k ± ± 0 0

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



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° *



* 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)



Photons from 0s in ’on MC and Data



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

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



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



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)



98% K°° (MC) ; ~2200 events/pb–1 on data

Evaluating efficiencies: K



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



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 “”



v TT

cos |v

MCData

Evaluating efficiencies: 4onT



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



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



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



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



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



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



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


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



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



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]



(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



(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



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



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:


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


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


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

k ± ± 0 0

Documents

mev ei

mev pdau

ei15 mev

kloe data

mev ej ek

tracks vertex tt

corresponding kloe acceptance

kaon tracks