1. Sabino Meola Charged kaon group meeting 14 December 2006 Status of analysis

2. Sabino Meola Charged kaon group meeting 14 December 2006 The aim is to measure two relative branching ratios Two normalization samples: - to events in order to obtain a cancellation of the systematic errors. - to events in order to keep under control the track-to-cluster association efficiency.

3. Sabino Meola Charged kaon group meeting 14 December 2006 K 00 e4 VS K 00  3 The measurement strategy is articulated in 5 steps: 1.Neutral vertex (4  ).  →   association. 3.Kinematic fit. 4.Track to cluster association. 5.Background rejection.

4. Sabino Meola Charged kaon group meeting 14 December 2006 Step 1: The neutral vertex method (4  ) Allows the selection of events with 2  0 in the final state  ±  →     X ± The neutral vertex must satisfy the following requests: 4 neutral clusters on time (t - r/c)  = (t - r/c)   = (t - r/c)  = (t - r/c)  consistency with Kaon time of flight Signal K 00  3 Ke3 783~6·10 5 2690 S/B ratio after: ~ 8·10 -2 Signal PDG value: (2.2±0.4)·10 -5 K 00  3 PDG value: (1.757±0.024)·10 -2 Ke3 PDG value: (4.98±0.07)·10 -2

5. Sabino Meola Charged kaon group meeting 14 December 2006 Charged vertex efficiency

6. Sabino Meola Charged kaon group meeting 14 December 2006 Step 2:  →  0 association Cut on   of the association  →   Cut on   =|   best –   near | Signal K 00  3 Ke3 239~1.8·10 5 326 S/B ratio after: ~ 7.5·10 -2

7. Sabino Meola Charged kaon group meeting 14 December 2006 Step 3: kinematic fit 4-momentum conservation    invariant mass clusters on time consistency with Kaon time of flight missing 4-momentum having zero mass   invariant mass clusters on time consistency with Kaon time of flight    3 hypothesis K 00 e4 hypothesis

8. Sabino Meola Charged kaon group meeting 14 December 2006 Step 3: kinematic fit Signal K 00  3 Ke3 234~1·10 5 179 S/B ratio after: ~ 4·10 -2

9. Sabino Meola Charged kaon group meeting 14 December 2006 The measurement method We consider the events distribution in the (m 2,p) plane.

10. Sabino Meola Charged kaon group meeting 14 December 2006 The measurement method K 00 e4 (blue region): -900 < m 2 < 3500 (MeV 2 ) 35 < p < 180 (MeV)    3 (violet region): m 2 < -1000 (MeV 2 ) 25 < p < 180 (MeV)

11. Sabino Meola Charged kaon group meeting 14 December 2006 Measure of the branching ratio The contribution of    background on data is:

12. Sabino Meola Charged kaon group meeting 14 December 2006 Step 4: Track to cluster association Signal K 00  3 Ke3 8111477 S/B ratio after: ~ 0.4

13. Sabino Meola Charged kaon group meeting 14 December 2006 Background analysis K 00  Is due to photon’s clusters wrongly associated to the secondary track. Cut on P/E. Ke3 Is due to Ke3 radiative events. Cut on minimum angle between the 4 photons and the secondary track Cut on E miss

14. Sabino Meola Charged kaon group meeting 14 December 2006 Background analysis: K ± →  ±    

15. Sabino Meola Charged kaon group meeting 14 December 2006 Background analysis: K ± →  ±    

16. Sabino Meola Charged kaon group meeting 14 December 2006 Background analysis: K ± →  ±     We require p/E < 3

17. Sabino Meola Charged kaon group meeting 14 December 2006 Background analysis: K ± →   e ± e (Ke3) Energies constrained by a kinematic fit

18. Sabino Meola Charged kaon group meeting 14 December 2006 Splitted clusters in Ke3 background Minimum tridimensional distance To reject Ke3 events with split clusters we cut on the minimum distance (in 3D) among each couple of clusters. Ke3 K 00 e4 cm

19. Sabino Meola Charged kaon group meeting 14 December 2006 Radiative Ke3 background We look at the minimum angle between the 4 photons and the secondary track. K 00 e4 Ke3  K 00 e4

20. Sabino Meola Charged kaon group meeting 14 December 2006 Background rejection Signal K 00  3 Ke3 717721 S/B ratio after background rejection cuts: ~ 0.7

21. Sabino Meola Charged kaon group meeting 14 December 2006 Measure of the branching ratio Relative error ~ 17%

22. Sabino Meola Charged kaon group meeting 14 December 2006 Measure of the branching ratio Where:

23. Sabino Meola Charged kaon group meeting 14 December 2006 K 00 e4 VS Ke3 The measurement strategy is articulated in 3 steps: 1.Neutral vertex (2  ). 2.Track to cluster association. 3.Background rejection.

24. Sabino Meola Charged kaon group meeting 14 December 2006 Step 1: The neutral vertex method (2  ) Allows the selection of events with 1  0 in the final state  ±  →   X ± The neutral vertex must satisfy the following requests: 2 neutral clusters on time (t - r/c)  = (t - r/c)  consistency with Kaon time of flight   invariant mass Signal K 00  3 Ke3 1859~1.5·10 6 ~5.7·10 6 S/B ratio after: ~ 4·10 -3 Signal PDG value: (2.2±0.4)·10 -5 K 00  3 PDG value: (1.757±0.024)·10 -2 Ke3 PDG value: (4.98±0.07)·10 -2

25. Sabino Meola Charged kaon group meeting 14 December 2006 Step 2: Track-to-cluster association -900 < m 2 < 3500 Mev/c 2 Signal K 00  3 Ke3 2292317~5.7·10 5 S/B ratio after: ~ 2.5·10 -3

26. Sabino Meola Charged kaon group meeting 14 December 2006 We perform a kinematic fit to constrain the photons 4-momentum. Step 3: Ke3 event rejection We consider the E 2 miss -P 2 miss variable

27. Sabino Meola Charged kaon group meeting 14 December 2006 Step 3: Ke3 rejection We require E 2 m -P 2 m < 2·10 4

28. Sabino Meola Charged kaon group meeting 14 December 2006 Background rejection We require two more neutral clusters in the calorimeter. Cut on p* to reject K ± →  0  ± events. Cut on P/E in order to reject events with a charged pion in the final state. Signal K 00  3 Ke3 91214195 S/B ratio after background rejection cuts: ~ 0.2

29. Sabino Meola Charged kaon group meeting 14 December 2006 Ke3 normalization method: Implement a kinematic fit in Ke3 hypothesis (almost done). To be done For both measurement strategy: Tracking efficiency (already done). TCA efficiency (almost done). Trigger efficiency (almost done). Tag Bias. Systematic checks.

30. Sabino Meola Charged kaon group meeting 14 December 2006 Step 3: K   event rejection p* < 150 Mev/c

31. Sabino Meola Charged kaon group meeting 14 December 2006 Conclusions The measurement method allows to estimate the K 00  3 background contribution directly from data. Normalization to    3 events guarantees a cancellation of the systematic effects. A second measurement method with normalization to Ke3 events would allow to keep under control the track-to- cluster association efficiency. Will benefit of 2 fb -1 statistics.