1. Status of the measurement of K L lifetime - Data sample (old): ~ 440 pb -1 (2001+2002) - MC sample: ~125 pb -1 ( mk0 stream ) 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 - π 0 and π 0 π 0 π 0 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. April 28 th, 2004

2. - 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:

3. Lifetime with a fixed number of clusters: We have to use all the photons if we want to avoid acceptance corrections

4. “Standard” neutral vertex algorithm: 1) for each neutral cluster build a L k 2) order the L k in ascending order along the K L flight direction 3) look for the closest 3 L k that satisfy |L k3 - L k1 | < 6 σ 1γ 4) If found, build. 5) Look ahead and behind if there are other L ki that satisfy |L ki - | < 6 σ tot σ tot = σ ( )  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).  L ki L kn L ki-1

5. Vertex reconstruction efficiency: π 0 π 0 π 0 from MC

6. First attempt: try to use the most energetic photon in the event Advantage: I can use the K L  π + π - π 0 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….)

7. 1) Decay path recontructed using the most energetic photon fit region: 35 cm – 165 cm (fit-data)/fit 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 L K. - The rejection of background introduces again some dependency of the efficiency with L k (which makes the idea useless).

8. “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 L ki. 3) Order the L ki in ascending order along the K L flight direction 4) Look for the closest 2 L k that satisfy |L k2 - L k1 | < 6 σ 1γ and build the weighted average. 5) Go ahead and behind to look for other clusters that satisfy: |L ki – | < 6 σ tot, σ tot = σ 1γ  σ 2γ 6) The event is kept if there is at least a third cluster in time with the closest two (MC probability ~ 99.4%) (validation).  L ki L kn L ki-1 Now I can use the K L  π + π - π 0 sample to evaluate everything

9. 1) Vertex reconstruction efficiency DATA: π + π - π 0 “selected” MC: π + π - π 0 “selected” MC: π + π - π 0 “true” MC: ε ( ) vs L K (true) L K (true) (cm) DATA: ε ( ) vs L K (π + π - ) L K (π + π - ) (cm)

10. K L  π + π - π 0 selection (I): K L  π + π - π 0 selection (I): Cut on the charged sector: Cut on the neutral sector: P miss - E miss E(π 0 )(expected) – E(π 0 )(γγ) The selection criteria must not bias the vertex reconstruction efficiency

11. K L  π + π - π 0 selection (II): K L  π + π - π 0 selection (II): Background ~ 1 % M (π 0 ) from the best two γ Background: Control plot:

12. 2) Resolutions: σ(1γ) σ(2γ) K L  +  -  0 data sample

13. 3) Weighted Average: With the K L  π + π - π 0 sample we can check the 1/  (E) behavior: σ(L K ) vs L K (π + π - ) σ(L K ) vs E γ

14. K L decay path: 0.38% stat (fit-data)/fit ±0.5% Fit region: 50–158 cm residuals:

15. K L decay path (II): L k fit vs L min L min χ 2 vs L min

16. K L decay path (III): L k fit vs L max L max χ 2 vs L max

17. K L decay path (IV): Check if the π 0 π 0 π 0 selection introduces some bias in the lifetime MC before selection: MC after selection: L k (true) The two results are in agreement within the errors

18. Cluster multeplicity Cluster multeplicity: Cluster energy: DATA QUALITY (I):

19. Total energy for N = 3 Total energy for N = 4 DATA QUALITY (II)

20. Total energy for N = 5 Total energy for N = 6 Total energy for N=7 Total energy for N=8,9,… DATA QUALITY (III)

21. Result:  PDG) (fit) = (51.7 ± 0.4) ns  (Vosburg, 1972) =  ±  ns - 0.4 Mevents  (KLOE) = (51.15 ± 0.2 stat ) ns - 14.5 Mevents – 440 pb -1 residuals τ (K L ) = (51.15 ±0.2) ns

22. Conclusions: Full data sample analysed (~ 440 pb -1 ). Decay vertex reconstructed using the weighted average of the two closest photons. Vertex reconstruction efficiency variations evaluated using π + π - π 0 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%. Systematic error at present seems below the statistical error.