1. Preliminary results on Ks  3p0 search......
M. Martini and S. Miscetti
Analysis outlook:
Comparison Data-MC, starting from DST dk0,mk0
Data pb-1
MC all avaible statistics (NeuKaon)
Kinematic fit procedure
Definition of pseudo-c2 to improve S/B
c22p
c23p
Study of the background shape Data vs MC
Adjusted simulation to reproduce observed bkg rate
Track veto, E gamma cuts
Preliminary determination of upper limit for BR
M.Martini 1

2. Standard Ks tag using KL interaction on EMC ( Kcrash )
Events filter
Standard Ks tag using KL interaction on EMC ( Kcrash )
  30% (24 x 106 with 4 cluster norm.)
Tuning of acceptance cuts (6 pb-1 Data, MC) looking for highest e while retaining 0 candidates in events with 6 neutral clusters: |T-R/c| = 3.5 st ; Ecut = 7 MeV ;  = 22,5°
  58% (starting sample events)
MC BKG
10Kevents MC
Ks  3p0
Kinematics fit applied using Ks momentum estimated by Kcrash
(and ) by requiring 4-momentum conservation on the Ks side (c2fit).
After applying a reasonable cut on the c2fit (< 30) a sizeable quantity of bkg events still remains. In order to improve signal/noise we have constructed two pseudo-c2 to discriminate between Ks2p0; Ks3p0
M.Martini 2

3. Kcrash + 4 prompt clusters
Construction of the c22p
c22p is built selecting 4 out of 6 clusters which better satisfy the kinematics of KS into 2 pions decay
The kinematics parameters used are:
Mass distributions
Opening angle between pions
in Kaon C.M. Frame
Four-momentum
conservation KL KS
All this is done using the reconstructed cluster parameters before applying the kinematic fit procedure
Calibration of the c22p is done using
Kcrash + 4 g (i.e. Golden Ks  2p0 sample)
Kcrash + 4 prompt clusters
•• DATA
-- MC
M.Martini 3

4. c23p At the moment, the c23p is based only on the 3
Data MC
At the moment, the c23p
is based only on the 3
reconstructed pion masses
M.Martini

5. Data MC comparison of c22p vs c23p 2001: a surprise!
In the data, a new category of BKG events (not simulated by the “standard” Kcrash MC) appears. This simulation takes into consideration only KL decaying after a cylinder bigger than DCH and smears the KL MC direction with the KL crash resolution observed in data.
M.Martini

6. c22p vs c23p 2002 sample Data MC Ks2p0 MC Ks  3p0
The MC has been adjusted inserting a calibrated quantity of “fake” Kcrash. Requiring in the MC reconstruction the same cuts used in the tag definition
( E , b*)
MC calibration performed without cutting on c2fit
Kcrash fakes (  3 %) are dominated by Ksp+p- , KL3p0 events, with pions
Interacting in Qcal, beam-pipe
MC Ks  3p0
Data
MC Ks2p0
M.Martini

7. Comparison “Data-MC” c22p, no c2fit cut
All c23p
c23p > 80
c23p < 80
c23p < 200
After MC adjustment
Result of normalization
Weight factors
Kcrash MC 
Kcrash fake 
M.Martini

8. Comparison “Data-MC” c23p, no c2fit cut
All c22p
c22p > 40
After MC adjustment
14<c22p < 40
c22p < 14
M.Martini

9. Definition of the Signal boxUp
Cup
Sbox
CSbox
Down
Cdown
M.Martini

10. Sbox Up Down CSbox Cup Cdown Comparison Data-MC NO CUTS on c2fit
The sample without any c2FIT is used to check the reliability of the “adjusted” simulation on reproducing the rate in the signal and control boxes.
NO CUTS on c2fit
BOX Name
Ndata
Nmc kkm
Sbox
304±17
313.6±16.6 Up
456±21
493.7±21.8
Down
356±19
401.1±13.6
CSbox
5141±72
5241.1±47.9
Cup
10523±103
±69.7
Cdown
22948±151
±97.0
M.Martini

11. Next cuts ... TRKveto We count only tracks coming from IP (numTRK)
No cuts applied
c22p > 40
All c22p
14<c22p < 40
c22p < 14
We count only tracks
coming from IP
(numTRK)
r(PCA) < 4 cm
Z(PCA) < 10 cm
Veto events with
numTRK>0
M.Martini

12. E(Ks) = Eks(KineFit)- Eg
Study of DECUT
After finding the 4  satisfying
the Ks2p0 kinematics (by c22p)
we evaluate the residual energy
on the Ks side:
E(Ks) = Eks(KineFit)- Eg
--- MCBG no 2fit cut
MCBG 2fit < 30
MCBG 2fit + TRKveto
MCSIG
KCRASH STANDARD MC
KCRASH FAKES
End of analysis:
2fit < 30
TRKveto
Signal Box
M.Martini

13. Next cuts ... DECUT (Rejecting DE < 9 MeV)
TRKveto+DECUT+c2<30
TRKveto+DECUT
TRKveto
All c22p
c22p > 40
14<c22p < 40
c22p < 14
M.Martini

14. Sbox Up Down CSbox Cup Cdown Comparison Data-MC
Comparison Data-MC after applying
c2fit<30, TRKveto and DECUT
BOX Name
Ndata
Nmc kkm
Sbox
5±2
3.1±1.3 Up
0±0
0.0±0.0
Down
16±4
22.3±3.1
CSbox
494±22
515.8±14.7
Cup
29±5
19.3±2.9
Cdown
5422±74
5485.5±47.9
M.Martini

15. VERY PRELIMINARY Calculation of the Upper Limit...
Efficiencies (after Kcrash tag)
Number of events with 1 Kcrash tag and 4 prompt g (Norm. Sample)
0.31 (PDG)
Upper limit determined using a classical frequentist method and using for BKG the average found –1 sigma (conservative approach):
Mean Expected Background=
BKG used = 1.7
Events observed = 5
With a1 weak amplitude for K0 to decay into I=1 final states
To be compared with NA48:
No assumption on CPT 1.4*10-6
Assuming CPT conservation 3.0*10-7
VERY PRELIMINARY
M.Martini

16. What needs to be finish for paper…
Maximization of upper limit on MC
For example with DECUT=100
MeV e3p=19% , UL could
improve by a factor of 1.5
check of “any” dependence on
and run conditions
Check efficiency as a function of
each cuts
Complete determination of upper
limit,
- compare with NA48
Constrain |000|
90% CL
M.Martini

17. Future plans for next running period
Use the MC/Data sample as a benchmark to maximize upper limit and definition of Sbox, tag used (for istance, hardening energy cuts DECUT 100 MeV, Ekcrash > 200 MeV  efficiency lowers from 0.3x0.26 to 0.24x0.19 but the Ncandidates greatly decrease).
Extend the Ks tag to KLpmn,pen,ppp, decays looking at charge vertecies on DCH ( Tag efficiency increases of
 1.5)
If the accidental background remains at the level of 2002 running we can still hope to see 0 candidates in 2 fb-1
M.Martini

18. Future plans for next running period
Assuming 0
candidates
from 2 fb-1
Ncand (2.3/7.6) x
Eff (26/19) x
Norm 1/6
= 0.069
BR < * 2.2x10-7
= 1.5x10-8
90% CL
M.Martini

19. Additional information
M.Martini

20. Comparison “Data-MC” c2fit, no c2fit cut
Result of normalization
Weight factors
Kcrash MC 
Kcrash fake 
Comparison chi2 fit
M.Martini

21. A NEW SIMULATION OF Klcrash (AcciK)
To understand these events whenever no Kcrash is found by the standard Kcrash MC
we add the possibility to find a Kcrash applying the standard data cuts (E and b*)
Running this new Kcrash simulation on 2002 MC we find other 1320 entries with
respect of to the 9657 events already simulated in the 6 prompt clusters sample.
There are three different sources of these new BKG events:
AcciKcrash  K crash by accidental (1)
T0stolen  Golden cluster by accidentals (2)
Klpipe  K crash by KL daughters inside Rt = 25 cm (3)
Ngam=6
Ngam=5
Ngam=4
Total events
1320
13677
5314 1 17 4 2
130
255 7 3
139
217 28
2*3 77 64
1*2
---
1*2*3
1+2+3
207
420 35
Type of fakes
M.Martini

22. Rate normalization Comparison “Data-MC” c2 2p, no c2 cut
All c23p
c23p > 80
Normalization with 6 g rate
reasonable in the overall plot but missing to reproduce the observed rate in these regions
c23p < 80
c23p < 200
Rate normalization
M.Martini

23. Check reliability of the “adjusted” simulation when a c2<30 cut is
Comparison Data-MC
Check reliability of the “adjusted” simulation when a c2<30 cut is
applied.
BOX Name
Ndata
Nmc kkm
Sbox
18±4
18.3±3.9 Up
1±1
0.0±0.0
Down
54±7
51.9±4.9
CSbox
820±29
871.2±19.2
Cup
32±6
20.6±3.0
Cdown
13278±115
±71.8
Table chi2 cut
M.Martini

24. Normalization plot Adjusted simulation Normalization kk1 c23p<80
Data MC
KcraMC
AcciK
Normalization kk1
c23p<80
Normalization kk2
c23p<200 MC
KcraMC
AcciK
Data
Normalization plot
M.Martini

25. Comparison “Data-MC” c2 fit, c2<30
Chi2 fit chi2<30
M.Martini

26. Comparison “Data-MC” c2 3p, c2<30
All c22p
c22p > 40
Normalization with
kkm values
14<c22p < 40
c22p < 14
Chi3 proj chi2<30
M.Martini

27. Definition of c2 2p
c2 2p is the c2 that we build searching the best combination of 4 out of 6 clusters
which represents a KS  2p0. The best combination is the one minimizing:
M.Martini

28. Before splash c2 3p At the moment, the c2 3p is based only on the 3
reconstructed pion masses
Data MC
Comparison Data-Mc
before splash filter
Splash filter consists of:
- Ngam = 6
Emean < 40 MeV
Mmean < 40 MeV
- Ngam = 4
Emean < 50 MeV
Mmean < 50 MeV
M.Martini

29. After splash c2 3p Comparison Data-Mc after splash filter M.Martini

30. Adjusted normalization
ID1 = Data ; ID2 = MC(Kcrash) ; ID3 = MC(AcciK)
ID1 = a1ID2 + a2ID3
Where:
Ndata = Number of entries of the c2 fit plot for data
Nmc = Number of entries of the c2 fit plot for mc
Normalization from two different plots:
kk  Coefficients calculated from c2 2p with c2 3p less then 80
kk  Coefficients calculated from c2 2p with c2 3p less then 200
kkm  The average value between kk1 and kk2
M.Martini

31. Comparison “Data-MC” c2 3p, no c2 cut
All c22p
c22p > 40
Normalization with
6 g rate
14<c22p < 40
c22p < 14
Chi3 rate norm
M.Martini

32. Comparison “Data-MC” c2 3p, no c2 cut
All c22p
c22p > 40
Normalization with
kk1 values
14<c22p < 40
c22p < 14
Chi3 kk1 norm
M.Martini

33. Comparison “Data-MC” c2 3p, no c2 cut
All c22p
c22p > 40
Normalization with
kk2 values
14<c22p < 40
c22p < 14
Chi3 kk2 norm
M.Martini

34. Data events Candidates... M.Martini At the end of analysis we have:
5 candidates from 450 pb-1
3 expected from 150 pb-1
Nrun: Nev: NTracks: Reconstructed pions masses: M1 = MeV
M2 = MeV
M3 = MeV
Chi2 fit: Chi2 pair: Chi3 pair: Number of kcrash: Ekcra: MeV Beta Kcra: Number of clusters:
Clusters parameters: Cluster Energy (MeV) Nsigma Angle
Data events
M.Martini

35. Preliminary calculation of the Upper Limit...
The efficiencies are:
The number of events with 4 g from data are:
To calculate the BR we can use:
Only assuming the Kcrash is the same in 2p and 3p
BR formula
M.Martini

36. Systematics on background evaluation: Dependence on c2fit
The events in the Up zone
have very high c2fit and the region becomes quickly empty
We fit the rate Data/MC
obtained with different
values of c2fit cut:
c2fit < 500
c2fit < 400
c2fit < 300
c2fit < 200
c2fit < 100
Data/mc vs chi2
M.Martini

37. Systematics on data/bkg for different cuts
Distribution of the Data/MC ratio for
all regions, (including
also signal BOX) for
all used c2fit cuts
No cuts
TRKveto
CONSERVATIVELY
assuming a systematic
error of ±20% on the
absolute amount of
expected background
TRKveto+DECUT
Data/mc syst
M.Martini

38. Prevision on BR M.Martini x10-9 Black dots= Current statistics
Red dots=2fb-1 MC
Using F.C.:
Actual BKG=
2fb-1 BKG=6-10
18*10-9
observed
0.75*10-9
M.Martini