Analysis of ratio BR( K 0 )/BR(K )

M. Martemianov, ITEP, October 2003

Analysis of ratio

BR(K 0)/BR(K )

M. Martemianov

V. Kulikov

Motivation

Selection and cuts

Trigger efficiency

Signal and Background fit

Selection efficiency

Result and conclusion


Motivation / I

2A

23)A(K

, 2

A32

0A

31 )A(K

,2

A6

10

A3

1-)A(K

0

000

0

ChPT theory for K decays gives total amplitude as mixture of two isospin (I=0 and I=2) amplitudes :

CPM (chiral pole model) predicts amplitude A(K+ + 0) by formula2)/22m-2

K(m)0(cos sin)A(K 0 ffccFGCPM

PDG values : GF = 1.16610-5 GeV (Fermi constant)

sinc = 0.2196 and cos c = 0.9734 (c - Cabibbo angle)

f+(0) = 0.96 and f = 93 MeV

GeV810764.1)A(K 0 CPM


Motivation / II

RFPK

MallK

KBRtot /28exp)A(K

00

Using PDG constants and the most precise experiment :

GeV810)012.0835.1(exp)A(K 0

Difference between prediction and experiment : 3.8 %

Best experiment,

LEAR (CERN), 1992

ν)μBR(K)0ππBR(K

First step :

measurement of

at precision around (less ?) 1 %

Precision 1.5 %


DST - version N 15 for kpm - stream

Run numbers : 23542-27133 (2387 DST - files)

All runs of 2002 year

Total statistics : 283.5 pb-1

Number of pions candidates : 1.649 106

Number of muons candidates : 4.919 106

Statistical estimation of result

Selected - window :

190 - 220 MeV/c

Selected - window :

220 - 260 MeV/c

- hyphotesis for

secondary particles

Statistical error on the level of 0.1 %


cos.

exp,)

KK()

KKR(

00

KvetoKselKfit.Ktrigger

window

Ktrigger - trigger efficiency, extracted from EXP. data

Kfit - efficiency of signals and background rejection,

based on MC data and performed of EXP data,

Ksel - selection efficiency, from MC and EXP. data

Kvetocos - efficiency of cosmic veto rejection, EXP. data

Tag strategy


0

Splitted tracks

“Wrong” orientation of tracks

At least one secondary kaon vertex with

40 cm < Rxy < 150 cm, |Z| < 210 cm

20 MeV/c < P sec < 320 MeV/c

Rejection of “Splitted” tracks

(events with |PK- P_sec| < 40 MeV/c . AND .

DF < 80 . OR . DF > 1720) , where

DF = | - | - acos (PK P sec)||

Secondary track selection

Kaon candidates from ECLO2

Only events with two kaons and Charge1 x Charge2 < 0

Selection by momenta in the first point in DC 40 < PK < 160

MeV/c


Trigger efficiency / I

,

2

1

K

K+

Drift Chamber

K

K+

Auto - triggering for K+, based on EMC trigger

Trigger effciency = 100 %

Pion trigger (from K+ +0) based on the maximal number of clusters = 3, muon trigger (from K+ +) number of clustres = 1

+ - trigger :

Based on DC track information

Two tracks go to ECL

Rejection tracks fired same ENDCAP


Trigger efficiency / II

Linear fit for both trigger (p0)

- auto - triggering : p0 = 0.3348 0.0008(stat.)


Trigger difference : 0.0007 0.0008 (trigger error = 0.2 % )

- tag, no auto-triggering : p0 = 0.3356 0.0004(stat.)


Trigger difference : 0.0014 0.0008 (trigger error = 0.4 % )


Selection of K decays

All selected events

Events with reconstructed as pions from K 0

Events selected as muons from K

Rejected clusters associated

to the neutral tracks

Minimum | (Ecl1 + Ecl2) -

M(0) | if 0 has common clusters

for both vertex

Procedure needs to get a clear signal for the both peak in windows

Good selection of - decay, small contamination of 0 - events survived

Selection didn’t change the shape of two peak’s shape

MC


Four main modes in geanfi :K K e0K 0K 0 0

Three-body decays

ppexp1

p)(

21

03 xxf

Sum = 15.3 % 0 - selection doesn’t change shape of three - body decays

2 = 1.2

MC data

MC data

MC data + 0 - sel.


Description of - peak

Exp. tails

Step N2 :

Experiment - extracting launch shape of peak for experimental data

Two contributions : and three - body background

Step N1 :

Pure MC - extracting launch shape of peak (3 Gaussians at the same mean value + 2 exponential functions due to effect of multiple scattering)

three-body backg.

- backg.


Description of - peak

Step N1 :

Pure MC - extracting launch shape of peak (4 Gaussians, each 2 Gaussians have the same mean value + 2 exponential functions)

Exp. tails

Step N2 :

Experiment - extracting launch shape of peak for experimental data

One contribution : - background

-backg.


Fit of two peaks

MCthreexfpxfpxfpxF

,)(

3)(

1)(

0)(

Fit gives a full description of all type of kaon decays in DC

f(x)three - extracted from MC


Total statistics

Run Set Signal( -peak)

Signal( -peak)

Bothsignals

23542-24071 201469 600392 80186124072-24626 203407 608802 81220924627-25166 206973 618981 82595425167-25627 208149 620540 82868925628-26065 208810 622589 83139926068-26390 210602 626575 83717726391-26759 207853 618144 82599726761-27133 201755 603302 805057

Total value 1649018 4919325 6568343`

All data diveded on 5 sets


Fit quality

Run Set Correctioncoefficient, %

2( -peak)

2( -peak)

2(both signals)

23542-24071 92.46 0.33 1.30 1.48 1.61

24072-24626 92.69 0.33 1.23 1.50 1.5824627-25166 92.26 0.33 1.32 1.29 1.6125167-25627 92.41 0.33 1.33 1.38 1.5125628-26065 92.55 0.33 1.34 1.48 1.6426068-26390 92.82 0.33 1.24 1.34 1.6026391-26759 92.68 0.33 1.41 1.38 1.6326761-27133 92.53 0.33 1.35 1.46 1.55

`


Correction coefficient on background

Ratio as function of data set

Linear fit gives : 0.3352 0.0003(stat.)

Stat error : 0.09 %

Correction coeff. physical background

Linear fit gives :

Kfit = 0.9255 0.0012(fit.)

Fit error : 0.13 %


Comparison data / MC

Fit can be checked by MC data using the same way :

KMC = 97.10 0.25 %

Kfit = 96.66 0.24 %

Ratio = 0.3174 0.0006

Ratio Kmc = (0.30863 0.00055)MC

Kfit = 0.9255 0.0012

Ratio = 0.3352 0.0003

Ratio Kfit = 0.3102 0.0012

MC : EXP :

On MC fit and real number of ratio coefficient are very close (difference = 0.44 0.35) (contribution to the syst. error)

Total MC correction coefficient : Ksel. = 1.080 0.002


Selection efficiency / I

Ksel = decay vertex window

decay - correction on decay of charged pions vertex - selection of vertex for pions and muons window - correction of signals for all momentum range

decay - can be extracted on MC only using a convenient cut on the track length of secondary particles

vertex, window - estimated on MC and EXP, must be different in MC and EXP. Data due different momentum resolution


Selection efficiency/ II

Distributions on MC and EXP are the same Cut for tracks length on all tracks (> 40 cm) gives

decay = 1.0443 0.0016 (stat.)

Calculation of decay

Main part of this value (1.036) can be calculated from PDG pion decay length, its mass and averaged laboratory momentum (205 MeV/c).

The rest can be attributed to pion decay at larger than 40 cm length with spoiled reconstraction of the pion track due to the presence of pion decay product.


Selection efficiency/ IV

Exp. data

Correction for pions : 96.3 %

Correction for muons : 99.5 %

Correction coefficient for

windows by fit :

1.030 0.002(stat.) (0.2 %)

MC. data Correction for pions : 97.2 %

Correction for muons : 99.2 %

Correction coefficient for

windows by fit : 1.019 0.003

MC real coefficient :

1.020 0.003

Calculation of window

Based on fit parameters

Calculates the percentage muons and pions inside window

Different for MC and EXP data


Selection efficiency/ V

Calculation of vertex

K

K+

+KK+

EMC - cluster

Two EMC clusters only for charged tracks, + - seleclted by momenta

Investigated vertex

vertex = vertex cuts

Investigated vertex

Two EMC clusters only for charged tracks, + - seleclted by momenta, two clusters from gammas

21


Selection efficiency/ VI

Mean value of efficiency (sum by all kaons momenta gives vertex efficiency :

Pions : 86.79 0.18 %, Muons : 86.65 0.08 %

Difference : 0.14 0.20 % (contribution of stat error for vertex efficiency)

Selected muons

Selected pions

Efficiency of vertex efficiency for muons and pions as function of kaons momenta


Selection efficiency/ VI

Calculation of cuts Calculated by MC and corrected by EXP

Includes cuts to reject splitted tracks and cuts on momenta of secondary tracks

MC : cuts = 1.0137 0.0016(stat)

Difference between MC and EXP based only on momenta cuts on high region (main contribution based on muons) and differnece equal to 0.5 %

EXP : cuts = 1.0086 0.0020(stat)

MC distribution of the secondary particles in the laboratory system for muons and pions

from K

from K 0


Summary of selection efficiency

Type Correction coefficient(MC/ EXP)

Syst. error,%

Selection and pions decays 1.0443 0.16

Vertex selection 1.0137 1.0086 0.16 0.26

Kinematical window 1.020 1.0302 0.3 0.2

Total value 1.080 1.085 0.38 0.36

`


Cosmic veto

S = N(vetocos=0) + N(vetocos=1,t3flag=0)+N(t3flag=1)

Kvetocos = 1+64N(t3flag=1) / S

Check cosmic veto for runs 26111-27133

Type of events vetocos = 0 vetocos =1 t3flag = 1 Kvetocos

+, 4.789106 4466 5564 1.00073 0.00010

+0, 0 0.621106 111 5 64 1.00051 0.00020

No difference between rejection of different type of event by cosmic veto on the level 210 4


Corrections and erros

Type Correctioncoefficient

Syst. error,%

Source

Trigger 1.0 0.2 EXP

Background / fit 0.9255 0.46 EXP

Selection and pions decays 1.085 0.36 MC/EXP

Cosmic veto 1.0 0.2 EXP

K decay 0.994 Nucl. Phys.,B115, 55*

Total value MC/EXP 0.9981 0.65

`

*) Taken from previous experiments, we plan to recalculate the coefficient, but now use the same value to compare with pevious experiments.


Comparison with world data

0.00220.00030.3346ν)μBR(K

)ππBR(K (syst.)(stat.)0

2(syst.)(stat.) 10)65.00.09(133.46


Conclusion

ν)μBR(K)ππBR(K 0

was measured

Result has a good agreement with world data

Statistical error is negligible due to the huge sample of kaon decays (more than 6.5 M).

Systematic error ( 0.65 %) dominates. It improves accuracy for the ratio by a factor of 2.7

In principal, result can be updated by further investigation of MC / EXP uncertanties and true calculation of K decay

Analysis of ratio BR( K 0 )/BR(K )

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