1.    Abi Soffer Colorado State University Super B Workshop, UH, Jan 19, 2004

2. Outline NP-independent  (incomplete list, hopefully representative) –sin 2  in B  D 0 K (GW, ADS) –Recent developments B  D 0 (CP) K B  D 0 (non-CP) K, D 0 K  Untagged B 0 –sin(2  +  ) B 0  D ( * ( * ))  ( * ) B 0  DK  D 0 K 0 Comparison to NP- sensitive results Penguins Mixing Cautious predictions for ~10 ab  1    NP

3. r e i(    ) +  e  i  D B+B+ b u u u c s K+K+ D0D0 B+B+ b u c u s u D0D0 K+K+ KK KK 1 Amplitude  bubu bcbc sin 2  with B  D (flavor+CP) K Atwood, Dunietz, Soni, PRL 78, 3257 (ADS) cos  D measurable @ charm factory A.S., hep-ex/9801018 Gronau, Grossman, Rosner, PLB508, 37, 2001 Atwood, Soni, hep-ph/0304085 (1  r e i(    ) ) CPES (CP eigenstate) r e i(    ) Initial a 2 /a 1 ~ 0.25: r ~ 0.1 B 0  D 0  0, etc., suggest r ~ 0.2    Gronau, Wyler, PLB 265, 172 (GW)  e  i  D

4. Sensitivity A.S., PRD 60, 054032 L~600 fb  1, r = 0.1 B  D ( * ) K ( * ) D  K  (n  ) +, CPES True  33 33  22 58 o S  :      S ± :     S  :      Resolved by large  D

5. New Developments More modes & methods – more statistics New methods reduce ambiguity to 2-fold More experimental experience Each of these methods satisfies the NIMSBHO principle: Not Inherently More Sensitive But Helps Overall (despite possible claims to the contrary…)

6. Don’t Measure BR  r 2 Jang, Ko, PRD 58, 111 Gronau, Rosner, PLB 439, 171 Determine r (  V ub /V cb  color suppression) indirectly, from Color-suppressed b  c modes NIMSBHO r

7. SCS non-CP D Decay Modes B+B+ b u u u c s K+K+ D0D0 B+B+ b u c u s u D0D0 K+K+ KK (1+r r D e i(    D  ) ) 1 Amplitude bubu bcbc K  K ... K  K ... (r D +r e i(    D  ) ) No need to measure BR’s  r 2, sensitive at O(r) BR measurable now S  resolved – ambiguity only 4-fold  r D = = 0.7 for K*K, measure with D*-tagged D 0 ’s  D = arg Grossman, Ligeti, A.S. PRD 67, 071301 KK NIMSBHO

8. D Dalitz Plot BaBar, hep-ex/0207089 22 fb  1 m 2 (K 0  + ) GeV 2 m 2 (K   + ) GeV 2 D0K0KD0K0K D0K0KD0K0K There is also the K + K   0 mode

9. D Dalitz Plot, D 0      0 CLEO, hep-ex/0305048 9 fb  1 m 2 (    0 ) GeV 2 m 2 (    0 ) GeV 2 r D = 0.65 ± 0.05  D =  4º ± 5º

10. B+B+ b u u u c s K+K+ D0D0 B+B+ b u c u s u D0D0 K+K+ KK CP even (K + K ...) 1 (1 + r e i(    ) ) Amplitude  bubu bcbc Special Case: CP Modes Gronau, hep-ph/0211282 CP odd (K s  0...) (1  r e i(    ) ) No need to measure BR’s  r 2, sensitive at O( r 2 ) 8-fold ambiguity (when used standalone) KK NIMSBHO

11. Sensitivity with CPES Only CP-even Belle CP-odd  ambiguity M. Rama BR already measured: BaBar

12. B  D (multi-body) K Giri, Grossman, A.S., Zupan, PRD68, 054018, 2003 Expand to multi-body decay: Model-independent analysis: bin the D Dalitz plot   B   f K   1 + r D 2 r 2 + 2 r r D cos(  B +  D –  ) |A(D  f)| Arg(D  f)  Arg(D  f) |A(D  f)| 2 |A(D  f) A(D  f)| cos [or sin]  D For a unique D final state f (such as a 2-body D decay): (From fit or charm factory: c i, s i 2 )  bin i  B   f i K      T i + T i r 2 + 2 r [ cos(  B –  ) c i + sin(  B –  ) s i ] (From D* +  D 0  + ) (From D*   D 0   )

13.  Application to Cabibbo-Allowed D Decays NIMSBHO Divide the D  K s      Dalitz plot into n bins (n  4) 2n observables:  (B + ) i &  (B  ) i in each bin n + 3 unknowns: c i, s i, r,  B,  m 2 (K s   ) GeV 2 m 2 (K s   ) GeV 2 ci  cisi  sici  cisi  si Resolves S . Resonances resolve S ± (essentially no model dependence) Belle Cabibbo-allowed: high statistics Dalitz plot suppression Best interference is around DCS decays This formalism is also needed for D  K     0 and K        (ADS/GW)

14. Assume Breit-Wigner Resonances in D Decay BB BB Belle, hep-ex/0308043, 140 fb   fb  More model dependence, smaller statistical error

15. Errors with 140 fb  r = 0.33 ± 0.10  = 95° ± 23° ± 13° ± 10°  = 162° ± 23° ± 12° ± 24° 90% CL: 0.15 < r < 0.50 61° <  < 142° 104° <  < 214° Asymmetry in B  D   syst has a significant 1/  N component

16. Removing Color Suppression  B+B+ b u u u c s K+K+ D0D0 B+B+ b u c u s u D0D0 K+K+  B+B+ b u c u s u D0D0 K+K+ u u 00 B+B+ b u u u s c D0D0 K+K+ u u 00 r ~ 0.4 instead of ~ 0.1 or 0.2 bubu bcbc Aleksan, Petersen, A.S., PRD 67, 0960XX

17. Dalitz Plot Suppression D s **+ D* 0 K* + bububcbc Expect mostly NR-NR & NR-K* interference NR Simulation Small K(1430) – D s (2450) overlap Oliver et al, hep-ph/9801363 K(1430) D s (2450)

18. Simulation Assuming NR/R ~ 0.4 (or equivalent interference), 400 fb  1, expect   ~ 0.2    Resolves S . Resonances resolve S ± (essentially no model dependence) NIMSBHO

19. 1 rf eiDrf eiD New:  from Untagged B 0 Decays Gronau, Grossman, Shumaher, A.S., Zupan B0B0 b d u d c s K0K0 D0D0 B0B0 b d c d u s K0K0 D0D0 f  (B  f K S ) = X(1+r f 2 ) + 2Yr f cos(  D +   )  Ar e i(    )  Untagged rates: where X  A 2 (1+r 2 ) Y  2A 2 r cos  B Depend only on the B decay For N D decay modes: N+3 unknowns:  D  N, , X, Y Solvable with N  3 (or a multibody D mode) For 2 B decay modes, need only N  2  (B  f K S ) = X(1+r f 2 ) + 2Yr f cos(  D    )

20. Analytic Solution Special case: CP odd and even eignstate and 1 flavor state:

21. Combining with B + Modes Best use of untagged B 0 modes is to combine them with results from B + decays (& tagged B 0 decays) with the same D modes: Every untagged B 0 mode adds 2 unknowns (X, Y) and 2 measurements (  (B  f K S ),  (B  f K S )) D decay parameters &  are the same as in the tagged/B + decays Expect significant improvement in overall sensitivity, since: Sensitivity is dominated by smallest interfering amplitude This amplitude has the same magnitude for B + and untagged B 0 (up to K S /K + reconstruction efficiencies, etc.)

22. S  = sin(2  ) b d hh  d b  c d d u D(*)D(*) d u c d hh D(*)D(*)    t t sin(2  +  ) with B  D ( * )  h  reirei ~0.02 , ,a 1 Dunietz, hep-ph/9712401

23. B  D ( * )    Analyses (full reconstruction) Belle, hep-ex/0308048, 140 fb  BaBar, hep-ex/0309017, 82 fb 

24. B  D*    with Partial Reconstruction BaBar, hep-ex/0310037, 76 fb  B  D* +    D 0   Reconstructed Not reconstructed Lepton tag Kaon tag Lepton tag Kaon tag

25. B  D ( * )    Results a  r (S + + S  ) = 2 r sin(2  ) cos(  ) = magnitude of A CP c  r (S + – S  ) = 2 r sin(  ) cos(2  ) 2 r D*  S + D*   0.092  0.059 (stat)  0.016 (syst)  0.036 (D*ln) 2 r D*  S  D*   0.033  0.056 (stat)  0.016 (syst)  0.036 (D*ln) 2 r D  S + D   0.094  0.053 (stat)  0.013 (syst)  0.036 (D*ln) 2 r D  S  D   0.022  0.054 (stat)  0.013 (syst)  0.036 (D*ln) Belle S   sin(2  a D   0.022  0.038 (stat)  0.020 (syst) a D*   0.068  0.038 (stat)  0.020 (syst) c D   0.025  0.068 (stat)  0.033 (syst) c D*   0.031  0.070 (stat)  0.033 (syst) BaBar (full reconstruction) a D*  (K tag)  0.054  0.035 (stat)  0.017 (syst) S + D*  (l tag)  0.078  0.052 (stat)  0.021 (syst) S + D*  (l tag)  0.070  0.052 (stat)  0.019 (syst) Avg. of a D*   & (S + D*  + S + D*  )/2:  0.063  0.024 (stat)  0.014 (syst) BaBar (partial reconstruction, D*  only) magnitude of A CP

26. B  D*    Systematics (example) Specific to partial reco. Need to measure in data (big statistical component) For 10 ab  1, need to reduce these systematics by a factor of ~5 – 10 sin(2  ) D  with partial reconstruction lepton tag Reduction by 2–3 seems very reasonable Both are currently quite conservative.

27.  from sin(2  +  ) Silva, A.S., Wolfenstein, Wu, PRD 67, 036004   True  Measured  True  few ab  1   So far  seems small  Allowed range      Resolving ambiguities is crucial

28. Sensitivity to r Hard to measure r from (1  r 2 )cos(  m t), need to take it from B  D s +   Angular analysis with B  D*     a  , exploit interference between the 3 helicity amplitudes to do away with r 2 terms London, Sinha, Sinha, PRL 85, 1807 The same can be done with B  D**    2 D** resonances & continuum Resonance mass shapes add to angular information, resolves ambiguities Sinha, Sinha, A.S. r 2 r 1 Enough to measure terms  r Expect significant improvement for this mode Perhaps large  ’s will resolve ambiguities More complicated fit

29. sin(2  +  ) with Tagged B  D ( * )  K s h  hh c d s u D(*)D(*) d u cs hh D(*)D(*) dd KSKS dd KSKS r ~ 0.4 Aleksan, Petersen, hep-ph/0307371 Dalitz plot suppression Ambiguity only 2-fold (   Expect   ~ 0.2 – 0.3 with 400 fb  1 NIMSBHO  

30. Tagged B 0  DK 0 Gronau, London, PLB 253, 483 Kayser, London, PRD 61, 116013 Atwood, Soni, PRD 68, 033009   r ~ 0.36 Data suggest r ~0.6  0.2   (10 9 B’s, sub-BR, tagging, no reco eff. Or bgd.) Belle, PRL 90, 141802 NIMSBHO

31.  with 10 ab  1 Use all methods –Will measure  to ~ 2° (%) (stat) or less! –Only  ambiguity is left Excluded theoretically? –The error is so small that ambiguities won’t matter  

32. Compare to  from Penguins Theoretical uncertainties in precision extraction of  Disagreement with “clean” measurements could be due to NP or EW penguins Theoretical understanding will improve by the time the machine is built B0B0 b d u d d / sd / s u   + /K +  B0B0 b dd u  u d / sd / s bd

33.   Compare to |V td | from Mixing b d / sd / sb d / sd / s Straight forward comparison of |V td | &  1.4%  0.5% with 0.5 ab  1 Ronga, CKM ’03 BaBar, PRL 88, 221803 10%  1-2% “soon” Shoji Hashimoto (SLAC, Oct.) P. Lepage O(%) @ CDF xsxs  x s / x s

34. New Physics in the “SM-only” Measurements “Clean” measurements may not be absolutely clean NP has to look like tree-level charged current interactions –Charged Higgs? Such NP will presumably have a different effect on loop diagrams & other measurements. D 0 mixing may affect B  DK. –Current limits on D mixing yield an effect at the few-degree level (Silva, A.S., PRD61, 112001) –The effect will decrease as D mixing limits tighten, or will be incorporated into the analysis once D mixing is measured

35. Conclusions Many (albeit related) clean ways to measure  –Frequent improvements & new ideas From foreseeable mixing, theory & lattice precision, the target for  precision should be ~1° –May decrease by the time the machine is built, depending on developments in theory and experiment With 10 ab  1 we will –Measure  to ~ 2° or less (statistical) –Resolve essentially all ambiguities –Understanding systematic errors at this level will be crucial This is a rough, cautious estimate. B factory data will provide much better estimates in 2-3 years

36. Backup slides Fraction of allowed range of  excluded by this exp. 0 0.51 A.S., PRD 60, 054032

37. Belle Dalitz fit

38. Sensitivity with CPES + K*K  CP modes K* + K  Combined True   0.5 ab 