F. Martínez-Vidal
IFIC – Universitat de València-CSIC
Measurement of the CKM-matrix angle (3)
(at B Factories)
OutlineIntroduction: CKM, UT and CPV observablesAccess to Experiments & analysis techniquesDalitz analysisConclusions and perspectives
International WE Heraeus Summer School on Flavor Physics and CP Violation
Technische Universität Dresden (Germany)September 2nd, 2005
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Introduction
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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The Cabibbo-Kobayashi-Maskawa matrix
• In the Standard Model, the CKM matrix elements Vij describe the electroweak coupling strength of the W to quarks
• Complex phases in Vij are the origin of SM CP violation
– Observing SM CP violation access to CKM angles
CP The phase changes sign under CP
Transition amplitude violates CP if Vub ≠ Vub*, i.e. if Vub has a non-zero phase
1)1(
1
)(1
23
22
32
2
2
AiA
A
iA
VVV
VVV
VVV
V
tbtstd
cbcscd
ubusud
CKM
(in Wolfenstein convention)
Mixes the left-handed charge –1/3
quark mass eigenstates d,s,b to
give the weak eigenstates d’,s,b’.
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Visualizing the phase – the “db” unitarity triangle
cbcd
ubudargVVVV
tbtd
cbcdargVV
VV
0*** tbtdcbcdubud VVVVVV
β
-i
-i
γ1 1
1 1 1
1 1
e
e
CKM phases (in Wolfenstein convention)
and are the two angles of the triangle ()
Surface proportional to amount of SM CPV
Phase of Vub (bu transition)
Vtd
Phase of Vtd (B0-B0 mixing)
Vtd
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Observables in CPV: interfering amplitudes
• How do complex phase affect decay rates (the basic input for any CPV observable)?
– Decay rate |A|2 phase of sole amplitude does not affect rate
• Case: 2 amplitudes with same initial and final state
– Decay rate |A1 + A2|2
+ |A1|2 + |A2|2 +
2|A1||A2| cos(1-2)=
2
A1 = |A1|*exp(i) A2 = |A2|*exp(i2)
|A1|
1
|A2|
2+ A1+A2=
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Observables in CPV: interfering amplitudes• Total interfering amplitude depends on phase difference
|A1|
1
|A2|
2+ = A1+A2
|A1|
1
|A2|
2+ = A1+A2
|A1|
1
|A2|
2+ =A1+A2
A1+A2
A1+A2
A1+A2
+ = +
CP
CP
CP
CP
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Observables in CPV: interfering amplitudes• Dependence on phase difference scales with amplitude ratio
– Observation in practice requires amplitudes of comparable magnitude
|A1|
1
|A2|
2+ = A1+A2
|A1|
1
|A2|
2+ = A1+A2
|A1|
1
|A2|
2+ =A1+A2
+ = +
A1+A2
A1+A2
A1+A2
CP
CP
CP
CP
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Observables in CPV: weak phase
)(exp||)( otherweakfB iAfBA
)(exp||)( otherweakfB iAfBA
CPhadro
niz
ati
on
hadro
niz
ati
on
• How disentangle weak phase from overall phase difference between amplitudes?
– Weak phase flips sign under CP transformation (CP-odd)
– Look at decay rates for B f and B f
CP
CP
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Observables in CPV: asymmetries
• …obviously, CP asymmetries depend on the weak-phase
+
+Bf
BfA=a1+a2
A=a1+a2
=
=
+
a1
a2A
-a1
a2
A
CP 22
22
||||
||||
AA
AAACP
depends on weak
CP
CP
CP
CP
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Observables in CPV: asymmetries
A
a1
a2
+weak
A
a1
a2
-weak
• …but also the CP-even (strong) phase
+Bf
A=a1+a2
A=a1+a2
=
=
CP 22
22
||||
||||
AA
AAACP
=0 need ≠0 !
+CP
CP
Bf
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Access to
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Access to : BD0K
0 0
0 0 Use interference between and decays
where the ( ) decay to a common final state B D K B D K
D D f
Vcb
Cabibbo & color favored
B
K
b c
D0
Vub
(Cabibbo & color)-suppressed
B
D0bu
K
Atot=A+A
A (D0K) 3
relative strong & weak phasesA (D0K) 3 ei(B-)
rB |A/A|~0.1-0.3
Size of CP asymmetry depdens on
CF[CS] ~(0.2-0.6) × )
Larger rB larger interference larger sensitivity to PLB557,198(2003)
~0.4
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Access to BD0K
• Different incarnations of same principle (all theoretically clean)
• CP violation effects depend on– : weak phase difference between B decay amplitudes– B : strong phase difference between B decay amplitudes– rB : relative magnitude of B decay amplitudes– D : strong phase difference of D decay amplitudes– rD : relative magnitude of D decay amplitudes
• For multi-body D decays, last two described by Dalitz decay model
GLW
ADS
Dalitz (GGSZ)
Atwood, Dunietz, SoniUse BD0[K+]K and BD0[K+]K decays
Gronau, London, WylerUse BD0[CP±]Kdecays
Bondar (Belle), Giri, Grossman, Soffer, ZupanUse multibody D decays, eg. BD0[K0
S]K decays
PLB253, 483 (1991)PLB265, 172 (1991)
PRL78, 3257 (1997)PRD63, 036005 (2001)
PRD68, 054018 (2003)PRD70, 072003 (2004)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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GLW method• Reconstruct BD(*)0K(*) with CP-even and CP-odd D0/D0 final states
• CP modes: quite small D0 branching ratio: e.g. Br(D0K+K)~4x10-3
• Many modes: •CP-even : K+K, + CP-odd : KS0, KS, KS, KS
• Observables
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
3 independent measurements (ACP+ RCP+ = ACP- RCP-) vs 3 unknowns (rB, B, )8-fold ambiguity(rB,B) different for BD0K, BD*0K, BD0K*
Normalize to D0 decay into flavour state (eg. K+)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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ADS method
ADSDBDBADS RrrKKDBKKDB
KKDBKKDBA /sin)sin(2)][()][(
)][()][()()(
)()(
cos)cos(2
)][(2)][()][( 22
DBDBDBADS rrrrKKDB
KKDBKKDBR
KDB 0
KDB0 KD
0
KD0favored
favoredsuppressed
suppressed
KK D][ KDB 0
KDB0 KD
0
KD0favored
favoredsuppressed
suppressed
KK D][
• Same idea as for GLW method, but different D0 final state: doubly-Cabibbo-suppressed decay, [K+]D , instead of CPES
• Small BFs (~10-6), but amplitudes of comparable size expect maximum CPV• Observables:
2 independent measurements vs 3 unknowns (rB, B, )The system can be solved with BD*0K decays
Diii
BD reeerKKBA DB )(
PLB592, 1 (PDG2004)
rD2 = (0.3650.021)%
D : D decay strong phase unknown (scan all values)
PRD70, 091503 (2004)
No DCS signal so far…
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Dalitz method
Schematicview of the
interference
2 0 2
2 0 2 ( ) ( )
S
S
m M Km M K
2m2m
2m2m
0 D 0 D
• Reconstruct BD(*)0K(*) with Cabibbo-allowed D0/D0KS
• If D0/D0 Dalitz f(m+2,m
2) is known (included charm phase shift D):
),(),()(),( 2222022
mmfeermmfKDBAmmM ii
BB
),(),()(),( 2222022
mmfeermmfKDBAmmM ii
BB
B:B+:
|M|2 =)( Bi
Ber
No
D m
ixin
gN
o C
P v
iola
tion
in D
dec
ays
• Relatively large BFs: BF[(B D0K)(D0 K0 )]=(2.20.4)10-5
• Only charged tracks in final state high efficiency/low bkg ambiguity only 2-fold ( ↔ )
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Dalitz method: sensitivity to
2m
2m
D0 KS
The highest the weight the more important the event for measurement
points : weight = 1
weight =
2
2
ln( )d L
d
22
2
1( ) ~
ln( )d Ld
rB=0.12
=70°
=180°
DCS D0 K*(892)+-
DCS D0 K0*(1430)+-
• Sensitivity varies strongly over Dalitz plane• Second derivative of the log(L) event-by-event weight the event
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Access to 2+B0D(*)+
Favored b c transition
2 *2i i i iu cdbA e e e V er V
c0B
d
bu
d
*D
h
*cb udA V V
Doubly-Cabibbo suppressed b u transition
d
bc
d
0B
u
*D
h0B
u,c,t
u,c,t
V*ub
Vcd
Vcb
V*ud
)(
)((*)0
(*)0(*)
hDBA
hDBArB
Use interference between
~
~
Similarly:
golden mode at LHCb
0 0( )s s sB B D K
PLB427, 179 (1998)
~0.02 from moduli (small CP asymmetry, ~2%)
• Favored decay has “large” branching ratio (~0.3-0.8%)• …but need huge statistics partial and full reconstruction• rB
(*) must be obtained from external measurements + SU(3) (theory error 30%, under discussion among theorists)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Experiments &analysis techniques
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Experiments: BaBar at PEP-II (SLAC)
“Storied Royal Elephant”DIRC PID)
144 quartz bars11000 PMs
1.5T solenoid
EMC6580 CsI(Tl) crystals
Drift Chamber40 stereo layers
Instrumented Flux Returniron / RPCs/LSTs (muon / neutral hadrons)
Silicon Vertex Tracker5 layers, double-sided sensors
e+ (3.1GeV)
e (8.9 GeV)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Experiments: Belle at KEK-B (KEK)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Analysis techniques
• Reconstruct D0/D*0 mesons in the various decay modes
• Combine with fast tracks K/ to make B candidates
KDDD 00* ,
Particle ID
Aerogel+ToF+dE/dx
Information combined into likelihoodsWide momentum coveragesCheck high momentum performance with D*D0samples
Primary K/ separation uses DIRC (C)Combine dE/dx from SVT and DCH
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Analysis techniques • Veto significant/potentially dangerous B decay backgrounds
– E.g. B[]DK has background from B [K]D
• Suppress continuum e+eqq (q=u,d,s,c) background using– Angular distribution: B flight direction– Event shape variables:
• Signal: almost at rest• Background: “jetty”• Use multivariate variables
– Fisher discriminant– Neural Net
– Resonance masses, decay angles, helicity in PPV, VPP decays (eg. DKS, K*KS)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Analysis techniques• Characterize B candidates using
– Beam constrained mass:• B mesons produced almost at rest
• Resolution ~3 MeV dominated by beam energy spread– Energy difference:
• Energy of B candidate almost equal to half beam energy
• Resolution ~10-50 MeV depends on neutrals in final state
• Select best B candidates based on invariant masses of daughter particles
• Signal extracted using maximum likelihood fits to mES, , Fisher, PID, etc.
• Use sidebands and control samples to check backgrounds
*beam
* EEB cepB /V M300~*
•Global Maximum Likelihood fit:•Yields (signal + bkg)•CP parameters
•Cut based signal selection•Signal region maximum Likelihood fit:
•CP parameters
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Example: exclusive reconstruction of BD0K*
K*B
+
KS +
0
00
*,
*,*,)(
cos
DKKsKs
DKKsKsDKKs
xxp
xxp
D0
=1 for signal events
+
KS+
B
+e-eY(4S)
B
X
-
0SK
0D
0DKs
0SK
*K
Ks
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Dalitz analysis
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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D0 KS Dalitz model
• Dalitz method requires knowledge of
• |f(m+2,m
2)| can be extracted from tagged D0 rates from e+e continuum
– Tag using charge of soft pion from D*+ D0+ decays
• …but phase difference variation D(m+2,m
2) requires assumption of Dalitz model
• In the isobar model formalism a three-body D0 decay proceeds mostly via 2-body decays (1 resonance + 1 particle)
• With CP-tagged DKS decays the amplitude is
– Can use tagged D mesons from CLEO-c to measure directly cosD, removing (or largely reducing) the model dependence
),(2222 22
|),(|),( mmi Demmfmmf
D0 ABC decaying through a resonance r=[AB]
PRD63, 092001 (2001)PRL89, 251802 (2002)
),(),( 2222 mmfmmf
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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D0 KS Dalitz model: nominal
• The D0 amplitude fAD can be parameterized as a coherent sum of Breit-Wigner amplitudes (quasi 2-body terms) plus a constant term (non-resonant)
),(),( 131201312
0
ssAeaeassA ri
rr
iD
r
rJrrDr BWMFFA
)(
1)(
2ijrrrij
ijr
siMMssBW
Lorentz invariant amplitude for resonance r containing angular dependence
Relativistic Breit-Wigner with mass dependent width
Relative amplitudes and phases
Vertex form factors of the D0 meson and the resonance r(model underlying quark structure of the D0 and the resonance r)Usually, parameterized using Blatt-Weisskopf penetration factors
rD FF ,
J. Blatt and V. Weisskopf,Theoretical Nuclear Physics.
John Wiley & Sons (1952), New York
H. Pilkuhn, The interactions of hadrons,North-Holland (1967), Amsterdam
JrM Angular dependence
sij=[s12,s13,s23] depending on the resonance KS(m2), KS+(m+
2), +
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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D0 KS Dalitz model: nominal
•17 amplitudes: 13 distinct resonances + 3 DCS K* resonances + 1 non-resonant term
• Not so good for S-wave need controversial (500) and ’(1000) scalars to describe reasonably well the data
• Masses and widths fixed to PDG2004 values except for and ’ (fitted)
2/dof3824/3022=1.27
DCS K*(892)
CA K*(892)
(770)
hep-ex/0504039
82k tagged D0 events, 97% purity
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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D0 KS Dalitz model: nominal
2/dof2.30 (dof=1106)
DCS K*(892)
CA K*(892)
(770)
PRD70, 072003 (2004)hep-ex/0411049
• D0 decay model identical to BaBar
• 19 amplitudes: 13 distinct resonances + 5 DCS K* resonances [same as BaBar + DCS K*(1680) + DCS K*(1410)] + 1 non-resonant term
DCS K*(1680) and DCS K*(1410) excluded in BaBar model because:•number of expected events is very small•the K*(1680) and the DCS K*(1680) overlap in the same Dalitz region the fit returns ~ the same CA and DCS amplitudes
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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D0 KS Dalitz model: nominal
Sum of fit fractions : 123%Sum of fit fractions : 124%
• The relative amplitudes ar and phases r as obtained from the ML fit
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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D0 KS Dalitz model: no scalars
La ThuileG. Li, BES Collaboration BJ/ data
• scalar seems to be confirmed by BES Collaboration
• And Dalitz fit to tagged D0 KS sample is clearly much worse
2/dof4757/3022=1.57 vs 1.27
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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D0 KS Dalitz model: no scalars
• …but adding BW’s in the isobar model:• breaks the unitarity of the S (scattering) matrix• BW is only valid for single, isolated resonance
• For broad, overlapping and many channel resonances we need a more general approach K-matrix formalism
(Argand diagram)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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D0 KS Dalitz model: K-matrix for S-wave
),( ),( 13120 ,0
2311312 ssAeasFssf rri
spinkspinrr
j
23-1
1j2323231 s si-1 jPsρKsF
• K-Matrix formalism overcomes the main limitation of the BW model to parameterize large and overlapping S-wave resonances– non trivial dynamics due to presence of broad, overlapping, and many channel resonances– avoid introduction ad hoc of not established scalars
• By construction unitarity is satisfied:– S : scattering operator– T : transition operator– : phase space matrix
• K-matrix D0 3-body amplitude
KiKT
iTS
SS
1)1(
21
1
S-wave amplitude
initial production vector (production)K-matrix (decay)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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D0 KS Dalitz model: K-matrix for S-wave
• Use V.V. Anisovich & A.V. Sarantev parameterization
2/
0.10.1 223
023
0
023
0
23223
mssss
s
ss
sf
sm
ggs A
A
Ascatt
scattscatt
ijr
jiij
K
scatt
scattprodj
jj
ss
sf
sm
g
023
01
232
0.1s
P
ig coupling constant of the K-matrix pole m to the ith channel:
1=, 2=KK, 3=multi-meson (4), 4=, 5=´
Adler zero term to accommodate singularities
scattscattij sf 0 , slow varying parameter of the K-matrix element (non-resonant), with
1 if 0 if scattij
Eur.Phys.Jour.A16, 229 (2003)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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D0 KS Dalitz model: K-matrix for S-wave
2/dof~unchanged)
(770)
S
-wav
e te
rm
Sum of fit fractions : 116%
• 9 distinct resonances + 3 DCS K* resonances + K-matrix S-wave
Unitarity guaranteed for S-wave component (by construction)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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BD(*)0K(*) selection
16209Nsig 858Nsig 736Nsig
D0K D*0K D0K**[KS]
hep
-ex/0
411049
hep
-ex/0
504013
hep
-ex/0
504039
Hep
/ex-0
507101
275×
10
6
BB
227×
10
6
BB
20282Nsig 1190Nsig 844Nsig
D0K D*0(D00)K D*0(D0)K D0K*[KS]
842Nsig
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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BD(*)0K(*) Dalitz plot distributions
B+D0K+ BD0K
B+D0K+ BD0K
Differences between B+ and B signifies direct CP violation
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Some peculiarities: BD*0Kstrong phase
Effective strong phase
shift of between D00
and D0 helps in the
determination of
• For BD*0K decays
• D*± decaying into CP eigenstates D00,D0
D* = D(-1)l=1 , l=1 for parity/angular momentum conservation
= -1⋅ D*
±→D0±0
D*±→D0
∓
PRD70, 091503 (2004)
Opposite CP eigenstate
BB
2B
20* cosr2r1aKDDB
BB
2B
2* cosr2r1aKDDB
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Some peculiarities: BD0K*amplitude
cpicppS eAXDBA
0
iiuppS eeAXDBA up 0
13120 , ssAeAfDA D
if
f
12130 , ssAeAfDA Df
if
121313120 ,, ssAeAssAeAXfDBA D
iupD
icppS
upcp
p= B decay phase space pointA = real amplitudeXS=[KS] state
• The K* has an non-zero intrinsic width (~50 MeV) B Dalitz plot• Selection of B±→DK*[KS] decays results in the interference of B±→DK*± and B±→D[KS±]non-K*
• A general parameterization of the B±→D[KS±] decay amplitude can be found wich accounts by construction for the K* and non-K* contributions
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Some peculiarities: BD0K*amplitude
2cp
2up
S0
S0
2S
A dp
A dp
XDBXDB
r
2up
2cp
iupcpi
A dpA dp
eAA dpe
p
S
SS i
SSi
SS erImy , erRex
*,,Im*,,Re2
,,
1213131212131312
2
121322
13120
ssAssAyssAssAx
ssArssAXKDB
DDSDDS
DSDSS
cpupp
• Let us introduce now the following notation:
• And the effective CP parameters
• The general decay rate is then:
• The effective CP parameters xS±, yS±, rS2 depend on the phase space selected
region without introducing any bias on the measurement
hep-ex/0211282
If K* intrinsic width ~ 0 (K case) =1, S=B, rS=rB
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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Fit results
violationCPdirect 0|sin|2 Brd
Determine x=rBcos(B), y=rBcos(B), for each decay mode from ML fit to B+ and B Dalitz distributions
D0K
D0K
D*0K
D*0K
D0K*
D0K*
B+
B
B+
B+
B+
B+
B+
B
B B
B B
dd
d d
d
d
y
xx xS
x x xS
y yS
y y yS
1- a
nd
2-
con
tou
rs f
or
=2
dof
l
nL
= 0
.5, 1
.921
)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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From (x,y) to , B and rB
Measured CP parameters: (x,y) B decay mode 12-dimensional spaceExcellent Gaussian behavior
Perform ~1010 pseudo-experiments(Toy Monte Carlo)
Frequentist distillery(Neyman’s construction for confidence intervals)
(,B,rB) parameters:(rB,B) B decay mode and 7-dimensional spaceNon-Gaussian for low stat. samples & near physical boundary (rB>0)
rB rB rS
D0K D*0K D0K*(stat.+syst.
uncertainties)
2 fold (±) ambiguities for both and B
1- a
nd
2-
con
tou
rs f
or
=7
dof
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
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, B and rB results
)el(mod11.)syst(13.)stat(2867
)2([email protected](50.0)KD(r
)el(mod03.0.)syst(03.0.)stat(10.017.0)KD(r
)el(mod04.0.)syst(03.0.)stat(08.012.0)KD(r
*0B
0*B
0B
)el(mod11.)syst(13.)stat(1568)KDKD(
*)Knon(8)el(mod11.)syst(9.)stat(35112)KD(
*)Knon(08.0)el(mod04.0.)syst(09.0.)stat(1825.0)KD(r
)el(mod04.0.)syst(02.0)stat.(12.0)KD(r
(model)04.0syst.)(03.0)stat.(08.021.0)KD(r
0*0
*0
*0B
16.011.0
0*B
0B
The importance of rB …
Significance of direct CPV2.32.4 …getting close to evidence
non-K* systematic error since non-K* contribution neglected in nominal fit
(min where CP is conserved, ie. rB=0 or =0)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
45
Comments on systematic uncertainties
• Experimental systematic uncertainty accounts for:– PDF shapes of selection variables (mES, DE, Fisher, etc.)– Background fractions and Dalitz shapes– Efficiency variations across Dalitz plane (including tracking efficiency)– Invariant mass resolution– Biases from control samples
• Dalitz model systematic uncertainty includes:– No scalars
• By far, the dominant contribution: ~11o
• Using K-matrix S-wave model, the effect goes down to ~3o
– Not yet used in current measurement (conservative for now)– Other variations have much smaller effects (ie. fine tuning of model ~ little
effect on ):• fit uncertainty of the phases and amplitudes from D0 tagged sample fit• Vertex form factors FD=Fr=1• Constant BW width• Alternative lineshape for (Gounaris-Sakurai)
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
46
from DK (all methods)
151263meas
71357CKM
• Constraints on from WA D(*)K(*) decays
(GLW+ADS) and Dalitz methods compared to the predictions from the global CKM fit (excluding these measurements)
• Constraints in the () plane on from WA D(*)K(*) decays
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
47
Conclusions &perspectives
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
48
Conclusions and perspectives
• Measurement of at B Factories seemed an impossible mission few years ago !
– ...certainly is not an easy task (need lot of data, many methods and channels, a lot of brainstorming,...)
• 3 clean methods towards extraction of in place:
– ...all hindered by smallness of rB
– ...but ready for more precise measurements in the coming few years
– Other methods studied or under study (not shown here), but not yet useful
• First meaningful measurements already available
– Dalitz method is the currently “golden” channel for , but need all channels and strategies to improve errors and resolve ambiguities
• Old Dalitz plot technique is becoming the new paradigm for other measurements too
– Getting close to evidence of direct CP violation in DK (3)
• What’s next?
151263meas
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
49
Conclusions and perspectives
13323 signal events
High background, difficult analysis (but possible). Not clear the gain in sensitivity
Exc
lude
KS0
eve
nts
Dalitz analysis from a tagged D0 sample
Expected ~90 BD(*)K events in 210 fb-1.Toy MC studies indicate small but not negligible gain on
• Improving statistical error:
– Larger data sample• Goal for B Factories is increase statistics 2x by ’06 and 4x by ~’08. On track...
– Add other D0 decay channels: KsK+K, 0, KS
hep
-ex/
0207
089
hep
-ex/
0505
084
227×106 BB
Int. WE Heraeus Summer School, September 2nd, 2005 F. Martínez-Vidal , Measurements of the CKM-matrix angle
50
Conclusions and perspectives
• Reduce Dalitz model dependence:– K-matrix for S-wave (KS channel)
– Use CP-tagged D mesons decaying to KS to measure directly the (cosine of)
phase difference variation (D)
• Overall, seems feasible an ultimate precision ~ 5o for 2 ab-1 (~2008)– Could be better or worse depending on ultimate value of rB (> or <0.1)