The K L   0  0 decays in KLOE Introduction  pairing Discriminant variables K L   0  0 counting : 3,4,5  ’s samples Control samples for efficiencies Stability in the F.V. Stability in time K L   0  0 counting: summary table Efficiency evaluation Dalitz pairs Ks from regeneration K L   0  0  0 events Ratio of the B.R.

K L   0  0  selection against K L   0  0  0  decays is based on the recognition of the 2-body kinematics Modest energy resolution for  0 is further spoiled by the combinatorial of the  pairing. The  pairing efficiency has been improved from 60% to 98% taking into account not only the residuals to the  0  mass, but also the residuals to the Kaon energy and momenta, normalized to the covariance matrix The results have been obtained using as discriminant variable the ratio of the likelihood (RTL), to have 1or2  0 s from 2-body decay against the hypothesis to have 1or2  0 s without any constraint on the energy. The counting is done comparing the signal and background in a large rtl-window. Introduction

Generalized  2 function for  pairing K L   0  0  and  K L   0  0  0  T T V -1  T M  0  T I = E Ia E Ib (1-cos  I ) I=1,2,(3) T E =    E Ia (E Ib ) T Px =   P xIa (E Ib cos  I, ) T Py =   P xIa (E Ib cos  I, ) K L   0  0  0  only Covariance matrix calculated by the derivatives on respect (E I, x I, y I, z I, R K )  (E I ),  (x I ),  (y I ),  (z I ) have been parameterized as in the Simona work on the  0  0  analysis  (R K ) from the K L   +  -  0 analysis For each pairing there are 2(n(  0  values of the function : the minimum is kept Miscellanea P K 

 0 mass distribution normalized to the  2   0 mc events 3  0 - Data

Test Hypothesis : H 0 2-body kinematics - K L   0  0  event Alternative hypothesis : H 1  0 X E  i =  k /4/  i (1   (1 – D) )  i =  k (1 -  k cos(ki) ) D = 8  i  j m 2 (  0 )/ m 2 (  0 ) / (1 – cos(ji)  E  i = m 2 (  0 ) / E  j / 2. / (1 – cos(ji)  L(n  0 ) =  I exp(-(Emes  i –E  i ) 2 /   i 2 ) / (   i  (2  ) ) I=1, …2n   i parameterized always in the same way. LRatio = max(L| H 0 ) / max(L| H 1 ) -2 log(LRatio) used (RTL) For each pairing there are 2(n(  0  values of the function : the maximum is kept Miscellanea

K L   0  0 counting Tag criteria, fiducial volume : same as in the K L   analysis Track veto criteria : reject the events having tracks not associated with K S      chain Efficiency measured with K L         6  Large RTL window to work at high efficiency (0.9 for 4  sample) Monte Carlo efficiency controlled by the signal selected with the global fit Signal counting by the fit of signal+bck distribution of RTL Monte Carlo distribution scale adjusted using QCAL events for the background AND events selected by the global fit for the signal Counting controlled by the fit of signal+bck distribution of  E for events selected by global fit

RTL : why? RTL  E calc Black histo : Data (4clusters) Red Histo : K L   0  0 Green Histo: Shape without K L   0  0 contribution Black histo : Data (4clusters) Red Histo : K L   0  0 Green Histo: Shape without K L   0  0 contribution Maximum of s/(b+s) max(s) Smoother behaviour of the background in the signal region

Data-MonteCarlo comparison after scaling Signal-Rich Sample Max_dist 1.2% prob 58% Qcal tagged background Max_dist 1.6% prob 13%

5cluster sample  2 = ± ±120 events Mc  =0.5x0.86  E ecal >0 required

 2 = ± ±320 events Mc  =0.77   )>0. required  2 = ± ±180 events Mc  =0.5x0.77 3cluster sample

4cluster sample  2 = ± ±360 events  =0.94(data)x0.95(mc)

Events selected by global fit RTL  E calc  2 = ± ±240 events  2 = ± ±300 events

Fiducial Volume  0  0 vs  0  0  0  events  0  0 + bck ( RTL < 10. required) distribution on the entire volume selected for the analysis Background level greater near the calorimeter Distance from the origin of the neutral vertex distribution for 30<Distance<140. blue points  0  0 + bck ( RTL < 10. required) Black histo :  0  0  0  (sample with > 4 clusters) Entries are those of the 3  0 sample, the blue points have been normalized to an equal number of events

Fiducial Volume Control : Signal counting (4  ) / 3   Signal (4-cluster sample)/ 3   in 9 (R,  not-overlapping regions of the fiducial volume 1. R<68.cm,  <-  /3. 2. R<68.cm, -  /3.<  <  /3. 3. R  / < R<111.cm,  <-  / <R<111.cm, -  /3.<  <  /  /3. 7. R>111.cm,  <-  /3. 8. R>111.cm, -  /3 <  <  /3. 9. R>111.cm,  >  /3.

Time Stability Control : Signal counting (4  ) / 3  0 Signal (4-cluster sample)/ 3   for 9 data subsamples 1. Nrun< <Nrun< <Nrun< <Nrun< <Nrun< <Nrun< <Nrun< <Nrun< Nrun>26800

K L  K S   0  0 counting N reg_gas / N kl   0  0 = 0.24  0.04 Event topology radial position of 25 cm (regeneration at the entrance of the DC) 3clust/4clust = 0.85  0.02 (see next slide) The high percentage of 3cluster events due to the “bad” position of the K S   0  0 vertices on the KL flight direction I assume for the regenerated events an extra-source of loss of clusters connected to the neutral vertex P 3reg = P 3 (1.- p loss ) 3 + P 4 (1.- p loss ) 3 p loss + P 5 (1.- p loss ) 3 p 2 loss P 4reg = P 4 (1.- p loss ) 4 + P 5 (1.- p loss ) 4 p loss P 3reg /P 4reg = 0.85 ; P 3,P 4,P 5 are the percentages for the “normal”  0  0 events. From above, I obtain: P loss = P 3reg = 0.38 P 4reg = 0.45 P 5reg = 0.05 I use the 3cluster and 4cluster events on the regeneration-peak, e.g. the events in a window 0.4 cm wide aroun 25 cm, to measure the percentages of events counted as signal in the analysis: 4-cluster events: 2500 regenerated events in the window : fit output: 525  30 (  2 =1.1) 3-cluster events: 2066 regenerated events in the window : fit output: 626  50 (  2 =1.1) The contribution to the 5cluster sample is negligible  3reg = 0.30  0.02  4reg = 0.21  clusters 0.24 x 0.38 x 0.30 N(K L   0  0 ) = 0.03 N(K L   0  0 ) 4clusters 0.24 x 0.45 x 0.21 N(K L   0  0 ) = 0.02 N(K L   0  0

Any cluster multiplicity > 2 Fit:  900 events 3cluster events Fit:  530 events Fit:  620 events

K L   0  0 counting Fit Regen Track veto Final MC from data Dalitz Final 3cluster sample 4276     cluster sample 1023    cluster sample     TOT    MC - >5cluster 140 Dalitz decays (810  30)  K L   0  0   N(K L   0  0  K L   0  0  0 ) = ( 4.48  0.11  ) 10 -3