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f 3 /g

f 3 /g. Abi Soffer Colorado State University. Super B Workshop, UH, Jan 19, 2004. Outline. -. = NP. g. NP-independent g (incomplete list, hopefully representative) sin 2 g in B  D 0 K (GW, ADS) Recent developments B  D 0 (CP) K B  D 0 (non-CP) K, D 0 K p Untagged B 0

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f 3 /g

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  1. f3/g Abi Soffer Colorado State University Super B Workshop, UH, Jan 19, 2004

  2. Outline - = NP g • NP-independentg(incomplete list, hopefully representative) • sin2gin BD0K (GW, ADS) • Recent developments • BD0(CP)K • BD0(non-CP)K, D0Kp • Untagged B0 • sin(2b+g) • B0D(*(*))p(*) • B0DKp • D0K0 • Comparison to NP-sensitive results • Penguins • Mixing • Cautious predictions for ~10 ab-1

  3. sin2g with BD(flavor+CP)K l2e-idD Gronau, Wyler, PLB 265, 172 (GW) Atwood, Dunietz, Soni, PRL 78, 3257 (ADS) s Amplitude K+ u bc b c K+p- 1 B+ D0 u u l CPES (CP eigenstate) l(1rei(dB+g)) l g b u K-p+ bu D0 rei(dB+g) rei(dB+g) + l2e-idD c B+ s K+ u u Initial a2/a1 ~ 0.25:r~ 0.1 B0 D0p0, etc., suggest r~ 0.2 (l2 ~ 0.05) cos dD measurable @ charm factory A.S., hep-ex/9801018 Gronau, Grossman, Rosner, PLB508, 37, 2001 Atwood, Soni, hep-ph/0304085

  4. True g 3s 3s 58o g c2 58o Sensitivity A.S., PRD 60, 054032 • L~600 fb-1, r= 0.1 • BD(*)K(*) • DK-(np)+, CPES S: g dB, dB g S± : g -g, dB -dB Sp :g g+p, dB dB+p Resolved by large dD

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

  6. Don’t Measure BR  r2 Jang, Ko, PRD 58, 111 Gronau, Rosner, PLB 439, 171 r Determine r ( Vub /Vcb color suppression) indirectly, from Color-suppressedbc modes NIMSBHO

  7. SCS non-CP D Decay Modes rD== 0.7 for K*K, measure with D*-tagged D0’s dD= arg Grossman, Ligeti, A.S. PRD 67, 071301 s Amplitude K+ u bc b c K+p- 1 B+ D0 u u l K*- K+... l(1+rrDei(dB + dD + g)) K*+ K-... l(rD+rei(dB - dD + g)) l g b u bu D0 K-p+ c B+ s K+ u u • No need to measure BR’s  r2,sensitive at O(r) • BR measurable now • S resolved – ambiguity only 4-fold NIMSBHO

  8. D0K0K-p+ D Dalitz Plot BaBar, hep-ex/0207089 22fb-1 D0K0K-p+ m2(K-p+) GeV2 m2(K0p+) GeV2 There is also the K+K-p0 mode

  9. m2(p+p0) GeV2 m2(p-p0) GeV2 D Dalitz Plot, D0p+p-p0 CLEO, hep-ex/0305048 9fb-1 rD = 0.65 ± 0.05 dD = -4º ± 5º

  10. Special Case: CP Modes Gronau, hep-ph/0211282 s Amplitude K+ u bc b c K+p- 1 B+ D0 u u l CP even (K+K-...) l(1+rei(dB+g)) CP odd (Ksp0...) l(1-rei(dB+g)) l g b u bu D0 K-p+ c B+ s K+ u u • No need to measure BR’s  r2,sensitive at O(r2) • 8-fold ambiguity (when used standalone) NIMSBHO

  11. g  d ambiguity Sensitivity with CPES Only • BR already measured: M. Rama BaBar CP-even Belle CP-odd

  12. |A(Df)| |A(Df)| Arg(Df) -Arg(Df) Gbin i (B-fi K-)Ti + Tir2 + 2r[cos(dB – g)ci + sin(dB – g)si] |A(Df)|2 |A(Df) A(Df)| cos [or sin]dD (From D*-D0p-) BD(multi-body)K Giri, Grossman, A.S., Zupan, PRD68, 054018, 2003 For a unique D final state f (such as a 2-body D decay): G(B-fK-) 1 + rD2r2 + 2rrD cos(dB + dD – g) Expand to multi-body decay: Model-independent analysis: bin the D Dalitz plot |A(Df)|2 (From fit or charm factory: ci, si2) (From D*+D0p+)

  13. Application to Cabibbo-Allowed D Decays • Cabibbo-allowed: high statistics • Dalitz plot suppression • Best interference is around • DCS decays • This formalism is also needed • for DK+p-p0 and K+p-p+p- • (ADS/GW) 2 • Divide the DKsp+p-Dalitz plot into n bins (n  4) • 2n observables: G(B+)i & G(B-)i in each bin • n + 3 unknowns: ci, si, r, dB, g ci ci si -si m2(Ksp-) GeV2 Belle m2(Ksp+) GeV2 Resolves S. Resonances resolve S±(essentially no model dependence) NIMSBHO

  14. Assume Breit-Wigner Resonances in D Decay More model dependence, smaller statistical error Belle, hep-ex/0308043, 140 fb-1, 140 fb-1 B- B+

  15. Errors with 140 fb-1 r = 0.33 ± 0.10 g = 95° ± 23° ± 13° ± 10° d = 162° ± 23° ± 12° ± 24° 90% CL: 0.15 < r < 0.50 61° < g < 142° 104° < d < 214° Asymmetry in BDp ssyst has a significant 1/N component

  16. Removing Color Suppression s K+ u Aleksan, Petersen, A.S., PRD 67, 0960XX s u p0 K+ u u bc b c b c B+ D0 B+ D0 u u u u s K+ u g u b u D0 D0 bu c c g B+ b u s p0 K+ B+ u u u u r~0.4 instead of ~0.1 or 0.2

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

  18. Simulation dB g g Assuming NR/R ~ 0.4 (or equivalent interference), 400 fb-1, expect sg ~ 0.2 Resolves S. Resonances resolve S±(essentially no model dependence) NIMSBHO

  19. New: g from Untagged B0 Decays G(BfKS) = X(1+rf2) + 2Yrfcos(dD-g) Gronau, Grossman, Shumaher, A.S., Zupan Untagged rates: G(BfKS) = X(1+rf2) + 2Yrfcos(dD+g) b c D0 u rfeidD B0 s K0 d d where X A2(1+r2) Y 2A2rcosdB Depend only on the B decay A f ~0.4 Ar ei(dB+g) 1 • For N D decay modes: • N+3 unknowns: dDN, g, X, Y • Solvable with N 3 (or a multibody D mode) • For 2 B decay modes, need only N 2 b u D0 c B0 s K0 d d

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

  21. Combining with B+ Modes • Best use of untagged B0 modes is to combine them with results from B+ decays (& tagged B0 decays) with the same D modes: • Every untagged B0 mode adds 2 unknowns (X, Y) and 2 measurements (G(BfKS), G(BfKS)) • D decay parameters & g 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 B0 (up to KS/K+ reconstruction efficiencies, etc.)

  22. sin(2b+g) with BD(*)+h- d d t b b t u B0 B0 d b ~0.02 g reid d u c d D(*)+ h- S = sin(2b+gd) p,r,a1 Dunietz, hep-ph/9712401 b d c h- D(*)+

  23. BD(*)+p- Analyses (full reconstruction) Belle, hep-ex/0308048, 140 fb-1 BaBar, hep-ex/0309017, 82 fb-1

  24. BD*+p- with Partial Reconstruction BD*+ p- Kaon tag Lepton tag D0p+ BaBar, hep-ex/0310037, 76 fb-1 Reconstructed Not reconstructed Lepton tag Kaon tag

  25. BD(*)+p- Results Belle Ssin(2b+gd) 2 rD*p S+D*p= 0.092  0.059 (stat)  0.016 (syst)  0.036 (D*ln) 2 rD*p S-D*p= 0.033  0.056 (stat)  0.016 (syst)  0.036 (D*ln) 2 rDp S+Dp= 0.094  0.053 (stat)  0.013 (syst)  0.036 (D*ln) 2 rDp S-Dp= 0.022  0.054 (stat)  0.013 (syst)  0.036 (D*ln) ar (S+ + S-) = 2 r sin(2b+g) cos(d) = magnitude of ACP BaBar (full reconstruction) aDp= -0.022  0.038 (stat)  0.020 (syst) aD*p= -0.068  0.038 (stat)  0.020(syst) cDp= 0.025  0.068 (stat)  0.033 (syst) cD*p= 0.031  0.070 (stat)  0.033 (syst) cr (S+– S-) = 2 r sin(d) cos(2b+g) BaBar (partial reconstruction, D*p only) aD*p(K tag)= -0.054  0.035 (stat)  0.017(syst) S+D*p (l tag)= -0.078  0.052 (stat)  0.021 (syst) S+D*p (l tag) = -0.070  0.052 (stat)  0.019 (syst) Avg. of aD*p& (S+D*p + S+D*p )/2: -0.063  0.024 (stat)  0.014 (syst) magnitude of ACP

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

  27. g from sin(2b+g) Silva, A.S., Wolfenstein, Wu, PRD 67, 036004 Allowed range few ab-1 •  p - f, d  -d •  f + p, d  d + p Measured g True g (f2b+g) •  d + p/2, d  f - p/2 So far dseems small d = 0 Resolving ambiguities is crucial True g

  28. r2r 1 Sinha, Sinha, A.S. • The same can be done with BD**-p+ • 2 D** resonances & continuum • Resonance mass shapes add to angular information, resolves ambiguities Sensitivity to r London, Sinha, Sinha, PRL 85, 1807 • Hard to measure r from (1-r2)cos(Dmt), need to take it from BDs+p- • Angular analysis with BD*+r-/a1-, exploit interference between the 3 helicity amplitudes to do away with r2 terms • Enough to measure terms r • Expect significant improvement for this mode • Perhaps large d’s will resolve ambiguities • More complicated fit

  29. u B0 d d d u sin(2b+g) with Tagged BD(*)+Ksh- Aleksan, Petersen, hep-ph/0307371 B0 d c s d d c r~ 0.4 s h- D(*)+ D(*)+ h- KS KS • Dalitz plot suppression • Ambiguity only 2-fold (f f + p) • Expect sg ~ 0.2 – 0.3 with 400 fb-1 NIMSBHO

  30. c2 d Tagged B0DK0 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 sd (109 B’s, sub-BR, tagging, no reco eff. Or bgd.) Belle, PRL 90, 141802 NIMSBHO

  31. g with 10 ab-1 • Use all methods • Will measure g to ~ 2° (%) (stat) or less! • Only gg+p ambiguity is left • Excluded theoretically? • The error is so small that ambiguities won’t matter ~2% g

  32. d/s b d/s p+/K+ p+/K+ u u B0 u b u B0 p- p- g d d d d b d Compare to g from Penguins • Theoretical uncertainties in precision extraction of g • Disagreement with “clean” measurements could be due to NP or EW penguins • Theoretical understanding will improve by the time the machine is built

  33. ~2% b d/s d/s b ~3% O(%) @ CDF 1.4%  0.5% with 0.5 ab-1 Ronga, CKM ’03 10%  1-2% “soon” Shoji Hashimoto (SLAC, Oct.) P. Lepage sxs /xs xs BaBar, PRL 88, 221803 Compare to |Vtd| from Mixing Straight forward comparison of |Vtd|&g

  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. • D0 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 g • Frequent improvements & new ideas • From foreseeable mixing, theory & lattice precision, the target for g 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 g 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. 0 0.5 1 Fraction of allowed range of g excluded by this exp. Backup slides A.S., PRD 60, 054032

  37. Belle Dalitz fit

  38. Sensitivity with CPES + K*K 0.5 ab-1 CP modes Combined c2 K*+K- True g/p True g/p g/p

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