1. A direct search for Ks  3  0 decay at KLOE
LNF Spring School Frascati, May 17th-21st, 2004
A direct search for Ks  3  0 decay at KLOE
M. Martini, INFN Frascati,
for the KLOE collaboration.

2. KS3p0 All KLOE statistics  0.9 signal events produced (e=100%)
This decay has never been observed but is allowed by SM
[CP violating, CP(3p0)=-1].
From theoretical point of view:
All KLOE statistics  0.9 signal events produced (e=100%)
Actually published value: BR(KS3p0) < 1.4x10-5 (SND, PL B )
The observation of this decay would confirm CP violation in KS
system.
Uncertainty on KS3p0 amplitude limits precision on CPT test
(Bell-Steinberger relation).
M. Martini, LNF Spring School 2004

3. KS3p0 KS identification: tagging from KL decay
KLCRASH
b0.22
KLCRASH (e~30%)
This algorithm search KL which interact directly on EMC.
KLCRASH calorimetric clusters are selected using energy and b*.
High bkg rejection needed:
major expected background: KS2p0 (BR31%) + 2 fake photons either from
shower fragments or accidental overlap with clusters from machine
background.
M. Martini, LNF Spring School 2004

4. Photons counting and Kinematic fit
DATA=450pb-1 ( ); MC =540pb-1 (all available statistics)
Preselected signal sample (KLCRASH and 6 photons): events
Normalization Sample (KLCRASH
and 4 photons): 23.5x106 events
-- KS3p0 (MC)
-- MC BKG
 Data
A kinematic fit is applied on the
Ks side requiring the conservation of
4-momentum (NDOF=11).
 c2FIT
c2FIT < 30 is not enough
(2/3 of bkg rejected)!
Other discriminating variable have to be used:
(c22p, c23p)
M. Martini, LNF Spring School 2004

5. The c22p
The c22p is built selecting 4 out of 6 clusters which better satisfy the kinematics of KS  2p0
The parameters used are:
mass distribution
opening angle between pions in
KS C.M. frame
4-momentum conservation
KLCRASH + 4 photons
 DATA
-- MC
The calibration is done using KS2p0 sample.
M. Martini, LNF Spring School 2004

6. The c23p The c23p is based only on
 KS3p0 MC
 DATA
 MCbg
The c23p is
based only on
the 3 “best reconstructed” pion masses
M. Martini, LNF Spring School 2004

7. DATA-MC comparison We define a signal box and 5 control boxes. c23p
M. Martini, LNF Spring School 2004

8. DATA-MC comparison
A small fraction of the background (3%) is constituted by fake KLCRASH
(KSp+p-) + KL3p0. Our MC well reproduces such fakes.
c23p
M. Martini, LNF Spring School 2004

9. Analysis summary To increase bkg rejection we use these analysis cuts:
Track veto:
to reject events with tracks
coming from IP.
DECUT:
After finding the four photons satisfying the kinematics
of KS2p0, the residual energy of the KS is measured:
E(KS) = EKs- Eg
2 bodies decay  E(KS) ~ 0 MeV
3 bodies decay  E(KS) ~ Mp
Rejecting events with:
DE(KS)<10 MeV
M. Martini, LNF Spring School 2004

10. Candidates We have optimized our analysis cuts looking at MC c22p c23p
c2FIT
DECUT
 DATA
 MC
c22p
c23p
e = (22.6±0.8)%
We count 4 candidates with
3.2±1.4±0.2
expected by MC
N3p ≤ CL
Folding the proper bkg
uncertainty.
M. Martini, LNF Spring School 2004

11. Upper Limit determination
We derive from our analysis:
This improves of a factor ~100 the previous limit.
Using PDG values and our limit:
Using this upper limit we can calculate some parameters
directly related to CP and CPT test.
M. Martini, LNF Spring School 2004

12. Related parameters M. Martini, LNF Spring School 2004
Our limit can be compared with NA48
No KS single beam: detecting interference
term between KSKL in the same final state
(proportional to Re(h000) and Im(h000)).
90% CL
KLOE
Im(h000)
Re(h000)
KLOE
KLOE versus NA48
(hep-ph/ )
90% CL
Assuming CPT invariance Re(h000)=Re(e).
We can calculate the contribution of
3p0 decay at Im(d) (Im(d)000) using
unitarity relation:
with:
M. Martini, LNF Spring School 2004

13. Related parameters
The most conservative approach is to assign a phase to a000
which gives the minimum and maximum values of Im(d)000:
Im(d)000
f000 (rad)
Since these are 2 opposite values,
we obtain a range for
90% C.L.:
This value is obtained using only unitarity, and increases the precision on CPT test, becoming negligible 3p0 uncertainty.
M. Martini, LNF Spring School 2004

14. Additional information

15. Good agreement DATA-MC in all the regions
The c23p
 DATA
 MCbg
The c23p is based only on the 3 reconstructed pion masses
“SPLASH” events
Due to DAFNE bkg which satisfy the trigger.
Reduced by our Splash Filter:
rmean > 70 cm
Emean > 70 MeV
 DATA
 MCbg
 KS3p0 MC
c2FIT < 30
Good agreement DATA-MC in all the regions
M. Martini, LNF Spring School 2004

16. ? DATA-MC comparison M. Martini, LNF Spring School 2004
MCbg
In the data, a new category of BKG events (not simulated by the standard Kcrash MC) appears. The simulation takes into consideration only KL decaying after a cilinder bigger than DCH and smears the KL MC direction with the Kcrash resolution observed in data.
FAKEKCRA
M. Martini, LNF Spring School 2004

17. The Kcrash fake background
A small fraction of the background (3%) is constituted by
a fake Kcrash and a KL 3p0 decay.
The fake KLCRASH is generated mostly by KS p+p- event,
where the pions, spiralizing around the pipe, interact on
the quadrupoles creating late clusters in the event.
We have add the simulation of these events in the MC and
calibrated their quantity.
M. Martini, LNF Spring School 2004

18. DATA-MC “fakes” comparison
Comparing events with tracks from IP.
EKLCRA b*
Outside the
KLCRASH b*
windows DATA are
dominated by fakes
In the central band
there is also a small
percentage of
KLCRASH. b*
 DATA
-- MC Fake
EKLCRA
 MC fakes only (i.e. no Kcrash)
 DATA dominated by fakes
 DATA
-- MC Fake
EKLCRA
M. Martini, LNF Spring School 2004

19. The agreement between DATA and MC is better than 10% in all
DATA-MC comparison
 103.8
24396  156
Cdown
 74.0
11249  106
Cup
 51.0
5502  74
CSbox
426.5  14.4
382  19
DOWN
479.8  21.2
493  22 UP
309.5  16.3
337  18
SBOX
Nev (MC)
Nev (Data)
Region
The agreement between DATA and MC is better than 10% in all
the regions. UP
SBOX
DOWN
Cup
CSox
Cdown
c22p
c23p
M. Martini, LNF Spring School 2004

20. Monte Carlo calibration
-- DATA
-- MC
-- KCRAMC
-- FAKEKCRA
c23p < 3.5
FIT data using shapes from MC:
ID(DATA) = a1 ID(MC)+ a2 ID(FAKES)
0.949
0.895
1.002
FAKEKCRA
0.447
0.446
KCRAMC
Mean
(B)
(A)
Normalized with the full sample Ng=6
Two different regions used:
c23p < (A)
c23p < (B)
After removing SBOX
M. Martini, LNF Spring School 2004

21. DATA-MC comparison (I)
c23p all
c23p > 3.5
c23p < 3.5
c23p< 8.8
 DATA
-- MC
Normalization with the mean values of the coefficients
M. Martini, LNF Spring School 2004

22. DATA-MC comparison (II)
c22p all
c22p > 40
14<c23p<40
c23p< 14
MC KS  3p0, BR=1.4x10-5
Normalization with the mean values of the coefficients
M. Martini, LNF Spring School 2004

23. The track veto
All events with tracks from IP are rejected rPCA < 4 cm ; |zPCA| < 10 cm
MC Signal DATA MC bkg
c22p all
c22p > 40
14<c23p<40
c23p< 14
MC signal, BR(KS3p0)=1.4x10-5
M. Martini, LNF Spring School 2004

24. The topological DECUT
-- MCBG no 2fit cut
 MCBG 2fit < 30
 MCBG 2fit + TRKveto
 MCSIG
After finding the four photons satisfying the kinematics of
KS 2p0, the residual energy of the KS is measured:
E(Ks) = Eks- Eg
DECUT < 10 MeV
Summarizing:
c2FIT<30
TRKveto
Sbox
M. Martini, LNF Spring School 2004

25. Syst1 =  9% (Calibration)
Analysis efficiency and bkg systematics
Analysis step
Survived events
KLCRASH
5211
ACC
2566
ACC  Sbox
1467
ACC  Sbox  Tr
1429
ACC  Sbox  Tr  DECUT
1426
All cuts
1111
Sample of 10 Kevents
KS  3p0
e3p = ( 21.30.7stat 0.3syst )
DATA/MC evaluated in Signal and control boxes varying the cut on the kin. Fit:
c2FIT = 500, 400, 300, 200, 100
No dependence observed as a function of this
cut
Syst.error on BKG
Syst1 =  9% (Calibration)
Syst2 =  10% (Data/MC)
Systot =  14 %
M. Martini, LNF Spring School 2004

26. Optimization of UL
We have optimized the UL by MC looking at 4 different
parameters:
c2FIT
c22p (both sides)
c23p
DECUT
Optimization is done by minimizing the expected 90% CL
upper limit (ref. J.F.Grivaz, F. Le Diberder LAL 92-37)
All is done varying cuts on MC only.
The best choice of the cuts is the following (CUTMAX):
c2FIT < 31
14 < c22p < 60
c23p < 3.7
DECUT > 37 MeV
M. Martini, LNF Spring School 2004

27. NA48 interference function
KL decay
KS decay
Interference KL-KS
K0 K0 Dilution factors
M. Martini, LNF Spring School 2004

28. Related parameters
The more conservative approach is to give at a000 a phase which
maximize Im(D)000:
Because there are 2 opposite values, we obtain a range for
90% C.L.:
Im(D)000 KLOE
Im(D)000 CPLEAR
Im(D)pln
This value is obtained using only unitarity, and increases the precision on CPT test.
Im(D)00
PDG 03
Im(D)+-
x10-5
M. Martini, LNF Spring School 2004