1. BaBar-France meeting, 16.10.2008 LPNHE, Paris
B+->D(*)+K(*)0
D. Derkach ( ) , V. Sordini, A. Stocchi
(LAL)
BaBar-France meeting,
LPNHE, Paris

2. Outline motivation of the study; analysis strategy; recent results;
perspectives.

3. Gamma measurement (from CKM08)
g = 88 ± 16 95% Prob.) g = -92 ± 16 95% Prob.)
Sensitivity on g crucially depends on the value of the r parameter

4. Today I’ll concentrate on annihilation..
The amplitudes for B->DK decays can be written in terms of common parameters (Assuming SU(2) symmetry)
Vcb
Vub
Unknowns:

5. What if?..
The two ratios are correlated

6. rB+->rB0
Using the branching ratios and assuming rB value we can predict rB0,
neglecting annihilation
Example with the results pre-ICHEP08
Annihilation can play a role in
 giving different rB+ for different modes (DK,D*K,DK*)
 different predictions and errors for the corresponding rB0
 It is also interesting per se.. see following

7. Annihilation can be neglected ?{ b d B+ d K0 u s

8. { { } Decays proceeding only through annihilation diagrams:
Some measurements have been already performed
Vcb b { c s
l2  (fB/m)
~l2  l2 B0 s K+ d u d b B0 { c
Vcb
Vus u s } K0
l2  l
Br(DsK) = (2.8 ± 0.5) × 10-5
Br(D0K) = (5.2 ± 0.7) × 10-5
Br(D*sK) = (2.2 ± 0.5) × 10-5
Br(D*0K) = (3.6 ± 0.7) × 10-5
Br(D0K*0) = (4.2 ± 0.6) × 10-5
l2  ln
n~1 ?
l2 or l ?
Dominated by something else ?

9. { Indeed we can have large final states rescattering u s Vus d b c VcbK+ B0 s d d
Large RESCATTERING Amplitudes
B. Blok, M. Gronau, J. Rosner,
Phys.Rev.Lett.78: ,1997

10. { { l3  l l3  (fB/m) ~l3  l2 ~l3  l
In the charged B->DK system.
Question b { u
Vub c
l3  l B+
Vcs s K+ u u c { b
l3  (fB/m)
~l3  l2 u B+ u K+ u
If dominated by rescattering s
~l3  l
Considering the previous case we can say that:
Typical order of magnitude of a Color suppressed Vub mediated (we have to use B0)
Br(B0 D0 K0 ) = (rB )2( 5.2 ±0.7) ~
rB ~ 0.3

11. We can measure annihilation diagram related to the previous one by SU(2):{ b d B+ d K0 u s c d
Vus s b { u
Vcb K0 B+ d u u
Following the previous arguments :
Br(B+ D+ K0 ) = can be up to
Let’s try to measure it

12. Previous Analysis
Previous analysis: F. Polci, R. Faccini, C. Voena BAD 830, 1035:
Negative fluctuation : N =
expected limit 7*10-6

13. Choice of Channels
Branching ratio of the signal is normalized to 5*10-6
Channels Used
Efficiency in previous analysis
Efficiency after reconstruction
Matched after reconstruction
Nevents rest for analysis, assuming BR=5*10-6
D+-->K0sp+
(18.8±1.4)%
(49.3±0.5)%
(41.1±0.5)%
(3.3±0.2)
D+-->K0sp+p0
(38.1±0.4)%
(21.4±0.3)%
(8.3±0.5)
D+-->K-p+p+
(18.4±0.5)%
(50.5±0.5)%
(41.7±0.5)%
(31.3±1.3)
D+-->K-p+p+p0
(40.8±0.5)%
(20.2±0.3)%
(9.5±0.5)

14. Strategy preselection; cut optimization; Fisher discriminant;
peaking background;
parameterization;
Toy MC studies;
Combination of channels.

15. 20K each secondary decay channel
Data Sets
Sample
Number of Events
Lumi, fb-1
On-resonance data -
Run1-Run6
Signal MC
20K each secondary decay channel
80K-1000K
B0B0bar MC
736M
1337
B+B- MC
731M
1329
ccbar MC
1132M
871
uds MC
938M
449
Dedicated peaking background
>2000

16. Cut Optimization
Maximizing

17. Cut Table (Example of for B->DK, D->Kpp)
signal
error
efficiency
B+B-
B0B0bar
ccbar
uds
Drho
Dpi
D0K0
D*0K*0 S 1
preselecton
30.8
0.34
40.9%
9009.1
581.3
95.3
70.2
41.0
0.052 2
PK > 0.2, Pp >0.15
29.6
0.33
39.4%
9737.6
8075.7
545.2
80.6
56.9
36.4 3
|MD-MPDG|<0.012
25.0
0.31
33.3%
1714.3
1956.7
357.3
20.2
9.1
7.5
0.097 4
|DEB|<0.02
0.28
26.9%
487.2
561.5
6410.4
102.3
7.8
2.9
2.3
0.147 5
|cosQB_cm|<0.76
18.9
0.27
25.2%
398.9
460.1
9022.3
5089.7
86.1
5.9
1.6
0.154 6
|MK_s-MPDG|<0.006
17.6
0.26
23.5%
181.6
217.5
5396.0
2938.7
36.3
2.0
0.188 7
log(aKs +1)<-8
17.1
0.25
22.7%
53.3
79.0
3559.9
1733.4
7.2
1.0
0.232 8
|cosqHelr|<0.8
14.1
0.23
18.7%
36.6
55.6
2812.8
1352.6
1.1
0.7
0.215 9
mes>5.27
4.9
9.8
355.0
197.7
0.6
0.0
1.3
0.582 10
Fisher>0.
9.5
0.19
12.6%
5.2
43.4
23.3
0.3
1.024

18. Fisher
Fisher discriminant was trained with the same set of observables for all the channels:
Peaking background

19. Parameterization of mes
Continuum background. Argus
BBbar background Argus
Signal
Gaussian
BBbar peaking background (before some cuts)
Crystal ball

20. Parameterization of Fisher
Continuum background. Double Bifurcated Gaussian
BBbar background. Gaussian
Signal
Double Bifurcated Gaussian
BBbar peaking background (before some cuts)
Gaussian

21. ToyMC studies Free parameters of the fit: Nsig, Nbbbar, Ncontinuum,
Shape of the Argus function for continuum background
Continuum
Mean
RMS
Argus Shape
Mean
RMS
BBbar
Mean
RMS

22. Number of generated events = 14.2
Average error = 11.2 events
Mean 14.0
Signal
Mean
RMS

23. Sensitivity for Kpipi channel
With 0 generated events we get an error of 3.8*10-6

24. The complete analysis has been done for other channels.
The details are not given
D+->K0sp+
signal
efficiency
B+B-
B0B0bar
ccbar
uds
Drho
Dpi
D0K0
D*0K*0 s
Cuts
1,7
21,3%
3,9
8,8
403,5
248,0
0,3
1,3
0,0
0,066
mes>5.27
1,6
2,6
47,9
34,9
0,7
0,181
Fisher>0
1,2
14,7%
1,0
8,5
0,291
D+->K0sp+p0
signal
efficiency
B+B-
B0B0bar
ccbar
uds
Drho
Dpi
D0K0
D*0K*0
Drho-pi0
Dpi-pi0 s
Cuts
2,4
6,2%
20,3
29,9
1390,2
843,9
1,0
0,0
0,3
0,050
mes>5.27
6,5
4,6
149,3
95,9
0,7
0,148
Fisher>0
1,9
4,9%
2,3
21,5
22,3
0,253
D+->K-p+p+p0
signal
efficiency
B+B-
B0B0bar
ccbar
uds
Drho
Dpi
D0K0
D*0K*0
Drho-pi0
Dpi-pi0 S
Cuts
2,6
5,5%
97,5
139,2
5112,4
2573,5
1,3
0,0
3,3
0,030
mes>5.27
12,4
21,5
600,2
291,6
0,7
1,6
1,0
0,086
Fisher>0
1,9
4,1%
9,2
12,7
92,9
26,2
0,161

25. Combination of ToyMC With 0 generated events we get an error of 3*10-6
To compare with ~ of the previous analysis

26. Tagging Categories? Could we improve our sensitivity ? Lepton Kaon 1
KaonPion+Pion+Other+No tag

27. Lepton Tagging Category
signal
B+B-
B0B0bar
ccbar
uds
Drho
Dpi
D0K0
D*0K*0 S 1
preselecton
3,0
157,7
181,4
1303,3
387,6
20,1
0,3
2,6
0,067 2
PK > 0.2, Pp >0.15
2,9
142,7
1224,9
362,4
18,5
2,0 3
|MD-MPDG|<0.012
2,5
25,5
55,6
302,6
58,1
13,7
0,0
1,0
0,115 4
|DEB|<0.02
6,9
17,6
86,9
25,2
3,6
0,168 5
|cosQB_cm|<0.76
1,9
5,9
13,3
70,9
18,4
3,5
0,174 6
|MK_s-MPDG|<0.006
1,7
4,9
49,9
12,6
0,9
0,202 7
log(aKs +1)<-8
1,3
2,3
34,0
8,7
0,2
0,241 8
|cosqHelr|<0.8
1,4
0,7
1,6
26,0
0,227 9
mes>5.27
1,5
0,662 10
Fisher>0.
0,814
Notice that for the lepton category no background is expected…
( and about 1 event at Br = )

28. Kaon1 Tagging Category mes>5.27 Fisher>0. signal B+B- B0B0bar
ccbar
uds
Drho
Dpi
D0K0
D*0K*0 S 1
preselecton
3,6
457,1
533,2
11257,9
10186,3
35,3
5,5
3,9
0,024 2
PK > 0.2, Pp >0.15
3,4
409,4
475,7
10540,8
9539,0
32,8
4,9
2,9 3
|MD-MPDG|<0.012
68,7
123,9
2248,6
1631,7
21,0
0,7
1,0
0,0
0,045 4
|DEB|<0.02
2,3
16,7
30,2
647,7
480,6
5,0
0,068 5
|cosQB_cm|<0.76
2,2
14,4
24,4
520,3
394,4
0,3
0,071 6
|MK_s-MPDG|<0.006
2,0
5,9
11,4
306,6
263,5
1,6
0,083 7
log(aKs +1)<-8
1,9
4,2
195,7
176,3
0,5
0,099 8
|cosqHelr|<0.8
151,3
129,8
0,096 9
mes>5.27
23,0
21,3
0,240 10
Fisher>0.
1,1
2,5
0,525

29. Kaon2 Tagging Category preselecton signal B+B- B0B0bar ccbar uds Drho
Dpi
D0K0
D*0K*0 S 1
preselecton
5,5
1570,7
1358,1
25383,0
20259,1
88,9
18,9
12,4
8,8
0,025 2
PK > 0.2, Pp >0.15
5,2
1400,5
1211,8
23750,7
18909,4
83,1
14,6
10,4
8,1 3
|MD-MPDG|<0.012
4,4
246,1
289,0
5026,0
3199,4
54,0
2,0
1,6
0,047 4
|DEB|<0.02
3,6
68,1
77,7
1418,7
919,5
14,9
2,9
0,3
0,072 5
|cosQB_cm|<0.76
3,4
54,3
61,1
1139,5
742,2
12,3
2,6
0,075 6
|MK_s-MPDG|<0.006
3,2
28,1
30,6
674,1
442,8
5,7
0,7
0,093 7
log(aKs +1)<-8
3,1
8,2
13,0
424,9
282,0
0,9
0,115 8
|cosqHelr|<0.8
2,5
4,6
336,1
217,0
0,2
0,0
0,106 9
mes>5.27
1,0
45,9
29,1
0,286 10
Fisher>0.
1,7
0,544

30. All Other Tagging Categories
signal
B+B-
B0B0bar
ccbar
uds
Drho
Dpi
D0K0
D*0K*0 S 1
preselecton
18,7
8782,7
7088,2
155017,7
107020,1
447,8
74,1
53,0
28,6
0,035 2
PK > 0.2, Pp >0.15
18,0
7901,2
6344,3
145141,5
100197,0
420,3
63,1
42,6
24,7 3
|MD-MPDG|<0.012
15,2
1378,6
1494,0
32090,8
17498,7
270,0
14,6
5,2
5,9
0,066 4
|DEB|<0.02
12,3
395,9
436,3
9255,5
4991,9
78,9
4,9
1,6
2,0
0,100 5
|cosQB_cm|<0.76
11,5
324,6
361,2
7296,5
3939,6
66,6
3,3
1,3
0,105 6
|MK_s-MPDG|<0.006
10,7
145,9
170,7
4368,3
2221,7
28,1
0,129 7
log(aKs +1)<-8
10,4
40,9
59,5
2907,2
1268,3
5,7
0,7
0,158 8
|cosqHelr|<0.8
8,5
29,1
40,6
2301,5
999,0
0,9
1,0
0,146 9
mes>5.27
4,3
284,6
146,3
0,5
0,0
0,398 10
Fisher>0.
2,9
35,5
19,4
0,3
0,685

31. Perspectives
Interest of measuring annihilation in Vub mediated processes.
An error at 3*10-6 can be obtained for BR(B+  D+K0).
Progress/work to do :
The error can be further improved (flavor tagging)
Analysis on data
Analysis for other channels D+K*0 and D*+K0

32. Backup

33. Choice of Channels
Branching ratio of the signal is normalized to 5*10-6
Channels Used
Efficiency in previous analysis
Efficiency after reconstruction
Real events after reconstruction
Nevents rest for analysis, assuming BR=5*10-6
D*+-->D0p+
D0-->K-p+
(18.9±0.9)%
(40.0±0.4)%
(36.3±0.4)%
(7.5±0.3)
D0-->K-p+p0
(6.79±0.3)%
(26.4±0.4)%
(19.8±0.3)%
(14.3±0.8)
D0-->K-p+p+p-
(10.5±0.5)%
(29.6±0.4)%
(23.6±0.3)%
(9.8±0.3)
D0-->Ks0p+p-
(10.8±1.0)%
(24.0±0.3)%
(19.9±0.3)%
(2.1±0.2)

34. Choice of Channels
Branching ratio of the signal is normalized to 5*10-6
Channels Used
Efficiency after reconstruction
Real events after reconstruction
Nevents rest for analysis, assuming BR=5*10-6
D+-->K0sp+
(39.3±0.4)%
(30.8±0.4)%
(4.8±0.2)
D+-->K0sp+p0
(29.8±0.4)%
(15.9±0.3)%
(12±1)
D+-->K-p+p+
(41.7±0.5)%
(27.0±0.4)%
(39±1)
D+-->K-p+p+p0
(34.6±0.4)%
(15.1±0.3)%
(13.8±0.8)

35. Method of Combination for ToyMC
1. Generate one ToyMC 2. 3.
4. Produce a lot of ToyMC and produce a combination

36. { { } } } Idea, Vcb channel u b B+ c Vcb Vus s K+ u b B+ c Vcb Vus s

37. Idea, Vcb channel } d b B0 { c
Vcb
Vus u s } K+

38. Idea, Vcb channel d b B0 { c
Vcb
Vus u s } K0

39. Idea, SU(2) symmetry

40. Idea

41. Idea
SU(2)

42. Idea
SU(2)

43. Equations & Unknowns Unknowns:
We solve these equation in Bayesian approach using flat priors for T, C, f and assuming the branching ratios to be Gaussian.

44. Results

45. Result

46. Idea, Vub channel b { u
Vub c
Vcs s B+ K+ u u u { b c B+ s K+ u u

47. Idea, Vub channel d { b c B+ s K0 u d

48. Idea, Vub channel u } { b
Vub c
Vcs } B+ s K0 d d

49. Idea

50. Putting all together
Unknowns: