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3/15/01 Colorado State University 1
sin2β in the BaBar ExperimentWalter Toki
Colorado State UniversityRepresenting the BaBar Collaboration
FRONTIERS IN CONTEMPORARY PHYSICS - II Vanderbilt University
March 5-10, 2001
3/15/01 Colorado State University 2
• CKM physics• Unitarity Triangle, Mixing, CP eigenstates
• PEPII & BaBar detector
• sin2β analysis• reconstruction, vertexing, tagging, fitting
• Summary
OUTLINE
3/15/01 Colorado State University 3
In the Standard Model for weak interactions the charged hadroniccurrent is
The weak eigenstate quarks are related to the mass eigenstate quarksby unitary transformations,
This can be combined into another unitary matrix V called the Cabbibo-Kobayashi-Masakawa (CKM) Matrix.
This 3× 3 unitary matrix can be parametrized by 3 real parametersand 1 complex phase, which introduces CP violation.
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==
tbtstd
cbcscd
ubusud
du
VVVVVVVVV
VUU †
LLcc duJ ′′= µµ γ
†uLL Uuu =′ LdL dUd =′
3/15/01 Colorado State University 4
This is simplified by the Wolfenstein parametrization to order λ3,Where λ=sinθC.
( )
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−−−−−
−−≅
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2/12/1
23
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32
ληρλλλλ
ηρλλλ
AiAA
iA
VVVVVVVVV
V
tbtstd
cbcscd
ubusud
A unitarity constraint (columns 1 & 3) yields,
( ) ( ) 011
01
0
*
*
*
*
***
=−−++++−
=++
=++
ηρηρ iiVVVV
VVVV
VVVVVV
cbcd
tbtd
cbcd
ubud
tbtdcbcdubud
These complex numbers form a triangle in the ρ−η plane
3/15/01 Colorado State University 5
η
ρ10
(ρ, η)*
*
cbcd
ubud
VVVV
*
*
cbcd
tbtd
VVVV
Unitary Triangle in the Complex ρ − η plane
��
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*arg
tbtd
cbcd
VVVVβ
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�−= *
*arg
ubud
cbcd
VVVVγ
γ
��
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�−= *
*arg
ubud
tbtd
VVVVα
α
We note that since is real, then *cbcdVV β2
*
*i
tbtd
tdtb eVVVV =
Notation: Belle uses φ1 for β
01 *
*
*
*=++
cbcd
tbtd
cbcd
ubud
VVVV
VVVV
3/15/01 Colorado State University 6
0
0.2
0.4
0.6
0.8
1
-1 -0.5 0 0.5 1
εK
∆ms/∆md
∆md
|Vub/Vcb|
ρ
η
Constraints for the (ρ,η) triangle apex
Bd mixing � ∆mdb→ ulν, B →ρlν � Vub , D*lν � VcbBs mixing � ∆ms / ∆mdKaon mixing & BK decays � εK
Blue blobs, 95% CL estimates of a set oftheoretical models
β
3/15/01 Colorado State University 7
Using K0 mixing formalism, the B wavefunction iswritten as, . The mass matrix is then,( ) ( ) 00 BtbBta +=ψ
( )( )
( )( )��
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Γ−Γ−Γ−Γ−
=��
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tbta
iMiMiMiM
tbta
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2/2/2/*2/
*12
*12
12�
( ) ( ) ( ) ( ) ( ) ( )
( ) [ ] *12
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12122/2/
000000
,121
,
Γ−Γ−=±=
+=+=
∆−∆Γ−−Γ−±
+−−+
iMiM
pqeeeetf
BtfBtfqptBBtf
pqBtftB
tdmitimtt
B meson time evolution,
BB Mixing
3/15/01 Colorado State University 8
B0 B0 Mixing into self tagging final states f and f
b
d
d
bu,c,t u,c,tW WB0 B0
d
bB0
W
W
b
dB0
The dominant diagrams use the top quark and the calculation yields, 2*
2
222
12 62 tbtd
BBtFd VVBfMmGMm
π==∆
If the final states f and f are self tagging distinguishing B0
or B0 decays, then we have conventional mixing via box diag.
( ) ( )( ) ( )
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��
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Γ−
Γ−
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2cos10
00
00
tmeftBB
tmeftBB
dt
dt Unmixed
Mixed
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( ) ( )( ) ( ) ( ) ( )
( ) ( )( ) ( ) ( ) ( )���
�
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�∆+∆
−−
+∝→Γ
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−+
+∝→Γ
Γ−
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mtmtetfB
tcp
tcp
sinImcos2
12
10
sinImcos2
12
10
220
220
λλλ
λλλ
( )( )cp
cpCP fA
fApqηλ ≡with and ( ) ( ) cpcpcpcp fHBfAfHBfA 00 , ==
Squaring the amplitudes leads to CP violation effects
B0
B0 SCP KJf ψ/=B0
If decays occur to a common CP eigenstate fcp, accessibleto both B0 and B0, there is mixing and interference via twoamplitudes,
B0 B0 Mixing into CP eigenstates fcp
( )CPCP fCP=η
3/15/01 Colorado State University 10
The best mode has the quark decay , with modes
( )( ) 1,
// 2
*
*
*
*
*
*≅==≡ − λ
ψψλ βi
cdcs
cdcs
cscb
cscb
tbtd
tbtd eVV
VVVV
VVVV
VVKsJAKsJA
pq
sccb →
dscc
d
bW-
0*
0*
0*
0*
,,
,,,
,',','
,/,/,/
cpcLcSc
cpcLcSc
cpLS
cpLS
KKK
KKK
KJKK
KJKJKJ
χχχ
ηηη
ψψψ
ψψψ
The golden mode, J/ψKs, has the largest measureable rate,λ directly measures the 2β phase, and has magnitude 1.
B0
CP= −1CP= +1
Measured by BaBar
Choice of fCP eigenstates
BB mixingB0→J/ψΚ0
Κ0 →ΚS
3/15/01 Colorado State University 11
dscc
d
bW-B0
dccs
d
b
gluonB0
u
Amplitude ~ VcbVcs*~Aλ2
Amplitude ~ VubVus*~Aλ4 (ρ-iη)Penguin contamination
Leading amplitude forB0→J/ψΚS
These “golden modes” are clean. The leading term is VcbVcs*whereas the Penguin term is VubVus*.
other VtbVts* term has same phase
3/15/01 Colorado State University 12
ddcc
d
bW-B0
dccd
d
b
gluonB0
t
Amplitude ~ VcbVcd*~Aλ3
Amplitude ~ VtbVtd*~Aλ3 (1-ρ-iη)Penguin contamination
Leading amplitude forB0→D+D−,J/ψπ0
Other possible quark decays include, b→ ccd, These include CP modes, B0→D+D−, J/ψπ0, However leading term, VcbVcd* , in this mode is not much larger than, VtbVtd* , so these modes are less desirable.
3/15/01 Colorado State University 13
B0
B0SCP KJf ψ/=,, πν DeD −+ ( ) 040 BsB �ϒ⇐
( ) ( )( )fBftBt
fB ttmettP −∆−=−Γ− sin2sin1, β
Since the velocity in the CMS is very small, measuringposition in the CMS is hopeless.
( ) ( )( )fBftBt
fB ttmettP −∆+=−Γ− sin2sin1, β
B’s are coherently pair produced, , in the reaction, . In the center mass system, ( ) 004 BBsee →ϒ→−+
Experimental Considerations( ) ( ) ( ) ( )1221 0000 BBBB −
Tagging B
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A special trick is used to measure the time difference usinga moving CMS in the lab frame. The Lorentz transform yields,
( ) ( )( )**
****
fB
ffBBfB
ttc
ctzctzzz
−≅
−−−=−
γβ
βγβγ
The time difference ∆t is translated into a ∆z difference.Hence we measure the difference in z ( boost direction ) Between the fCP and the recoiling/tagging B, ∆z ~ few 100 µm
Other experimental challenges• reconstructing the fCP CP eigenstates, • reconstructing vertices • flavor of the Recoiling B.
Moving CMS � Asymmetric Collider
3/15/01 Colorado State University 15
( )( )
( )( )tme
fB
tme
fB
t
t
∆∆−
=→Γ
∆∆+
=→Γ
∆−
∆−
cos1
) (
cos1
) (
0
0
( )( )( )
( )( )( )tme
fB
tme
fB
tCP
tCP
∆∆−
=→Γ
∆∆+
=→Γ
∆−
∆−
sin1
sin1
0
0perfect ∆z resolution smeared ∆z resolution
Expected ∆z distributions for Mixing into states f, f ,fCP
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�
3/15/01 Colorado State University 16
PEPII e+e- Collider
• Beam energies, e−/e+ , 9/3.1 GeV provide γβ=.56 • e+/e− currents of 2.14/.92 amperes• Peak Luminosity ~3.1 x 1033 cm-2s-1
• SLAC Linac highly efficient injector for PEPII• BaBar detector data logging efficiency +95%• Max. integrated luminosity in one day is 170 pb-1
• overall performance has been astonishingly good
3/15/01 Colorado State University 17
02000400060008000
100001200014000160001800020000220002400026000
6/1/997/1/998/1/999/1/9910/1/9911/1/9912/1/991/1/002/1/003/1/004/1/005/1/006/1/007/1/008/1/009/1/0010/1/0011/1/00
Tota
l del
iver
ed l
umin
osity
(pb
-1)
BaBa
r rec
orde
d lu
min
osity
(pb
-1)
PEPII Delivered Luminosity
Total Recorded Luminosity
Off-peak Recorded Luminosity
Integrated Luminosity October 1999 to November 2000
RunI ~23fb-1, 23M BB produced in October 99 -November 00
New Run started, expects to log >32 fb-1 by August 31
3/15/01 Colorado State University 18
0
100
200
300
400
500
600
700
1 2 3 4 5 6 7
0
5
10
15
20
25
30 Series2Series3Series1
1999 2000 2001 2003 2003 2004 2005
Inte
grat
e lu
min
osity
(/fb
)Projected annual PEPII Luminosity
Peak
lum
inos
ity (1
0+33 )
peak L integrated L/year total integrated L
=> Terrific motivation for grads. & postdocs to join BaBar
3/15/01 Colorado State University 19
BABARBABAR CollaborationCollaboration9 Countries72 Institutions554 Physicists
USA [35/276]California Institute of TechnologyUC, IrvineUC, Los AngelesUC, San DiegoUC, Santa BarbaraUC, Santa CruzU of CincinnatiU of ColoradoColorado StateFlorida A&MU of IowaIowa State ULBNLLLNLU of LouisvilleU of MarylandU of Massachusetts, AmherstMITU of MississippiMount Holyoke CollegeNorthern Kentucky UU of Notre DameORNL/Y-12U of OregonU of PennsylvaniaPrairie View A&MPrincetonSLACU of South CarolinaStanford UU of TennesseeU of Texas at DallasVanderbiltU of WisconsinYale
Italy [12/89]INFN, U of BariINFN, U of FerraraLab. Nazionali di Frascati dell' INFNINFN, U of GenovaINFN, U of MilanoINFN, U of NapoliINFN, U of PadovaINFN, U of PaviaINFN, U of PisaINFN, U of Roma and U "La Sapienza"INFN, U of TorinoINFN, U of Trieste
Norway [1/3]U of Bergen
Russia [1/13]Budker Institute, Novosibirsk
United Kingdom [10/80]U of BirminghamU of BristolBrunel UniversityU of EdinburghU of LiverpoolImperial CollegeQueen Mary & Westfield CollegeRoyal Holloway, University of LondonU of ManchesterRutherford Appleton Laboratory
Canada [4/16]U of British ColumbiaMcGill UU de MontréalU of Victoria
China [1/6]Inst. of High Energy Physics, Beijing
France [5/50]LAPP, AnnecyLAL OrsayLPNHE des Universités Paris 6/7Ecole PolytechniqueCEA, DAPNIA, CE-Saclay
Germany [3/21]U RostockRuhr U BochumTechnische U Dresden
3/15/01 Colorado State University 20
DIRC (PID)144 quartz bars
11000 PMs
1.5T solenoid
EMC6580 CsI(Tl) crystals
Drift Chamber40 stereo layers
Instrumented Flux Returniron / RPCs (muon / neutral hadrons)
Silicon Vertex Tracker5 layers, double sided strips
e+ (3.1GeV)
e- (9GeV)
BaBar Detector
• SVT: B vertex z resolution ~70 microns• Tracking : σ(pT)/pT = 0.13% × pT ⊕ 0.45%• DIRC : K-πseparation >3.4σ for P<3.5GeV/c• EMC : σE/E = 2.3%⋅E-1/4 ⊕ 1.8%See Stefano Bettarini’s talk, Monday parallel
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BaBar DetectorPhoto
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BaBarControl RoomPhoto
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Red line is PEPII luminosity. nearly continuous
Green Bar; BaBar logging data
Black Bar; BaBar not loggingdata while PEP beams available
High efficiency data loggingand high peak L leads tovery high integrated L
PEPII refill time is afew minutes!!
Daily Operations PEPII Performance Plot
3/15/01 Colorado State University 24
• Reconstruction of exclusive fCP or BCP eigenstates
• Reconstruction of the vertices• reconstruction of CP state• reconstruction of recoiling/tagging B
• B flavor tagging mistag rates• reconstruction of self tagging Bflav modes to measuremistag rates and dilutions of tagging categories
• Fitting and extracting sin2β• fit sin2β and dilutions using both BCP and Bflav modes
Analysis Steps
3/15/01 Colorado State University 25
Reconstruction of CP states( ) ( )
( ) ( )( ) L
S
S
KeeJ
KJee
KeeJ
−+−+
−+−+−+−+
−+−+−+
µµψ
ππψππµµψ
ππππµµψ
,/
/,,'
,,,/ 00
• R2 Shape, cosθthrust cuts to reject continuum • BB events are spherical
•Particle ID on Leptons• EMC and IFR cuts
• Helicity angle cut on Lepton (λψ= ±1)• signal ~ sin2θH , bkgd cosθH~ ±1
• J/ψ, ψ′, π0, KS mass cuts• KS vertices detached• ∆E ( = EB −Ebeam) and MES (= sqrt(Ebeam
2−PB2 ) ) cuts
• variables are uncorrelated, bkgd is usually flat
Y(4s)
B0
J/ψ sin2θH
sin2θB
e+
e−
3/15/01 Colorado State University 26
Plots
• ∆Ε versus MES
• MES
• ∆Ε
Reaction is very clean and backgrounds are uniformlydistributed
J/ψ(µ+µ−) Ks (π+π−)
3/15/01 Colorado State University 27
J/ψ(µ+µ−) Ks (π+π−)
Identified K−
Indicates a recoiling B0.
Candidate Event
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Final sample of KS modes for CP fitting
387 events in the KS mode, ~96% purity MES>5.27 GeV, ∆E<3σ
3/15/01 Colorado State University 29
J/ψKL Analysis• KL will produce hadronic showers in the EMC and IFR
• Require EMC shower (>200 MeV) and the IFR hits (2 layers) not associated with a charged track
• Combine KL direction and reconstructed J/ψ momentum to kinematically predict KL energy.
• Increased efficiency at the cost of larger backgrounds
• CP Opposite to golden KS modes
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∆E=E(J/ψ)-E(KL )- Ebeam, Signal peaks at zero
386 Events total in the KL mode, ~39% purity
J/ψKL Analysis
EMC IFR
3/15/01 Colorado State University 31
Vertexing BCP and Btag
BCP
Btag
P(e-)= 9 GeV
∆z
P(e+)= 3.1GeV
• ∆z = γβc∆t= .56 c ∆t• B lifetime, ∆z = ~250 microns• z vertex resolution of J/ψ of BCP ~70 µm (core ~45 µm)• z vertex resolution of BTAG is ~170 microns
• charm decays removed by refitting w/o high χ2 tracks• identified KS and Λ tracks directions used in fit
• B direction is used to correct ∆z event by event• final ∆z resolution is ~190 microns
3/15/01 Colorado State University 32
B flavor Tagging
• B0 tagging in separate mutually exclusive categories• fast lepton, pe >1 GeV, pµ >1.1 GeV • sum of charged Kaons ≠ 0, • neural net 1, mostly isolated unidentified leptons• neural net 2, mostly slow pions from c → D*→ π+D
• Each category has different• efficiencies ε, mistag rates w and dilutions, D=1-2w • effective tagging efficiencies, Q= ε(1-2w)2 , σ(sin2β) ∝ 1/sqrt(Q)
• Each category is measured with data and cross checked with MC• Fit dilution & sin2β in both BCP and Bflav modes simultaneously.
b c
µ−,e−
s K−
B0W−tag
3/15/01 Colorado State University 33
Bflav modes (f and f ) separated by tag category
Self tagging Bflavmodes includeD∗+ π−, D∗+ ρ−,D∗+ a1
−, D+π−,D+ρ−, D+a1
−,J/ψΚ∗0 (Κ+π−)
3/15/01 Colorado State University 34
Results of fitting for mistag rates
• efficiency ε• average mistag rate [w(B0)+w(B0)] /2 • difference in mistag rate between w(B0)- w(B0) • effective tagging efficiency Q• values reproduced using separate D*lν sample
3/15/01 Colorado State University 35
∆t distributions for self tagged Bflav modes by B0/B0 tag
Preliminary mixing results∆md=0.519 ± 0.020± 0.016 ps-1
Cross checks with other physics, fit for ∆md
Asymmetry
∆z distributions ( ) ( )( ) ( )
( )tmtNtNtNtNA
d
unmixmix
unmixmix
∆∆∝∆+∆∆−∆=
cos
Raw
3/15/01 Colorado State University 36
Mixing ∆md
Comparisons
See BaBar talk fromGregory Dubois,Wednesday parallel
3/15/01 Colorado State University 37
separated KS & KL Modes whichhave opposite CP => opposite shifts in ∆t.
∆t distributions for BCP Modes by B0/B0 tag
3/15/01 Colorado State University 38
• Simultaneously fit CP events (BCP) and Mixing (Bflav) events to extractsin2β (1 parameter ) and the dilutions for each tag category anddilution differences between B0 and B0 (2 x 4 parameters )• This uses all measured information and properly correlates errors• other parameters
• ∆z resolution (9 parameters )• background dilutions ( 8 parameters )• background resolutions ( 3 parameters )• backgrounds ∆t distribution ( 6 parameters )
• TOTAL 35 parameters• Fix ∆md =0.472 ps-1 and τB =1.548 ps to PDG values
Likelihood
3/15/01 Colorado State University 39
Other remarks• J/ψKL bkgd fit has non-symmetric CP for J/ψKLπ0 bkgd(-.68=sin2β)• Dilutions allowed D(B0) and D(B0) allowed to differ• A(cp) value was hidden to avoid people bias until 2wks before conf.Checks
• lifetime consistent PDG (1.55), τ(B0) =1.51± .05± .03ps • mixing consistent with PDG, • toy MC checks on fitting, fitting MC samples, • fitting non-CP data, split data sets, • independent fitting and tagging programs
CP Vertex Parametrization• event by event ∆z errors used in fit• 3 gaussians, core (88%)+tail(11%)+outlier(1%)• fit variables
• scale factors of core and tail (2) • fractions of tail and outlier (2)• ∆z bias for 4 tagging categories and tail (5)
3/15/01 Colorado State University 40
Likelihood Function for CP and mixing events( )�
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i
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=RtMDDe tBtagCPN
isinIm
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4ln
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200 BB DD
D+
= 00 BB DDD −=∆
CP
data
sets
f
f
f
fB
flav
or d
ata
sets
3/15/01 Colorado State University 41
• uncorrected forDilution and backgrounds
KL modeηcpsin2β = 0.87± .51 (stat)
KS modeηcpsin2β = 0.25± .22 (stat)
( ) ( ) ( )( ) ( )tNtN
tNtNCPA
tagBCP
tagBCP
tagBCP
tagBCP
∆+∆
∆−∆= 00
00
Raw Asymmetry
( )CPCP fCP=η
3/15/01 Colorado State University 42
KL modeKS modes Combined fit
± 1σ
Loglikelihood of sin2β measurements
sin2β=0.34 ±0.20(stat) ±0.05(sys)
3/15/01 Colorado State University 43
CP fitting selected samples
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Cross ChecksSeparate by mode and tagging categories, results randomlyscattered about median value
Ks mode only
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Systematic sin2β Error Estimates
• largest ∆t error due to Dch-SVT alignment• some KS and KL errors anti-correlate and tend to cancel infull sample fits
3/15/01 Colorado State University 46
sin2β values
Other experiments
World Average
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sin2β measurement and Unitarity Triangle
3/15/01 Colorado State University 48
Parameter Value � Error(s)
jVudj 0:97394� 0:00089
jVusj 0:2200� 0:0025
jVubj (3:49� 0:27� 0:55)� 10�3
CKM
jVcdj 0:224� 0:014
Parameters
jVcsj 0:969� 0:058
jVcbj (40:75� 0:40� 2:0)� 10�3
j�Kj (2:271� 0:017)� 10�3
CP violating
�md (0:487� 0:014) ps�1
and
�ms WA (Beauty2000) amplitude spectrum
Mixing Observables
sin2�BaBar 0:34� 0:21
sin2�WA 0:49� 0:16
mt (166� 5) GeV
mK (493:677� 0:016) MeV
�mK (3:4885� 0:0008)� 10�15 GeV
mBd
(5:2794� 0:0005) GeV
Experimental
mBs
(5:3696� 0:0024) GeV
Parameters
mW (80:419� 0:056) GeV
GF (1:16639� 0:00001)� 10�5 GeV�2
fK (159:8� 1:5) MeV
mc (1:3� 0:1) GeV
BK 0:87� 0:06� 0:13
�cc 1:38� 0:53
�ct 0:47� 0:04
Theoretical
�tt 0:574� 0:004
Parameters
�B(MS) 0:55� 0:01
fBdpBd (230� 28� 28) MeV
� 1:16� 0:03� 0:05
Parametersof theUnitarityTriangle
3/15/01 Colorado State University 49
Summary• Worlds most precise sin2β measurement
• Other cross checking CP modes to be added, J/ψK*0, χKS
• Many other BaBar analyses presented and underway• see BaBar talks by Dubois, Vasseur, Colberg, Soffer
• New run started, data should be >doubled by August 2001
• By 2005 BaBar should log ~500 fb-1
sin2β=0.34 ±0.20(stat) ±0.05(sys)