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K tracking efficiency & geometrical acceptance : a K (p K , q K )

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### Tag Background evaluation

K tracking efficiency & geometrical acceptance : aK(pK,qK)

- We use the tag in the handle emisphere to have in the signal emisphere a “pure” beam of K+(K-)
- The signal is flagged as Kaon with standard cut on momentum and IP distance
- Background to the signal is mainly due to early 3 body decay of the K, whose secondary can mimic a K
- We use the minimum distance between the signal track and the extrapolated track from the handle as check parameter
- The shape of the DR distribution forbackgroundis taken fromMC
- “ “ for signal is taken from MC and from double tagged event

Handle K track

extrapolated

aK(pK,qK) signal selectionOnce we found a “signal” K compute the distance of closest approch between the first hit of its track and the track extrapolated from the handle:

Four K definition cuts :

1) q opposite to the “handle”

2) 70 < PK < 130 MeV

3) Rpca < 10 cm

4) -20 < zpca < 20 cm

We monitor the background contamination of the signal looking at the tracks minimum distance computed at the point of closest aproach.

K track eff. = fit to Dr

BLUE K from MC

RED K from 2 tag

GREEN bck from MC

The fit to the distribution of the distance of minimum approach between the signal track and the extrapolated track is made using MC and 2 tag shape for the signal and MC for the background shape

Dr (cm)

K shape uncertainties

The Dr distribution in the K region is slightly overestimated by the fit with K shape from MC and underestimated by the fit with the K shape from 2 tag. The differences between the 2 fits gives the sistematic on the K shape

Fit – signal : MC shape

Dr (cm)

signal

Fit – signal : 2tag shape

Dr (cm)

Dr (cm)

aK- versus time

Handle : K+

Signal : K-

aK-

2001

We check the stability of aK versus time. The 2001-2002 data were divided in chunk of 6 pb-1each. The two different results account for the 2 different shape choice for the K contribution.

2002

IntLum/6 (pb-1)

Sistematic : handle tag

Systematic on the K tracking eff. can be due to what happen in the opposite emisphere. Thus we measured the tracking efficiency with respect to the kind of handle tag

aK-

BLUE: Kpp0

RED : Kmn

BLACK: all tag

All the variations seem to be within statistical error.

There is no evidence for dependence of the eff from the handle tag.

IntLum/5 (pb-1)

aK+vsaK-

BLUE = aK+

RED = aK-

aK

The nuclear interactions of K- in the beam pipe and in the DC wall reduce aK-in comparison to aK+ by more than 1 %

IntLum/6pb-1

aK+ with respect qK and pK

We divide the qK in 6 bin in the range 30< qK <90 and the K momentum in 6 bin in the range 70< pK<130 (Mev/c)

aK-

Nevents

qbin

Pbin

qbin

qbin = 10 deg

Pbin = 10 MeV/c

Pbin

Summary

- The K tracking efficiency times the geometrical acceptance aK has been measured using the tag tecnique at fraction of % level
- The aK has been measured independently for positive and negative K
- The sistematics due to the uncertainty on shape of the signal and due to tag bias have been evaluated
- The aK has been measured versus the time in step of 6pb-1
- A memo is in preparation

The use of the K+(K-) tag decay ( Kmn and Kpp0) allow us to select a pure K-(K+) beam. Eventual pollution of the tag reflects in a systematic underestimation of the absolute BR measured. We made a first attempt to estimated this background using a sample of 4 pb-1 of 2002 data

- We assumed that the background fraction in the events with one tag decay is small.
- There is no background in the events where both K+ and K- undergo a tag decay (double tagged events)
- We compare the single and double tag kinematic distribution: the differences can be due to the background ( and , to some extent, to slightly different acceptance )
- The statistical power of this analysis is limited by the rate of double tagged decay in K+K- events ( 10% of the total in the stream)

Tag bck: Kinematic variables

- The control variables was chosen both in the lab and in the center of mass frame:
- Momentum of the K charged secondary in the K frame
- Angle between the K flight path and the charged secondary in the K frame
- Angle between the charge secondary and the K in the lab
- Number of clusters associated at the K decay product ( ≤1 for Kmn and ≤3 for Kpp0)
- Energy of the cluster associated to the charged secondary
- Time of flight of the charged secondary

Only the shape can be compared due to the different yelds of single and double tag events

Charged secondary momentum in K frame

Linear

scale

Log

scale

Mev/c

Mev/c

Normalized comparison between single and double tag events

Red = difference of the 2 histo

Blue = statistic uncertainty

Mev/c

Cos(q) between K and secondary in K frame

Linear

scale

Log

scale

Red = difference of the 2 histo

Blue = statistic uncertainty

Number of secondary cluster associated

Linear

scale

Log

scale

Ncluster ≤1 for Kmn

Ncluster ≤3 for Kpp0

Red = difference of the 2 histo

Blue = statistic uncertainty

Background statistic estimator

To build a conservative background estimator I have to measure the deviation from statistic fluctuation of the difference of the two sets of histos. We define:

d(n) = abs [ his2tag(n) – his1tag(n) ]

For bin n

sd(n)2 = ( shis1(n))2 + (shis2(n))2

For each bin I consider the quantity e(n) = d(n) - sd(n) . This variable gives the deviation of d(n)from the statistical fluctuation and is > 0 if the bin is bigger then statistica fluctuation and < 0 is underfluctuate. The sum over all the bins of e(n) is a upperlimit to the background.

First results on 3 pb-1 of 2002

Positive Tag

First results on 3 pb-1 of 2002

Negative Tag

Backgroung on negative tag?

The difference between the 1 tag and the 2 tag distribution settles in the signal region.. True background ???

- Conclusion:
- There is no evidence for a clear background contamination in the single tag events, at least at fraction of % level
- We are working out a robust statistic estimator for the background level (or limit)
- Work in progress..

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