K±±00
Measuring Branching Ratioand Dalitz plot parameters
A. Ventura E. Gorini M. Primavera
Branching Ratio World data
K±±00 measuring branching ratio and Dalitz plot parameters
PDG (units 10–2)
1.73±0.04 (fit)1.77±0.07 (average)
Best experiment is 3.5% error,and bases on only 1307 events:CHIANG 72 (1.84±0.06)10–2
A. Ventura – KLOE Otranto 2002
’ K±±00
Present statistics analized at KLOE
• Data : 6.33 pb–1 (December 2001)
• MC : 1.8 106 all (~0.6 pb–1) 7.0 105 K–K+, K±±00,Kall (~13 pb–1)
– DBV-12 default datarec version– MC samples include proper DC & EMC bckg simulations
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
Filter algorithm (I)Preliminary requirements
Cosmic Veto (DC+EMC) Trigger Any of the 5 EvCl algorithms
K± track a unique 2-tracks vertex in DC involving the K±
Distance between the two tracks’ first/last hit < 50 cm Angle at vertex between the two tracks > 2° *
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
* Redundant cut with new retracking
Filter algorithm (II)Further requirements
4 “ontime” non-associated clusters with Ei>15 MeV coming from the charged vertex: |ti–tj–(Li–Lj)/c|<3t(Ei,Ej) i,j=1,..,4
Best pairing of the quartet of clusters: 80 MeV < m12 , m34 < 190 MeV ( 3m cut )
460 MeV < m < 530 MeV ( 3m cut )
Charged product track momentum: |pdau| < 135 MeV in K± frame
all contamination ~0.5% (MC)
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
Photons from 0s in ’on MC and Data
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
Energy distribution: Ei [20,180]MeV
00
MC genMC rec
Inv. M
(M) (M°°)
MC 18.3 MeV 13.2 MeV
Data 20.7 MeV 14.4 MeV
Tagging strategies
Daughter momentum: 199 MeV < |pdau| < 211 MeV in K frame Missing mass at K vertex: 122 MeV < mm < 148 MeV 2 ontime non-associated clusters: 90 MeV < m < 180 MeV
all contamination ~0.35% (MC)
all contamination ~0.3% (MC)
Daughter momentum: 226 MeV < |pdau| < 245 MeV in K frame Missing mass at K vertex: |mm|< 5 MeV
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
K±±0
K± ±
BR measurement method
BR(K±00) = [N’]tag
Ntag
1’
BR(0)=(98.80±0.03)%, tag = 0,
’ does not depend on FILFO , EvCl , tag
’ independence from trig to be tested
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
1[1–BR(0)]2
’ = K vtx 4onT pair M pdau
Evaluating efficiencies on MC and on Data
All the cuts applied have been separately studied on proper Samples of Normalization (SoNSoNs) in order to evaluate efficiencies directly from data.
Equivalent MC samples have been used just to control and reduce contamination in all SoNs.
Each is meant to be convoluted with the corresponding KLOE acceptance and to be averaged over ’ kinematics
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
Evaluating efficiencies: K
SoN#1 : tag+4 A K° or a K on one side, as defined for tagging 4 non-tag neutral clusters with E>15MeV (“”) :
• 20 MeV < Ei < 180 MeV• 125 MeV < Ej+Ek< 195 MeV (j=min and k=max) or (j=2nd and k=3rd)• 1 cluster >110 MeV• 2 clusters <60 MeV• max(|tj–tk|) < 9 ns (j,k=1,..,4)
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
98% K°° (MC) ; ~2200 events/pb–1 on data
Evaluating efficiencies: K
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
Kaon tracks in tag+4K
# of “”
|pFH|
Track’slength
cot
New tracking algorithms still to be used on analysis
Track’s radius at First Hit
MCData
MCData
Evaluating efficiencies: vtx
SoN#2 : tag+4+K
A tag+4 subsample with the other K reconstructed
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
vtx = v TT cos |v
v : finding a 2-tracks vertex
TT: distance between tracks < 50 cm
cos: angle between tracks > 2°
|v: no other decay vertices for K
Evaluating efficiencies: vtx vs # of “”
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
v TT
cos |v
MCData
Evaluating efficiencies: 4onT
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
4onT = tw6 [1–Pwtw
4]N
tw : finding 2 clusters (photons) coming from the same vertex
(0) in a 3t time window
Pw : physical probability for a “” not coming from a given 0
to be ontime with its 2 correct clusters (e.g.: accidentals, split clusters, TCA faults, …)
N : mean number of non-’ “”s in a generic ’ event
A possible parametrization:
Evaluating efficiencies: tw
SoN#3 : Kp+1
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
99.7% cluster 1 from K° (MC) ; ~60000 events/pb–1 on data
(K track + dau track) at a 2-trks vertex 199 MeV < pdau< 211 MeV in K frame Missing mass at vtx: 122 MeV<mmiss<148 MeV cluster 0 associated with dau track neutral cluster 1 : E1<(>)Emiss/2 ontime with 0 and such that: |E1–E1
*|<35.7%/E1(GeV) , with E1
*=m°2/2[Emiss– pmissc1] 0
1 2
tw : finding a cluster 2 such that:
a) E2>(<)Emiss/2
b) 2 ontime with 1c) 80 MeV<m12<190 MeV
Evaluating efficiencies: tw in Kp+1
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
MCData
tw
Etw as a function of the
cluster 2 expected energy
Distance between cluster 2 and the expected impinging point
MCData
Cluster 2not found
tw =(90.94±0.07)% on MC(86.11±0.04)% on Data
Evaluating efficiencies: Pw
SoN#4 : Kp+2
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
A Kp+1 subsample in which cluster 2 has been found
0
1 2
Pw tw4 : finding a “wrong” cluster W
which is ontime with clusters 1 and 2
W
Pw =(2.16±0.07)% on MC(3.39±0.03)% on Data
Pw
MCData
Evaluating efficiencies: N
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
The mean number of non-’ “”s in a ’ event (N) can be estimated in tag+4 , in tag+4+K , in the final analysis sample itself
N =(1.27 ± 0.02)% on MC(1.531±0.008)% on Data
N+4
N any possible “” observed in a
’ event apart the 4 ’ neutral clusters
MCData
Evaluating efficiencies: pair
SoN#5 : Kp+1+1
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
A Kp sample in which both the 2 clusters have been separately found with the procedure as for kp+1 and are ontime.
0
1 2
: the 2 clusters in Kp+1+1
satisfy: 80 MeV<m12<190 MeV
E =(0.975±0.002)% on MC(0.941±0.001)% on Data
N
pair = 2
DataMC
Efficiencies: summary
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
MC Data
K0.560±0.0
320.471±0.0
12
vtx0.731±0.0
340.626±0.0
17
4onT0.553±0.0
020.392±0.0
01
pair0.952±0.0
020.885±0.0
01
M0.963±0.0
020.964±0.0
01
pdau0.980±0.0
020.978±0.0
01
}K0tag
’ 0.203±0.014 0.096±0.004
Estimation of statistical error on BR(’)
MC (~1.8·106 all events)N’ =2204 , [N’]°tag=169 , Ntag=49912
BR(’) = (1.71±0.16stat)%
Data (~6.33 pb-1, December 2001)N’ =20778 , [N’]°tag=726 , N°tag=421626
BR(’) = (1.83±0.09stat)%• ~ 115 ’|0tag events/pb-1
2001 data are enough for BR(’) below 0.8stat
%
• Systematics to be tested at % levelK±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
QUADRATIC COEFFICIENT h0.057±0.018 (average)
Dalitz plot parameters World data
LINEAR COEFFICIENT g0.652±0.031 (average)
QUADRATIC COEFFICIENT k 0.0197±0.0045±0.0029 (BATUSOV 98)
ASYMMETRY (g+- g-) / (g++ g-)NEVER MEASURED
si = ( PK – Pi )2 i = 1,2,3
s0 = isi/3 = (mK2 + m
2 + 2m°2)/3 X = (s1 – s2)/m
2
Y = (s3 – s0)/m2
F(X,Y;g,h,k) = 1+gY+hY2+kX2
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
Before fit After fit
m° 18.3 MeV 1.27 MeV
mK 13.2 MeV 1.05 MeV
Ev 11.2 MeV 0.27 MeV
pvx
i
~16 MeV ~0.15MeV
s0~4500 MeV2 ~22 MeV2
Clustersenergyresolutions(MC)
m
m
Kinematical fit (for Dalitz plot only) Based on 4-momentum conservation, m’s and s0
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
X and Y resolutions (MC)
X=(3390)10-3 Y=(2051)10-3
X[-2.39,2.39] Y[-1.39,1.31]
Dalitz plot floored by 10x20 bins in [-3,3]x[-2,2]
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
(Y) is also evaluable from data (Y=.033)
Dalitz plots and efficiencies (MC)
Y Y
X X
GENerated REConstructed
(X,Y)
(X,Y)dY
(X,Y)dX
(X,Y) = # REC# GEN
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
(X,Y)dX (from data)
Extraction of Dalitz plot parameters
F(X,Y;g,h,k) = 1+gY+hY2+kX2
YX
6.33 pb-1
~15500 K°°
(MC normalized)
KLOE 6.33 pb–
1 PDG
g 0.607±0.026 0.652±0.031
h 0.026±0.027 0.057±0.018
k0.0080±0.0037
0.0197±0.0054
F
2 = bins[(Fexp –
Ftheo)/Fexp]2
minimized with g, h, k free
A0(g,h,k) =
F(X,Y;g,h,k)dxdy
normalization applied
Maximum Likelihood
method under study
VERY
PRELIMINARY
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
Event selection and errors estimation
~3330 K00 / pb–1 for BR (before kine fit)
~2500 K00 / pb–1 for g,h,k (after kine fit)
• All 2001 data should yield ~0.5stat% on Dalitz plot parameters and asymmetries
K±±00 measuring branching ratio and Dalitz plot parameters
A. Ventura – KLOE Otranto 2002
Study on K±00e±e
Study on K±00e±e (Ke4)
• signal : ~105 K–K+, K±00e±, Kall (~2 fb–1)• 1st bckg: 3.0 106 K–K+, K±±00,Kall (~60 pb–1)• 2nd bckg: 1.5106 K–K+, K±0e±,Kall (~10 pb–1)
Branching Ratio(2.1 ± 0.4 ) 10–5 (PDG fit)(2.54±0.89) 10–5 (BARMIN 88, 10 evts)
Highest statistics in: (00e±e)/(0e±e) = (4.2±1.0)10–4 (BOLOTOV 86, 25 evts)
Monte Carlo samples used:
A. Ventura – KLOE Otranto 2002
Ke4 Filter algorithm
Study on K±00e±e
All cuts as in K00, except for: 460 MeV < m < 530 MeV |pdau|<135 MeV in K frame
K°° fit unsuccessful
cluster associated to charged product’s track
2 based on 0 missing mass, E conservation (in mass hypothesis), charged product 1, charged product t.o.f. compatible with e (not or ):
2 < 5 (MC tuned)
K°°
Ke4
A. Ventura – KLOE Otranto 2002
Background subtraction (MC)
Contamination due to K±±00: (5.9 ±3.1)%
Contamination due to K±0e±: < 10%
Possible contamination from KL+–0
Study on K±00e±eA. Ventura – KLOE Otranto 2002
In (00e±e)/(±00) many systematics cancel out
Selection Efficiency on MCand events collection on data
Study on K±00e±e
1515 selected Ke4 events of 102600 MC generated
MC1.48% ~0.9 Ke4/pb–1 are expected on data
m
me
Only 2 Ke4 have been found in 6.33 pb–1
m
me
MC rec Data
A. Ventura – KLOE Otranto 2002
Conclusions and outlook
K 00 , BRFilter and data-extracted efficiencies already testedTrigger effects and systematic errors to be evaluatedtag , EvCl , trig corrections to be studied
K 00 , Dalitz Plots parameters MC differential efficiency used for fit to be correctedMaximum Likelihood Method under study
K 00e , BRAll 2001 data statistics to be analizedData-extracted efficiencies to correct MC predictions
K±±00 and K±00e±eA. Ventura – KLOE Otranto 2002