1. 1 Warsaw Group: Marek Szczekowski and Artur Ukleja 2015 Search for CPV in four-bodies charm decays using the kNN method Outline The goal of analysis The data sets and selections The unbinned kNN method Studies using control decay Studies using Monte Carlo Summary and future plans

2. The goal of analysis 2 Use the k nearest neighbor (kNN) method to search for CPV in SCS decays D 0 →  -  +  -  + and D 0 →K - K +  -  + The first, the kNN method should be checked to give the reasonable answer and the detector effects should be well understood. We check it in:  CF decay D 0 →K -  +  +  -  Monte Carlo SCS generated events  sidebands of SCS decays Today we discuss studies in control decay D 0 →K -  +  +  - and MC signal decay D 0 →K - K +  -  +

3. Data sets 3 We use full 2011 and 2012 data sets (3/fb) We analyze D 0 →  -  +  -  +, D 0 →K - K +  -  +, D 0 →K -  +  +  - from D* + →D 0  + s The selection criteria we took from LHCb-ANA-2014-037 (A search for CPV in D 0 →K - K +  -  + decays via measurements of T-odd triple product asymmetries) DstarPromptWithD02HHHHLine Stripping line Charm Stream Reco 14 Stripping 20

4. The available statistics 4 Plots for 2012 D 0 →K -  +  +  - SCS decay D 0 →K - K +  -  + 2011: ~102k 2012: ~246k Total: ~350k events SCS decay D 0 →  -  +  -  + 2011: ~0.57M 2012: ~1.46M Total: ~2M events CF decay D 0 →K -  +  +  - 2011: ~5M 2012: ~13M Total: ~18M events D0→-+-+D0→-+-+ D 0 →K - K +  -  + For further analysis we take events in mass window ± about 2  around PDG values

5. Unbinned method – k-nearest neighbor technique To compare probability distribution function of phase space for D + and D - we define a test statistic T which is calculated for a pooled sample of D + and D - :  I(i,k) = 1 if i th event and its k th nearest neighbor have the same charge (D + —D +, D - —D - )  I(i,k) = 0 if pair has opposite charge (D + —D  ) T is the mean fraction of like pairs in the pooled sample of the two data sets We calculate p-value for case of no CPV by comparing T with expected mean If n + = n - then  T ≈ 1/2 (mean value) and The kNN method 5 x y D-D- D+D+ query event n k =10

6. The kNN method 6 The kNN method allows to find differences between two samples if they come from: normalization, if n + ≠ n - then  T ≠  TR (  TR is calculated for hypothesis n + =n -  TR = ½ (n-2) / (n-1) ) shape, if f + ≠ f - then T ≠  T we calculate the two p-values CP asymmetry can be manifested by different normalization and shape For shape the p-value is the area under the expected curve from measured T to 1. in case of CPV, p-value ≪ 1 Expected distribution generated using Eqs.  T,  T Measured T p-value

7. The kNN results in CF decay 7 D 0 →K -  +  +  - 2012 Mass window: ±2  around PDG values |M-M PDG |<16 MeV and |  m-  m PDG |<0.7 MeV Sidebands: regions where the distribution is flat M 1900 MeV and  m 148 MeV To check the systematic effects we will change above definitions Sideband Side- band

8. The kNN results in CF decay 8 D 0 →K -  +  +  - We define regions around resonances A few regions are overlapped

9. The kNN results in CF decay D 0 →K -  +  +  - 9 We use n k =50 for all presented results Production asymmetry: (Paper…..) 2011: triangles, 2012: dots

10. The kNN results in CF decay D 0 →K -  +  +  - 10 2011: triangles, 2012: dots No additional asymmetry (except production and detector) is observed in control decays

11. The kNN results in sidebands of CF decay 11 D 0 →K -  +  +  - Observed asymmetry in left sideband agrees with the production asymmetry. Left sideband is not clear combinatorial background, it has admixture of D 0 Hypothesis: it comes from five-body decays D 0 →K -  +  +  -  0 where the  0 is not reconstructed To be investigated…..

12. The kNN results in sidebands of SCS decays 12 D0→-+-+D0→-+-+ D 0 →K - K +  -  + In both sidebands No asymmetry in sidebands of SCS decays is observed

13. Toy MC studies 13 350k generated SCS decays D 0 →K - K +  -  + using Mint (Many thanks to Jonas for help) The statistics is comparable to the combined 2011 and 2012 data sets We use the following intermediate states:  D 0 →  (→K -  + )  (→  +  - )  D 0 → K* (892) (→K +  - ) K -  +  D 0 → K* (892) (→K -  + ) K +  - The sensitivity to CP violation is investigated with different amplitude and weak phase differences

14. Toy MC studies in D 0 →K - K +  -  + 14 The available phase space we divide into regions to increase the sensitivity of the method To maximize the sensitivity we choose regions where the asymmetry has the same sign. Example shows how regions are defined in one dimension We divide sample into two in one dimension. We choose the best regions separately for CPV in amplitude and weak phase. The perfect solution chosen for amplitude we use for phase and vice versa. It allows the power of the method if regions are imperfectly chosen.

15. Toy MC studies in D 0 →K - K +  -  + 15 Region definition in other variables of 5D phase space. There are 16 regions.

16. Toy MC studies in D 0 →K - K +  -  + 16 Asymmetry is introduced in resonance D 0 →K*K -  + as 10% in amplitude Regions R1,R2,R5,R6,R7,R8, R11,R12,R13,R14 chosen perfectly for asymmetry in amplitudes R3,R4,R5,R6,R9,R10,R11,R12, R15,R16 chosen for asymmetry in weak phase Regions defined perfectly for weak phases allow to see an asymmetry if it is implemented in amplitudes and vise versa.

17. Toy MC studies in D 0 →K - K +  -  + 17 Conclusion: It does not mean how regions are chosen: perfectly or not. An idea of regionalization allows to increase the sensitivity of the method, less important is how regions are chosen Asymmetry is introduced in resonance D 0 →K*K -  + as 40 0 in weak phase

18. Sensitivity of the method for D 0 → K - K +  -  + 18 We have checked that the kNN method has a sensitivity if CP asymmetry is larger than 4% in amplitudes or 15 0 in weak phases in the intermediate resonance D 0 →K*K -  + (350k generated decays of D 0 → K - K +  -  + ) An idea of regionalization allows to increase the sensitivity of the method but less important is how regions are chosen (perfectly or not)

19. Toy MC studies in D 0 →K - K +  -  + 19 CP asymmetry is introduced in the intermediate resonance D 0 →K*K -  + 15 0 in weak phases4% in amplitudes

20. The sensitivity of the kNN method in D 0 →  -  +  -  + 20 1400k generated SCS decays D 0 →  -  +  -  + using Mint (4 times larger than D 0 →K - K +  -  + ) with the intermediate states: D 0 → a1(1260)  - where a1(1260) →  0  + ← here we introduce asymmetry sprawdzić czy jeszcze jaki stan Plots are for no CP asymmetry

21. The sensitivity of the kNN method in D 0 →  -  +  -  + 21

22. The sensitivity of the kNN method in D 0 →  -  +  -  + 22 We checked that the kNN method has a sensitivity if CP asymmetry is larger than 2% in amplitudes or 5 0 in weak phases in intermediate resonance D 0 → a1(1260)  - (1400k generated decays of D 0 →  -  +  -  + ) It is comparable with the energy test method (Shanzen’s presentation on 23/09/15)

23. Summary 23 Summary  … Next steps  Better understand the detector effects and compare in details with the energy test results  ANA-Note in preparation

24. Backup 24

25. 25 2011 D 0 →K - K +  -  + Sample consists of prompt D 0 and D 0 come from D* decays By two-dimensional fit to M and  m we choose D 0 from D* decays

26. Toy MC studies in D 0 →K - K +  -  + 26 The available phase space we divide into regions to increase the sensitivity of the method To maximize the sensitivity we choose regions where the asymmetry has the same sign. Example shows how regions are defined in one dimension

27. Toy MC studies in D 0 →K - K +  -  + 27 Region definition in other variables of 5D phase space. There are 16 regions.

28. The kNN results in CF decay D 0 →K -  +  +  - 28 Part of 2011 data