Status of the measurement of KStatus of the measurement of KL L lifetimelifetime

- Data sample: ~ 440 pb-1 (2001+2002)- MC sample: ~125 pb-1 ( mk0 stream , january production)

Selection:

• standard tag (|S| < 5 MeV, |p*|< 10 MeV) : • t0 reconstructed assuming a bunch crossing every 5.43 ns: ~ 100% correct identification• filter request: a tag plus at least 2 neutral cluster on EMC. both π+π-π0 and π0π0π0 in the same filtered data sample• 3 selection as in the PLB 566(2003) 61 (KLOE note n.182 in details)• Neutral vertex algorithm modified.• New method using χ2 minimization.

May 19th, 2004

“Modified” neutral vertex algorithm:

1) Select events with a vertex in DC and 2 clusters not associated to tracks.2) For each neutral cluster build a Lki.

3) Order the Lki in ascending order along the KL flight direction

4) Look for the closest 2 Lk that satisfy |Lk2- Lk1| < 6 σ1γ

and build the weighted average.

5) Go ahead and behind to look for other clusters that satisfy:

|Lki – <LK > | < 6 σtot , σtot = σ1γ σ2γ

6) The event is kept if there is at least a third cluster in timewith the closest two (MC probability ~ 99.4%) (validation).

<Lk>

LkiLkn

Lki-1

Now I can use the KL π+π-π0 sample to evaluate everything

KKL L decay path:decay path:

0.38% stat

(fit

-dat

a)/f

it

±0.5%

Fit region: 50–158 cm

residuals:

KKL L decay path (II): decay path (II):

Lk fit vs Lmin

Lmin

χ2 vs Lmin

KKL L decay path (III):decay path (III): Lk fit vs Lmax

Lmax

χ2 vs Lmax

New method: χ2 minimization

),(

)(2

202

Kii

KKi

LE

LL

• For each event build χ2 and minimize it by moving LK 0

from –5 cm to +5 cm around the starting value.

• The starting value has been chosen as the weighted average of the two closest clusters.

• Define χ2 as:

χ2 method (II):

),(

)(2

202

Kii

KKi

LE

LL

LK0 ranges from –5 cm to + 5 cm

around the starting value:

dataMC

dataMC

χ2 distribution:

The χ2 is minimum at the starting value

χ2 method (III):

Lmin

Lmax

LK (fit)

LK (fit)

Comparison between different methods in the same fit region (50-158 cm):

Weighted average with the 2 closest photons 341.2 ± 1.3 cm 54/53

Weighted average using all the photons: 340.9 ± 1.3 cm 53/53

χ2 method : 340.8 ± 1.3 cm 50/53

Most energetic cluster : 343.4 ± 1.4 cm 115/53

Background analysis (I):

remaining background ~ 1.2%(mainly from 4 γ sample)

Background analysis (II):

Background distributes uniformely along decay region

N=4

β (KL) (lab) β (KL) (cdm)

LK = βγcτ

Result:Result:

PDG) (fit) = (51.7 PDG) (fit) = (51.7 ±± 0.4) ns 0.4) ns(Vosburg, 1972) =(Vosburg, 1972) =±±ns - 0.4 Mevents (PRD 6 (1972), 1834)ns - 0.4 Mevents (PRD 6 (1972), 1834)(KLOE) = (51.15 (KLOE) = (51.15 ±± 0.2 stat ) ns - 14.5 Mevents – 440 pb 0.2 stat ) ns - 14.5 Mevents – 440 pb-1-1

residuals τ (KL) = (51.15 ±0.2) ns

7.5 ns (50 cm) 23.6 ns

(158 cm)

Lifetime with a fixed number of clusters:Lifetime with a fixed number of clusters:

We have to use all the photons if we want to avoid acceptance corrections

Lifetime with a fixed number of clusters (data-MC comparison):Lifetime with a fixed number of clusters (data-MC comparison):

N=3 ( 0.6%) N=4 ( 9.2%)

N=5 (31.4%)N=6 (55.8%)

Fit region Fit region

Fit region

Fit region

Lifetime with a fixed number of clusters (data-MC comparison):

N=7 (~3%) N=8 (~0.1%)

• For N=7 and N=8 populations there is a bump at Lk ~ 30 cm not observed in MC.• MC was not corrected for discriminator threshold and merging.

Lifetime with a fixed number of clusters (data-MC comparison):

Rt (cm) z (cm)

Sample with 7 photons:Sample with 7 photons:

Tγ – TK (ns)

All the photons are in-time The total energy is OK

Etot (MeV)

Cluster multeplicity in different zones of FV:

40 cm < Rt < 160 cm (ALL)

40 cm < Rt < 80 cm (first zone)

80 cm < Rt < 120 cm (second zone)

120 cm < Rt < 160 cm (third zone)

Discrepancy due to different cluster thresholds in DATA-MC

To do:• Filter new Monte Carlo production and put threshold on MC clusters: 1) to check cluster multeplicities distributions; 2) to understand the nature of the bump in decay distributions for N=7 and N=8 populations; 3) to check behaviour of decay distributions near inner wall (regeneration zone).

• Remove π0π0 and γγ background through cut on invariant mass.

• Evaluate how much are close the two closest clusters for 3π0 and π+π-π0 samples as a function of Lk.

•Evaluate vertex reconstruction efficiency using the χ2 method with the π+π-π0 sample.

• …………………………

Conclusions:Conclusions:

• Full data sample analysed (~ 440 pb-1).

• Decay vertex reconstructed using the weighted average of the two closest photons.

• New method (χ2 minimization) confirms validity of weighted averages algorithms.

• Vertex reconstruction efficiency variations evaluated using π+π-π0

data sample.

• Fit region defined as the maximum range with minimum efficiency variations and minimum spread of the residuals:

• Statistical error in fit region is 0.38%.

Old measurement of KOld measurement of KLL lifetime: lifetime:

Experiment performed at Princeton Pennsylvania Accelerator where KL beamwas created at 90° with respect to the 3 GeV proton beam incident on Pt target.

The beam has a pronounced time structure : each bunch is ~1 ns wide andseparated from the others by ~ 33 ns: this time structure is used to determine TOF of decaying particles ( KOPIO’s method ).

Detector and collimator were mounted on carts that were moved of ~ 24 m corresponding to 1.5-3.7 mean lives of KL in the momentum range detected (150-500 MeV) The data taking consists of 6 different runs at 6 different positions (different acceptance, different momentum range of Kaons,..) for a total of 0.4 Mevents collected.

The detector consists in 4 telescopes placed around the vacuum chamber andconsist of two 1.28 cm plastic scintillators separated by 0.6 cm steel plate + cosmic vetos.A telescope is considered if there is a coincidence between signals of the two innerscintillator counters: if two or more telescope are fired in absence of any cosmic-ray veto counter the signal is kept and used for TOF measurement.

Only flux of protons can be measured: monitors were sensitive inA different way to the number of protons striking the production target.The normalization procedure rests on the assumption that the KL flus is proportional to therate of these monitors for a given momentum of the primary proton beam.

The number of KL decays is: N (D,P) = N0 (P) ε (D,P) Ω(D) exp(-MD/Pτ)Where N0(P) = is the production intensity (from protons monitors) Ω(D) = solid angle subtended by the detector (evaluated using Monte Carlo) ε (D,P) = efficiency (evaluated using Monte Carlo)

Lifetime is obtained through a least squares fit which determines also a setof 9 parameters that describe the kaon production spectrum at the synchrotron targetAfter multiplication bu the efficiency for detecting a kaon in the apparatus.The explicit form of the χ2 is:

6

1

30

1

222 /)(j k

jkjkjkjk FKW

Where j runs on the 6 runs, k runs on the momentum bins,Wjk =1, 0 if the bin is considered or not, Kij is the normalized detected kaon rateΔjk is its uncertainty, Fjk is the N(D,P) for each momentum bin (here enters the 9 parameters needed to fit the momentum spectrum).

- The main characteristic of this decay is to have a large number of photons and the strong point of this analysis is to keep (almost) all the photons that are produced (N 3) . This method makes the effects of the cluster reconstruction efficiency and the acceptance very small.

-Two things must be taken under control: 1) the background; 2) the variation of the reconstruction efficiency of the decay vertex with the decay path. is it possibile to use data in some way?

Considerations and open questions:

1) Vertex reconstruction efficiency1) Vertex reconstruction efficiency

DATA: π+π-π0 “selected”

MC: π+π-π0 “selected”

MC: π+π-π0 “true”

MC: ε (<Lγγ>) vs LK (true)

LK (true) (cm)

DATA: ε (<Lγγ>) vs LK (π+π-)

LK (π+π-) (cm)

KKLL π π++ππ--ππ00 selection (I): selection (I):

Cut on the charged sector: Cut on the neutral sector:

Pmiss- Emiss E(π0)(expected) – E(π0)(γγ)

The selection criteria must not bias the vertex reconstruction efficiency

KKLL π π++ππ--ππ00 selection (II): selection (II):

Background ~ 1 %M (π0) from the best two γ

Background: Control plot:

2) 2) Resolutions:Resolutions:

σ(1γ)

σ(2γ)

KKL L ++--00 data sample data sample

3) Weighted Average:3) Weighted Average:

E

aL

E

ELL

i

ikik ~)( ifonly allowed is

2

122)(

E

ppL

With the KL π+π-π0 sample we can check the 1/(E) behavior:

σ(LK) vs LK (π+π-) σ(LK) vs Eγ

“Standard” neutral vertex algorithm:

1) for each neutral cluster build a Lk

2) order the Lk in ascending order along the KL flight direction

3) look for the closest 3 Lk that satisfy |Lk3- Lk1| < 6 σ1γ

4) If found, build <Lk>.

5) Look ahead and behind if there are other Lki that satisfy |Lki - <LK>| < 6 σ tot

σ tot = σ (<L>) σ (1γ)

6) Build the weighted average with all the photons that satisfy these criteria.

No way to test reconstruction efficiency uniformity using data (no control sample with 3 photons).

<Lk>

LkiLkn

Lki-1

Vertex reconstruction efficiency: π0π0π0 from MC

First attempt: try to use the most energetic photon in the eventFirst attempt: try to use the most energetic photon in the event

Advantage: I can use the KL π+π-π0 sample to check the variation of the vertex reconstruction efficiency with the decay path.

Disadvantage: I loose resolution (but for lifetime is not so critical….)

1) Decay path recontructed using the most energetic photon1) Decay path recontructed using the most energetic photon

fit region: 35 cm – 165 cm

(fit

-dat

a)/f

it

more data than foreseen…..regeneration? background? efficiency?

±1%

- If I use the most energetic photon I cannot avoid background.- Background is mainly concentrated at low LK.- The rejection of background introduces again some dependencyof the efficiency with Lk (which makes the idea useless).

KKL L decay path (IV): decay path (IV):

Check if the π0π0π0 selection introduces some bias in the lifetime

MC before selection: MC after selection:

Lk(true) Lk(true)

The two results are in agreement within the errors

Cluster multeplicityCluster multeplicity: Cluster energy:Cluster energy:

DATA QUALITY (I):

Total energy for N = 3Total energy for N = 3 Total energy for N = 4Total energy for N = 4

DATA QUALITY (II)

Total energy for N = 5Total energy for N = 5 Total energy for N = 6Total energy for N = 6

Total energy for N=7Total energy for N=7 Total energy for N=8,9,…Total energy for N=8,9,…

DATA QUALITY (III)

New talk

Lk dal cluster piu’ energetico tra quelli selezionati da twogam: (id=412)

Lk dalla media pesata tra quelli selezionati da twogam: (id=416)

Lk dal piu’ energetico piu validazione: (id=422,kcp_one)

Come si distribuisce il fondo lungo Lk:

Cluster energy (40 cm < rt <160 cm):