Download - Study of CP Violation in B 0 Ksπ 0 at Belle
Study of CP Violation Study of CP Violation in Bin B00 Ksπ Ksπ00 at Belle at Belle
Niigata-University T.ShibataNiigata-University T.Shibata
KEK T.HiguchiKEK T.Higuchi
Taiwan-University K.F.ChenTaiwan-University K.F.Chen
Belle CollaborationBelle Collaboration
ICEPP Symposium in Hakuba 2004/02/15ICEPP Symposium in Hakuba 2004/02/15
Introduction to
Ks π0 Mode
Ks π0 Mixing Indirect CP-Violation Mode likely JψKs
Dominant!
Ks
u
uπ
s
d
0
d d
sd
d
Ks
π0
Penguin typeTree type
0000
0000
)(
KsKs
KsKstcp
tmStmAKsKs
sincos 00
34 ie22.0
2
Very Small Effect
≪( no phase )
In
Standard Model
00 KsA
12sin0
KsS
Physical Motivation
If New Physics in loop …
physicsnew 11
?2sin0
KsS
BaBar Result of LP03
newie
10.028.0
27.040.00
KsA
11.047.0
38.048.00
KsS
Events=122±16
Ks π0 is sensitivity for new physics in loop diagram.
d d
sd
d
Ks
π 0
Rb~
Rs~
*gb s
Today’s TopicsEvent Selection & Signal Yield
Analysis process
B0 reconstruction
(1) Event Selection
(2) Signal & Background Yield Extraction
CP-Fit Analysis
(1) Define the Resolution of Δt for Ksπ0 mode
(2) Δt & CP-Asymmetry Fitting
Event SelectionKEK
Ks&π0 Selection
B0 Reconstruction
Vertex Reconstruction
Background Rejection
Data Sample for Analysis
∫(Luminosity)dt = 140fb-1
#BB = 150×106
Estimate Events
( Physics Letters B407(1997))Br( B0 Ksπ0 ) ~ 4×10-6
Br( π0 → γ γ ) ~ 98.8%
Br( Ks → π+π- ) ~ 68.6%
~ 400eventsEfficiency=100%
1999.5 2001.11 2003.7
140fb-1
Ks & π0 Selection
B0 Reconstruction
π0 → γ γ
Ks → π+π-
118< Mγγ<150 MeV/c²
|Mππ–497.672| < 15MeV/c²
cmsBeam
cms
22 cmscmsBeambc
Beam Constrained Mass
Energy Difference
)(29.5 GeVcmsBeam
: Beam Energy cms : Energy of B cms : Momentum of B
All of them are CMS
Ks Mass (MeV/c2)
π0 Mass (MeV/c2)
)/(29.520.5 2cGeVbc
)(5.0 GeV
Vertex Reconstruction
B0 Vertex region
e- e+
3.0mm 2.7cm200μm
Ks
B0
Calculate Ks Momentum
Vertexing processVertexing process
Vertex Fit used Ks with B0 Vertex region constrained
Vertexing efficiency
B0Ks π0 : ε=25.9%
B0J/ψ Ks : ε=95.8%(Not official value)
True – Reconstructed ( μm )
55.6μm
103.6μm(RMS)
(RMS)
Ks π0 MC
J/ψKs MC
Background Rejection
Main Background is Jet events ( e+e-qq )
Rejected used difference of Topology of events
: Jet event
12
ijcos
1cos ijcandidate B0
Z θB
Super Fox-Wolfram(SFW) ( cosθij )
cosθB
cosθij
B eventqq event
B eventqq event
cosθB
(=beam direction )
345i
j
Background Rejection
Likelihood Ratio Cut
)(cos)(, BqqBB LSFWLL
qqBB
BB
LL
LLR
Likelihood RatioLikelihood
qqsig
sig
NN
N
Select
Cut by LR > 0.80LR>0.8 was defined as
became Maximum
L(SFW)=SFW shape
L(cosθB)= cosθB shape
Nsig,qq…#of signal,qq
Signal Yield Extraction
Tukuba hall in KEK
Signal Yield is calculated by
Unbinned Maximum Likelihood Fit to Mbc&ΔE
Pbkg shape = Sideband data
),(1
bcLLikelihood i
i
),()1(),(),( bcPfbcPfbcL bkgdigsigsigi
Signal Region
5.27<Mbc<5.29(GeV/c²) -0.15< ΔE < 0.10 (GeV)
bc
Mbc(GeV/c2)
ΔE
(GeV
)
Psig shape = Signal MC
bc
Fitting Result without(L) & with(R) Vertexing
Signal Yield =26.2±5.6
LR>0.80Signal Yield =92.8±11.3
LR>0.80
DataFit(sig+bkg)Fit(sig)
DataFit(sig+bkg)Fit(sig)
Reconstruction Efficiency
Reconstruction Efficiency was Calculated by Monte Carlo
W/o Vertex CutNot LR Cut LR>0.80
Cut
W/ Vertex Cut7.6%4.7%
30.6 %18.8 %
Mbc & ΔE distribution
ΔE(GeV)Mbc(GeV/c2)
SummaryUsed data sample140fb-1
Vertex Efficiency 25.9 (%)
w/o Vertexing Signal Yield Reconstruction Efficiency
LR > 0.8 Cut 92.8 ± 11.3 18.8 (%)
w/ Vertexing Signal Yield Reconstruction Efficiency
LR > 0.8 Cut 26.2 ± 5.6
4.7(%)
We could estimate the Ksπ0 events without vertexing (93), but vertex efficiency is very small(25%). The #events for CP-fit is 26.
Future PlanBackground Study by MC
Estimate peaking background
Measurement CP-Asymmetry
Define the special ‘Δt’ Resolution,
because this resolution is different
from J/Ψ mode( Golden mode )
This is very difficult problem
Finish until JPS(2004 Spring) ???
Appendix
Physics Motivation LP03 Conference
Ksd 0
sin2φ1eff = -0.96 ±0.50+0.09-0.11
Theoretical uncertain is
Small in Standard Model
Clean Mode for New Physics
sin21 (Belle 2003,140 fb-1) =0.733±0.057±0.028
Belle Result
1Measurement by B0 Mixing
Introduction to CP-Violation(1)
Dynamics of Physics = Lagrangian
Lphysics = L + Lh.c
Particle Anti-Patrticle
CP transformation
In Weak Interaction
Introduction to CP-Violation(2)
CP Conservation & CP Violation
(i) U*ub=Uub LH.C = Lcp = L Particle = Antiparticle CP Conservation
(ii) U*ubUub LH.C Lcp L Particle Antiparticle CP Violation
WU
gL buub
w 5* 12
WU
gL ubub
wCH
5. 1
2
WUg
L ububw
CP5* 1
2
Hermite
CP
Introduction to CP-Violation(3)
Requirement for CP-Violation Observation
1) More than Two Decay Process
2) Current has complex phase ( CKM matrix )
B0 decay to CP eigenstate
cpfB 0
0BMixing
cpcp ffCP :
20000cpcpcp fff
Interference !!
If complex phase is included in Amplitude, it will appear in interference term.
Introduction to CP-Violation(4)Time Dependent CP Violation in B-B Mixing
00)2/(0
2sin
2cos
mt
p
qi
mtet tMi
00)2/(0
2sin
2cos
mt
q
pi
mtet tMi
mtef tcp cos11
220 mt sinIm2
)(
)(0
0
cp
cp
f
f
p
q
cpcp
cpcp
ff
ffcp
00
00
mtmt
sin
1
Im2cos
1
122
2
Time Dependence & CP-Asymmetry
0cpf
Time dependent
B Wave function
Introduction to CP-Violation(5)
Physical Region
mtSmtAcpcp ffCP sincos
cpfA
1
12
2
cpf
S1
Im22
11
)Re(22
222
cpcp ff SA
122 cpcp ff SA
Afcp
Sfcp
Event Selection
Ks,π0 Selection Criteria
π0
Ks | Mππ – 497.672(MeV/c ²) | < 15MeV/c²
(No match with Charged track) 0.118< Mγγ<0.150(GeV/c²)
Fang-san’s Cut IF Both π tracks have SVD_zhit > 0 dz<2.0cm IF One of πtrack has SVD_zhit(1)>0 dr>0.1mm IF Both π track have no SVD_zhit dΦ<2.0cm
Other Cut
Eγ>50MeV
B0 Reconstruction
Background Rejection by Super Fox-Wolfram
Fisher discriminant
Super Fox-Wolfram (moment )
ijljji
isol pp cos
,
: Legendre Function
414,2 looo
ool
il
soo
sol
iF
jklkkj
jool pp cos
,
α,β are optimized with
Signal MC & Sideband Data
iP : B-Candidate Particle
jP: Other Particle
kP
bc
5.27 5.29
-0.2
0.20.5
0.1
-0.15
(charge&neutral) ijm
l cos0
Background Rejection by New Super Fox-Wolfram
I used N-SFW in this Analysis
14,04,0 n
ntl
ool
l
sol PRRNSFW
EE
HHHR
beam
so
lgmislmso
lneutralnso
ledchcsol
l
sinarg
i j
ijljsol
so
lX
X
XXPpH cos
2
1
2
1)4(
2
nn
nns PEEmm
0sin so
lgmisso
lneutral HH
i j
ijljjisol
so
ledch
X
XXXPpQQH cosarg
Missing Mass
solXH 3,1
solXH 4,2,0
Divide mm2 region into 7 region for correlation between SFW and mm2
Total Parameter = (11+5+1) 7
14,04,0 n
ntl
ool
l
sol PRRNSFW
2
cos
EE
PppQQ
Rbeam
j kjklkjkj
ool
ool
2
cos
EE
Ppp
Rbeam
j kjklkj
ool
ool
oolR 3,1
oolR 4,2,0
1n
ntP : Scalar sum of the transverse momentum
N-SFW(2)
Optimized N-SFW 7 Missing Mass
Regions
mm2<-0.5
-0.5<mm2<0.3
0.3<mm2<1.0
1.0<mm2<2.0
3.0<mm2<6.0
2.0<mm2<3.0
6.0<mm2
K-SFW (7 Missing Mass region )
bc
5.27 5.29
-0.2
0.20.5
0.1
-0.15
Parameters are optimized with Signal MC &
Sideband Data
Unit = GeV/c2
N-SFW(3)
Black …Signal Blue…Background
Background Rejection
Likelihood Ratio Cut
)(cos)(, BqqBB LSFWLL
qqBB
BB
LL
LLR
Cut by
LR > 0.80
Likelihood Ratio
Likelihood
Threshold was defined by Figure of Merits
qqsig
sig
NN
NMoF
..
LR at Max of F.o.M
Likelihood Ratio
Select
Unused Slid
e(1)
Background Rejection
Second Likelihood Ratio Cut
We want to use more events
Even if LR<0.80
Likelihood Ratio Cut in
0< LR<0.80
0.8 1.0 0Likelihood Ratio region Loose Cut : 0.4 < LR 0.8
6 r-regions ( r = Wrong tag fraction
)
Fitting Function(Signal Shape)
Signal Shape is obtained from Signal MCSignal Mbc : Single Gaussian
2
2
2exp
2
1)(
Mbc
bcMbc
Mbc
normbc NP
Signal ΔE : Single Gaussian
22exp:
12
1exp:
)(
norm
norm
Na
an
a
aNa
P
μMbc 5.2792(GeV/c2)
σMbc 34.1(MeV/c2)
μΔE -9.3(MeV/c2)
σΔE 39.0(MeV/c2)
a 0.6518
n 11.934
Fitting Function(Background Shape)
Background Shape is obtained from Sideband data
Background Mbc : ARGUS function
22
1exp)(
beam
bc
beam
bcbcbcP
Background ΔE : Chebyshev Function
121)( 221 CaCaNP norm
minmax
maxmin0.2
C
α -22.63
Emax 0.5 ( GeV/c2 )
Emin -0.2 (GeV/c2)
a1 -0.7961
a2 0.1421
Fitting Result before(L) & after(R) Vertexing
Signal Yield =1.4±5.5
0.4<LR<0.80Signal Yield =38.9±13.0
0.4<LR<0.80
Reconstruction Efficinecy by MCUsed Signal MC( 200,000events )
Ks efficiency 125510 62.77(%)
π0 efficiency 97749 48.89(%)
B0 efficiency 74719 37.37(%)
Genhep Infomarion
Reconstruction efficiency ( Before & after Vertexing )
Before Vertexing After Vertexing
Reconstructed B0
all Mbc&ΔE region
71184
True : 70276 = 35.14(%)
Reconstructed B0
before LR cut
61795
True : 61187= 30.60(%)
15346
True : 15226 = 7.61(%)
Reconstructed B0
after LR cut
37922
True : 37611= 18.81(%)
9528
True : 9470 = 4.74(%)
B0-Vertexing by Ks
B0-Ks Vertexing process ( Ks π+π- Long Lifetime )B0-Ks Vertexing process ( Ks π+π- Long Lifetime )
Ks track
IPB vertex
Ks track
IPB vertex
e+
e-
B0-J/ψ Vertexing process ( J/ψe+e- Short Lifetime )B0-J/ψ Vertexing process ( J/ψe+e- Short Lifetime )
B0J/ψ Ks
B0Ks π0
<z> = 46 mz (cm)
z (cm)
0.35(cm)
0.35(cm)
Unused Slid
e(2)
Measurement of
CP-Asymmetry
CP-Fit Fitting ‘Δt’ distribution & Asymmetry which
free parameter are Afcp & Sfcp
tmStmAtcpcp ffCP sincos)(
)()(
)()()(
11
11
tPtP
tPtPtcp
tmStmAqetPcpcp
Bff
t
q
sincos14
1)( 0
0
)1(
Free Parameters
J/Ψ mode presented at ICHEP2002
CP-fit : Resolution Function(1)
Most important work is define a Resolution Function of ‘Δt’
Resolution Function = Response Function of Δt
Resolution fucntionΔt
Input :P(Δt)
Δt
Output P’(Δt)
tdttRtPtP )()(
)( ttR Resolution Function
CP-fit : Resolution Function(2)P(Δt) include Resolution Function
tmStmAwqetPcpcp
Bff
t
qsig
sincos)21(14
1)( 0
0
)1(
tfefq
tP bg
t
bg
bgqq
)1(
22
1)(
Signal Probability Density Function
Background (qq) Probability Density Function
tdttRtPfttRtPfftP qqqqqqsigsigsigol1
tPf olol
Proper time difference include resolution function
CP-fit : Resolution Function(3)
Component of Resolution Function
(1) Detector Resolution
(2) Secondary Particle effect
(3) Kinematic Approximation
In Belle, Resolution Function
Parameters are defined by B0
Lifetime Fitting by Unbinned
Maximum likelihood fit used
Control Sample.
D π , D*π, D*ρ,D0 π,J/ψKs, J/ψK+
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