1. F. Martínez-Vidal IFIC – Universitat de València-CSIC (on behalf of the BaBar Collaboration)  from B ±  D (*)0 [K S     ]K (*)±  in BaBar Outline  from B   D 0 [K S     ]K  Dalitz model Selection criteria and data sample Extended ML fit and (x ±,y ± ) results Experimental and Dalitz model systematic errors Statistical interpretation Summary & Outlook CKM’06 Workshop, WG5 Session December 12 nd, 2006 hep-ex/0607104 hep-ex/0507101 PRL95, 121802 (2005)

2.  from B -  D 0 [K S     ]K - Interference between b  cus and b  ucs decay processes The interference (sensitivity) is a function of the Dalitz plot position Cabibbo & color favored (Cabibbo & color)-suppressed r B =0.12  =70°  B =180 ° D0D0 D0D0

3. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 3 Dalitz model: reference BW model extracted from high statistics (390k) and high purity (97.7%) tagged D 0 data, obtained from D *+  D    decays from continuum Use as reference isobar model with coherent sum of Breit-Wigner amplitudes –3-body D 0 decays proceed mostly via 2-body decays –BaBar model: 16 resonances (3 DCS) + 1 NR, with all parameters from PDG except: K * 0 (1430), taken from E791 experiment (E791 uses isobar model while PDG quotes LASS parameterization) “Ad hoc”  (500),  ’(1000) resonances (required to describe the  S-wave), extracted from D *+  D    fit Kopp et al., PRD63, 092001 (2001) Angular dependence of the amplitude depends on the spin J of the resonance r. Includes F D and F r form factors (  Blatt-Weisskopf penetration factors) Relativistic Breit-Wigner with mass dependent width  r depending on the resonance K S  , K S  ,    . M r is the mass of the resonance

4. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 4 Dalitz model: reference BW model K * (892) K * DCS  (770)  S-wave Non-resonant CA K*  DCS K*   P,D- waves  2 /dof  1.2 Total fit fraction: 120% m 2  (GeV 2 /c 4 ) m 2  (GeV 2 /c 4 ) m 2  (GeV 2 /c 4 )m 2  (GeV 2 /c 4 )

5. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 5 Dalitz model:  S-wave K-matrix model  S-wave CA K*  DCS K*   P,D- waves Total fit fraction: 111%  2 /dof  1.2 unchanged, since dominated by K  P-wave Main limitation of the BW model: significant violation of unitarity due to large and overlapping scalar  resonances Use K-matrix formalism to overcome the problem Anisovich & Sarantev, Eur. Phys. Jour. A16, 229 (2003) K-matrix Phase space matrix Used to assign  S-wave systematic error Initial production vector m 2  (GeV 2 /c 4 )

6. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 6 Selection criteria D 0 K D* 0 K (D 0 p 0 )D* 0 K (D 0 g)D 0 K* |cos q T |<0.8 <0.8<0.8<0.8 |mass(D 0 )-PDG|<12 MeV <12 MeV<12 MeV <12 MeV |mass(K S )-PDG|<9 MeV <9 MeV<9 MeV<9 MeV E(  )----- >30 MeV>100 MeV----- |mass(  0 )-PDG|----- <15 MeV---------- Kaon Tight Selector Yes YesYes----- |Dm-PDG|----- <2.5 MeV<10.0 MeV----- cos a Ks >0.99 >0.99>0.99>0.99 |mass(K * )-PDG|----- ----------<55 MeV |cos  H |----- ---------->0.35 |DE|<30 MeV <30 MeV<30 MeV<25 MeV Efficiency 15% 7%9%11% cos  Ks suppresses fake K S |cos  T | suppress jet-like events Kaon Tight Selector and |  E| suppress D (*)  events <5% of signal (D 0  )K from (D 0  0 )K cross-feed. Common events assigned to (D 0  0 )K sample For each D (*)0 K (*) channel we also reconstruct its own control sample: D 0 , D *0  (D 0  0 ), D *0  (D 0  ), D 0 a 1 

7. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 7 B -  D (*)0 K -, D 0 K *- data sample Selected candidates and Dalitz distributions D 0 K 398±23 D* 0 K, D* 0  D 0   97±13 hep-ex/0607104 347x10 6 B  hep-ex/0507101 227x10 6 B  B -  DK - B +  DK + D* 0 K, D* 0  D 0  93±12 Signal D Bq D 0 K* 42±8 Differences between B + and B - signifies CPV

8. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 8 Extended ML fit

9. CKM’06 Workshop, WG5, 12 th December General signal decay rate: Generalized CP cartesian coordinates –Account for natural width of X S system, for generic B   D 0 X s Cases –B   D (*)0 K  : Null width  –B   D *0 [D 0  0 ]K , D *0 [D 0  ]K  : –B   D 0 K  : Don’t know   Fit for Gronau, PLB 557, 198 (2003) Extended ML fit: signal parameterization Bondar, Gershon, PRD 70, 091503 (2004)

10. CKM’06 Workshop, WG5, 12 th December Extended ML fit: (x ±,y ± ) results D0KD0K D *0 K D0K*D0K* 22 r B- rB+rB+ d B-B- B+B+ B-B- B+B+ All results are preliminary ! Perform simultaneous ML fit to B ± decay rates vs Dalitz model systematic error

11. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 11 Experimental systematic errors Experimental systematicsDalitz model systematics ≳ Statistical error >>

12. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 12 Dalitz model systematic error  S-wave: – Use K-matrix  S-wave model instead of the nominal BW model  P-wave –Change  (770) parameters according to PDG –Replace Gounaris-Sakurai by regular BW  D-wave –Zemach Tensor instead of Helicity formalism as spin factor K  S-wave –Allow K * 0 (1430) mass and width to be determined from D *+  D 0  + fit –Use LASS parameterization with parameters from D *+  D 0  + fit K  P-wave –Use B  J/  K S  + data as control sample for K *+ (892) parameters –Allow K *+ (892) mass and with to be determined from D *+  D 0  + fit K  D-wave –Zemach Tensor instead of Helicity formalism as spin factor BW running width: consider a fixed value Blatt-Weiskopf penetration factor Remove K 2 * (1430), K * (1680), K * (1410),  (1450) Dalitz plot normalization

13. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 13 Residual for the (x , y + ) coordinates wrt the nominal CP fit Yellow band is the nominal fit statistical error (  100 data statistics) Assign as (conservative) systematic uncertainty the quadratic sum of all models Dalitz model systematic error: (x ±,y ± ) biases for alternative models

14. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 14 Statistical interpretation Use frequentist method with Neyman confidence intervals construction for interpretation of CP cartesian parameters (12 for 3 modes) in terms of fundamental parameters (r B, ,  B ) 22 11 B  D (*)0 K combined 5D-confidence regions projections Dalitz model error B  D 0 K * 3D-confidence region projection

15. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 15 Summary and Outlook For now (preliminary): Good precision on the measurement of (x ±,,y ± ) but the improvement on error of  (for both, stat. and syst. errors) also depends on the value of the r B parameter –Our current values significantly smaller than Belle Critical to constraint better r B and improve  is –More data –To combine with GLW and ADS –Help from Nature… Updating with full Run1-Run5 for all modes –Combination with D 0 K * Expect ~ 85 signal events –Trying to include D 0  K S K + K  in combined fit Dominated by CP component  help on x ± coordinates (like GLW) Dalitz model error prediction r B = 0.1

16. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 16 Backup

17. 17 Dalitz model:  S-wave K-matrix model Main limitation of the BW model: significant violation of unitarity due to large and overlapping scalar  resonances Use K-matrix formalism to overcome the problem Anisovich & Sarantev, Eur. Phys. Jour. A16, 229 (2003) Initial production vector K-matrix Phase space matrix Adler zero, to accommodate singularities Coupling constant of pole  to i th channel Slowly varying term

18. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 18 Dalitz model systematic error: D wave Zemach Tensor vs Helicity formalism –Enforces transversity of the mesons (M 2 AB  M 2 r in angular dependence) –In D S       the NR term is much smaller (5%) in Zemach Tensor than in Helicity model (25%) Monte Carlo simulation using f 2 (1270)  MC Zemach MC Helicity Data Data D s   Affects seriously spin 2 resonances

19. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 19 Dalitz model systematic error: K * (892), K * 0 (1430) K * (892) –PDG parameters are from 1970’s (low statistics, ~5000 events), we have ~200k –If we allow mass and width to float, observe ~+1 MeV (  5 MeV) shift on mass (width) with respect to PDG Same behavior from partial wave analysis of B  J/  K  control sample (no S-wave, very clean) –By far, this gives the largest contribution to the  2 /ndof K * 0 (1430) –If we allow mass and width to float, results are consistent with E791 experiment Improved ! K*(892) K * 0 (1430)

20. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 20 (D 0  )K-(D 0  0 )K cross-feed Overlapping in data among different modes only appears between (D 0  0 )K and (D 0  )K samples Confirmed from Monte Carlo simulation: the cross-feed between the samples is due to events of (D 0  0 )K where we loose a soft  and we reconstruct it as a (D 0  )K Since the cross-feed goes in one direction, (D 0  0 )K  (D 0  )K, we assign common events to the (D 0  0 )K signal sample After all the cuts and after this correction applied we expect <5% of signal (D 0  )K from cross-feed A systematic effect to the cross-feed has been assigned adding a signal component according to the (D 0  0 )K Dalitz PDF and performing the CP fit The systematic bias of the fit with and without (D 0  0 )K has been quoted as systematic error Negligible with respect to the other systematic error sources

21. CKM’06 Workshop, WG5, 12 th December F. Martínez-Vidal,  from B ±  D 0 [K S     ]K (*)  in BaBar 21 BaBar vs Belle results: HFAG BaBar has better precision on (x ±,y ± ), but Belle has larger separation between the blows –Need more data to better constraint r B ! [plots do not include Dalitz model errors] PRD 73, 112009 (2006)