j. albert caltech october 7, 2004
DESCRIPTION
Measurement of and. 2b+g. g. (or φ 3 and 2 φ 1 + φ 3 ). J. Albert Caltech October 7, 2004. The Angle of the Unitarity Triangle. We expect to be approximately (57 ±9)º , if the Standard Model is consistent . But how to directly measure it…. - PowerPoint PPT PresentationTRANSCRIPT
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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)
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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
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 3
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
*
*
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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)
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 4
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)
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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,)
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 5
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
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BB-- DD00CPCPKK(*)-(*)- yields from yields from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 6
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-)
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BB-- DD(*)0(*)0CPCPKK-- yields from yields from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 7
B+ D1*0 K+ B+ D1
*0π+
B+ D2*0 K+ B+ D2
*0π+
B+ D10 K+
B+ D20 K+
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GGronauronau-L-Londonondon-W-Wyleryler Method Results: Method Results:
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 8
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
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GGronauronau-L-Londonondon-W-Wyleryler Method Results: Method Results:
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 9
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
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The Atwood-Dunietz-Soni MethodThe Atwood-Dunietz-Soni Method
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 10
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
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BB-- DD(*)0(*)0ADSADS((KK++ππ--)) KK-- at at
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 11
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)
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BB-- DD(*)0(*)0ADSADS((KK++ππ--)) KK-- at at
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 12
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
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ADS Constraints onADS Constraints on r rBB from and from and
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 13
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
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The The DD(*)0(*)0((DD003-body)3-body)KK++ Dalitz Method Dalitz Method
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 14
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
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DD00(K(Kssππππ))KK++ Dalitz Fit fromDalitz Fit from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 15
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:
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DD(*)0(*)0(K(Kssππππ))KK++ yields from and yields from and
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 16
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
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Dalitz Method Constraints on Dalitz Method Constraints on from from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 17
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
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Dalitz Method Constraints on Dalitz Method Constraints on from from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 18
Errors using toy MC experiments and frequentist approach
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Sin(2Sin(2ββ++) from ) from DD(*)(*)π/Dπ/D(*)(*)ρρ
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 19
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
~ ~
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Lepton tag Kaon tag
D*Combinatoric BBPeaking BB Continuum
DD(*)(*)ππ sin(2 sin(2ββ++) results from) results from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 20
• 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
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DD(*)(*)ππ sin(2 sin(2ββ++) results from) results from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 21
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]
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DD(*)0(*)0KK(*)0(*)0 results from results from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 22
(*)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
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DD(*)0(*)0KK(*)0(*)0 results from results from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 23
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
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NEW!solution for
(in V-V and P-P modes)
A Different ApproachA Different Approach:: Using B Using B D D(s)(s)(*)(*)DD(*)(*)
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 24
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:
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Constraints on gamma from Constraints on gamma from DD(s)(s)(*)(*)DD(*)(*)
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 25
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:
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ConclusionsConclusions
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 26
“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(*)
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Backup Slides
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DD00(K(Kssππππ))KK++ Dalitz Fit fromDalitz Fit from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 15
)(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
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DD00(K(Kssππππ))KK++ yields from and yields from and
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 16
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)
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Dalitz Method Constraints on Dalitz Method Constraints on from from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 18
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
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DD(*)(*)ππ sin(2 sin(2ββ++) results from) results from
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 21
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
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A Different ApproachA Different Approach:: Using B Using B D D(s)(s)(*)(*)DD(*)(*)
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 25
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:
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How can How can DD(s)(s)(*)(*)DD(*)(*) decays measure decays measure gammagamma??
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 26
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(*)
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Extracting gamma from Extracting gamma from DD(s)(s)(*)(*)DD(*)(*) decaysdecays
FPCP-2004 Oct. 7, 2004 Measurement ofMeasurement of and and 22ββ++ J. Albert 27
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: