV in
B± → D(*)K(*)± decays
x  x (Dalitz  GLW)  0.175  0.040
4.4s significance of CPV in B±→DK± only,
Dalitz+GLW combined
ICHEP 2010, Paris
Fernando Martinez Vidal
18
Summary and outlook
Experiments providing most of
analyses today
• Recent progress on g, the hardest UT angle to
measure
• BaBar Dalitz plot method approach drives the
3.1 GeV e+
9 GeV e–
468M BB pairs
measurement and benefited from synergy with Dmixing analysis (e.g. reduction of experimental
uncertainties inherent to the model uncertainty)
3.5 GeV e+
8 GeV e–
(see Matt Bellis talk later in this session)
o
657M BB pairs ~10-15
• First sign of an ADS signal in B
±
→ DK± and
B± → D* K±
Experiments that can also give
results in near future
• Compelling evidence of direct CPV in
B± → D(*)K(*)± decays
• Close to “last word” from BaBar (~10-15 error)
• Still statistics limited, even with full data sets
• BaBar “legacy” g average from GLW, ADS
o
~2-3o
Planned facilities
and Dalitz plot methods in progress
<1o
ICHEP 2010, Paris
• Need to reduce the error in order to see possible
deviations
Fernando Martinez Vidal
18
Backup
BaBar detector and data sample
Delivered luminosity
Recorded luminosity
Instrumented
Flux return
(Muon and hadron
reco.)
Recorded Υ(4S): 432 fb-1
Recorded Υ(3S): 30.2 fb-1
Recorded Υ(2S): 14.5 fb-1
3.1GeV
e+
Off peak
Magnet
(1.5 T)
Υ(3S)
Υ(2S)
e9GeV
Υ(4S)
Detector of Internally
Reflected Cherenkov
(PID, Kaon separation
from pions)
Drift Chamber
(Main tracking system)
Silicon Vertex Tracker
(Tracking at low momentum
and vertex reconstruction)
Electromagnetic
Calorimeter
(Detection of neutral
particles)
•
BaBar data taking ended on 7th April 2008
• BaBar recorded 470M BB at Υ(4S)
γ from D Dalitz plot method
• Signal yields as used in the final fit for CP parameters
arXiv:1005.1096.
Sub. to Phys. Rev. Lett.
PRD81, 112002 (2010)
B decay mode
BaBar (KS+-)
468 M BB
BaBar (KSK+K-)
468 M BB
Belle (KS+-)
657 M BB
B±→DK±
896±35
154±14
757±30
B±→D*(D0)K±
255±21
56±11
168±15
B±→D*(Dg)K±
193±19
30±7
83±10
B±→DK*±
163±18
28±6
(not updated to
657 M BB)
• Efficiencies
improved substantially (20% to 40% relative) with respect to previous BaBar
measurement (383 M BB) PRD78, 034023 (2008)
• Reprocessed data set with improved track reconstruction
• Improved particle identification
• Revised K selection criteria: negligible background from D→  h h and B→Da (1260)
S
+ - + -
1
D→KS+-,KSK+K- amplitude analysis
arXiv:1004.5053. Accepted by Phys. Rev. Lett.
• Extract D amplitude from an independent analysis of flavor tagged D mesons (D →D π )
• Experimental analysis using complete data sample benefits from synergy with D-mixing analysis
0
0
*+
0
Model determined without (reference) and with D-mixing
+
• Fit for amplitudes relative to CP eigenstates [K r(770) and K a (980)] and assume no direct CPV
S
540 800±800
S 0
79 900±300
See Matt Bellis talk in this session
for more details
γ from D Dalitz plot method
• CP violation parameters are extracted from simultaneous unbinned maximum likelihood fit to B
±
→ D(*) K(*)± data using mES, DE, Fisher and the Dalitz plot distributions (s+,s-) arXiv:1005.1096.
Sub. to Phys. Rev. Lett.
B-→DK-
B+→DK+
Most precise measurement of (x,y)
Consistent results with latest Belle
results
PRD81, 112002 (2010)
ICHEP 2010, Paris
γ from D Dalitz plot method
arXiv:1005.1096.
Sub. to Phys. Rev. Lett.
γ from D Dalitz plot method
arXiv:1005.1096.
Sub. to Phys. Rev. Lett.
Other hadronic parameters relevant for g
• Updated search for B →D K and B+→D K
• Can only proceed through annihilation or rescattering
+
+ 0
+ *0
•Allows an estimation of r for B from r for B needed for
• B →D K measures r sin(2b+g) in time-dependent asymmetry
• B →D K measures g in direct CPV (similar to B )
• BaBar analysis with full data sample: 468 M BB arXiv:1005.0068.
Submitted to PRD
• No evidence for signals
0
B
0
0
0
0
0
*0
0
B
+
0
B
+
BaBar vs WA
24
-16
( 73
)
Courtesy of V. Tisserand and the CKM fitter group
21
( 71-25
)
Backup
CKM angle g
•
ui  u, c, t
The electroweak coupling strength of W± to
quarks described by the CKM matrix
d
s
2


u  1

2

2


c
Vij  

1
2
 3
2
A

(
1

r

i
h
)

A

t


d j  d , s, b
b

A ( r  ih ) 


2
4
A

O
(

)


1



3
Wolfenstein parameterization
~0.22
A~0.8
r~0.16
h~0.34
Unitarity condition from 1st and 3rd columns
Overconstraint apex coordinates
• CP violation measurements give angles
• Semileptonic decay rates (and other
methods) give sides
• Precise measurement of SM parameters
• Search for NP in discrepancies of
redundant measurements
CKM angle g
γ from B→DK decays
Decay amplitude
No D-mixing nor CPV
D  K S 

0
CP-even
CP-odd
0





 
A( B  [ K S   ]K )  

π+ π

K- K +
K0sπ0
K0sω
K0sΦ
K0sρ
GLW-like method
D  K S   
 rB e







ig  id B
b→c
b→u
D  K S   
D 0  K S   
GLW
0




 

A( B  [ K S   ]K )  

Large interferences in some Dalitz plot regions


Strong phases varying over the Dalitz plane
Gronau, London, Wyler, PLB 253, 483 (1991); PLB 265, 172 (1991)







 rB e ig id B
b→c
b→u
γ from B→DK decays
K+π-
D  K S   
 rB e
ig  id B
b→c
b→u
D  K S   
D 0  K S   




 

A( B  [ K S   ]K )  
CF

Large interferences in some Dalitz plot regions


Strong phases varying over the Dalitz plane
Atwood, Dunietz, Soni, PRL 78, 3357 (1997)
0

CF K*(892)+π-
D  K S 




 
A( B  [ K S   ]K )  



K+π-π0 ADS
K+π-π+π-
No D-mixing nor CPV
DCS K*(892)+π-
Decay amplitude

0
ADS-like method
0
K*(892)+π-
b→c
 rB e ig id B
DCS K*(892)+π-
b→u













