1. Sabino Meola Charged kaon group meeting 12 October 2006 Status of analysis

2. Sabino Meola Charged kaon group meeting 12 October 2006 The K ± →     e ± e decay Allows the study of  -  scattering Selection rule  I = ½ Form factor F PDG value: (2.2±0.4)·10 -5

3. Sabino Meola Charged kaon group meeting 12 October 2006 at KLOE  high production cross section  possibility of  -e discrimination  low efficiency for low momentum tracks  high backgrounds  and Ke3 

4. Sabino Meola Charged kaon group meeting 12 October 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.

5. Sabino Meola Charged kaon group meeting 12 October 2006 K 00 e4 VS K 00  3 The measurement strategy is articulated in 4 steps: 1.Neutral vertex (4  ).  →   association. 3.Kinematic fit. 4.Track to cluster association. 5.Background rejection.

6. Sabino Meola Charged kaon group meeting 12 October 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

7. Sabino Meola Charged kaon group meeting 12 October 2006 Step 2:  →  0 association Cut on   of the association  →   Cut on   =|   best –   near |

8. Sabino Meola Charged kaon group meeting 12 October 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 hypotesis K 00 e4 hypotesis

9. Sabino Meola Charged kaon group meeting 12 October 2006 Step 3: kinematic fit

10. Sabino Meola Charged kaon group meeting 12 October 2006 Step 4: Track to cluster association

11. Sabino Meola Charged kaon group meeting 12 October 2006 Background analysis: K ± →  ±    

12. Sabino Meola Charged kaon group meeting 12 October 2006 Background analysis: K ± →  ±    

13. Sabino Meola Charged kaon group meeting 12 October 2006 Background analysis: K ± →  ±     We require p/E < 3

14. Sabino Meola Charged kaon group meeting 12 October 2006 Background analysis: K ± →   e ± e (Ke3) Energies constrained by a kinematic fit

15. Sabino Meola Charged kaon group meeting 12 October 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

16. Sabino Meola Charged kaon group meeting 12 October 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

17. Sabino Meola Charged kaon group meeting 12 October 2006 The measurement method We consider the events distribution in the (m 2,p) plane. 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)

18. Sabino Meola Charged kaon group meeting 12 October 2006 Measure of the branching ratio The contribution of    background on data is:

19. Sabino Meola Charged kaon group meeting 12 October 2006 Measure of the branching ratio

20. Sabino Meola Charged kaon group meeting 12 October 2006 Measure of the branching ratio Where:

21. Sabino Meola Charged kaon group meeting 12 October 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.

22. Sabino Meola Charged kaon group meeting 12 October 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

23. Sabino Meola Charged kaon group meeting 12 October 2006 Step 2: Track-to-cluster association -900 < m 2 < 3500 Mev/c 2

24. Sabino Meola Charged kaon group meeting 12 October 2006 Step 2: Track-to-cluster association (m 2 cut)

25. Sabino Meola Charged kaon group meeting 12 October 2006 Step 3: K   event rejection p* < 150 Mev/c

26. Sabino Meola Charged kaon group meeting 12 October 2006 Step 3: Ke3 event rejection We look for two more neutral clusters in the calorimeter.

27. Sabino Meola Charged kaon group meeting 12 October 2006 We perform a kinematic fit to constrain the photon 4-momentum. Step 3: Ke3 event rejection We consider the E 2 miss -P 2 miss

28. Sabino Meola Charged kaon group meeting 12 October 2006 Step 3: Ke3 rejection We require E 2 m -P 2 m < 10 4

29. Sabino Meola Charged kaon group meeting 12 October 2006 Step 3: Ke3 rejection

30. Sabino Meola Charged kaon group meeting 12 October 2006 Step 3: Ke3 rejection

31. Sabino Meola Charged kaon group meeting 12 October 2006 We have to inquire Ke3 events with two fake neutral clusters (e.g. radiative + splitting). Look to P/E variable to reject K 00  event. To be done

32. Sabino Meola Charged kaon group meeting 12 October 2006

33. 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.