Aug 6, Charm γ/φ 3 Impact from CLEO-c Using CP-Tagged D→K S,L ππ Decays Eric White - University of Illinois Qing He - University of Rochester for the CLEO Collaboration Charm 07

August 6, Charm 2007 Eric White, University of Illinois 2 Path to Measuring γ/φ 3 B-B- D0K-D0K- D0K-D0K- N ~ |f D | 2 + r B 2 |f D | 2 + 2|f D ||f D |r B [cos(  D )sin(  B -  ) – sin(  D )cos(  B -  )]  Use B ± →DK ± decays, followed by Dalitz plot analysis of D→K s π + π -.  Developed by Giri, Grossman, Soffer, Zupan (GGSZ)[1] / Belle [2] -- exploit interference between D 0 and D 0 channels (K S ππ)K - K S ππ Dalitz Plot favored path ~ V cb V us suppressed path ~ V cs V ub fDfD fDfD Additional unknowns due to D 0 -D 0 interference 5 parameters: r B, δ B, γ, cos(  D ), sin(  D ) Measure at CLEO-c Introduction Data K L -K S Binned Analysis Conclusion [2] A.Bondar, Proceedings of Belle Special Analysis Meeting on Dalitz Analysis, Sept. 2002, BINP, Novosibirsk (unpub. [1] Giri et al. Phys. Rev. D 68, (2003)

August 6, Charm 2007 Eric White, University of Illinois 3 Current γ/φ 3 Measurements BaBar: 92 o ± 41 o (stat) ± 11 o (syst) ± 12 o (model) (211 fb -1 ) Belle: 53 o ± 17 o (stat) ± 3 o (syst) ± 9 o (model) (357 fb -1 ) 10 o model uncertainty will dominate → CLEO-c can help lower this number Introduction Data K L -K S Binned Analysis Conclusion Statistical uncertainty will go down to about ~ 6 o with projected 2 ab -1 (r B = 0.16) (LHCb projects ~ 3 o -5 o uncertainty after 5 years… ) BaBar Collaboration, B. Aubert et al. hep-ex/ Belle Collaboration, A. Poluektov et al. Phys. Rev. D73 (2006)

August 6, Charm 2007 Eric White, University of Illinois 4 Measuring c i with CP-tagged K S ππ Dalitz Plots Introduction Data K L -K S Binned Analysis Conclusion M ~ |f D | 2 + |f D | 2 ± 2|f D ||f D | cos(  D ) For CP-tagged Dalitz plots, number of events in Dalitz plot is Divide the (K S  )D Dalitz plot in to bins, symmetric under interchange of π + ↔ π – interchange. Ψ(3770) D K S,L ππ CP Tag Correlated DD pairs (C = -1) are produced at CLEO-c We tag the K S ππ sample by reconstructing D→CP± eigentstates D CP± = D 0 ± D 0 √2 Define → c i = i c i can be determined by counting CP-tagged bins i -i Binned Dalitz plot CP-tagged flavor-tagged

August 6, Charm 2007 Eric White, University of Illinois 5 Tagged K S π + π – Data from CLEO-c Event selection cuts |ΔE| < 30 (MeV) |K S mass| < 3σ |M bc - M D | < 4.2 (MeV) (M bc ≡ √((E beam ) 2 – (p D ) 2 ) Very low background We use 398 pb -1 of correlated Ψ(3770)→DD decays Flavor-tagging modes: D 0 →K - π +, K - π + π 0, K - π + π - π + (plus charge-conjugate) CP+ tags: K + K - π + π - CP- tags: K S π 0 K S η Only two-body CP tags are used – provide clean signal with very little background Flavor Tagged Data CP+ Tagged Data CP- Tagged Data Mode K + K - π + π- K S π 0 K S η Yield Introduction Data K L -K S Binned Analysis Conclusion

August 6, Charm 2007 Eric White, University of Illinois 6 What about K L ππ? Introduction Data K L -K S Binned Analysis Conclusion  Why not use K L ππ?  Similar structure, opposite CP  More than doubles overall statistics

August 6, Charm 2007 Eric White, University of Illinois 7 Tagged K L π + π - Data Use same flavor and CP tag modes as K S ππ, with same basic event selection Mode K + K - π + π - K S π 0 K S η Yield Require additional π 0, η veto CP+ tags: K + K - π + π - CP- tags: K S π 0 K S η Same two-body CP tags are used as K S ππ: K L ππ events are reconstructed using “missing mass” technique Flavor Tagged Data CP+ Tagged Data CP- Tagged Data m K 2 (GeV) 2 m K 2 = Introduction Data K L -K S Binned Analysis Conclusion

August 6, Charm 2007 Eric White, University of Illinois 8 K L π 0 vs. K S ππ Similar event selection, with additional cuts:  Require zero tracks  3σ cut on π 0 mass  Additional π 0 s vetoed Reconstruct missing mass of K L Doubles number of CP-even tags Additionally, we use K L π 0 as CP-even tag for K S ππ mode This mode contains highest background level ~ 5% Yield: 190 events m K 2 (GeV) 2 K L π 0 Tagged Data Introduction Data K L -K S Binned Analysis Conclusion

August 6, Charm 2007 Eric White, University of Illinois 9 CP-tagged K S π + π - Dalitz Plots KSρKSρ K S ρ 0 resonance enhanced in CP-odd Dalitz plot CP-odd K S ρ 0 resonance absent in CP-even Dalitz plot Introduction Data K L -K S Binned Analysis Conclusion M 2 (K S π + )

August 6, Charm 2007 Eric White, University of Illinois 10 CP-tagged K L π + π - Dalitz Plots KLρKLρ Since CP of K L is opposite to K S, K L ππ Dalitz plot contains opposite CP structure to that of K S ππ K L ρ 0 resonance enhanced in CP-even Dalitz plot Introduction Data K L -K S Binned Analysis Conclusion

August 6, Charm 2007 Eric White, University of Illinois 11 Flavor-tagged K S,L π + π - Dalitz Plots There is a clear difference in the DCS K* + peak Appears constructively in K L ππ, and destructively in K S ππ The K S,L ππ Dalitz plots are not exactly equal Must take this into account before combining c i measurements for K L ππ and K S ππ samples M 2 (K S π + ) M 2 (K S π - ) Introduction Data K L -K S Binned Analysis Conclusion

August 6, Charm 2007 Eric White, University of Illinois 12 Combining c i from K S ππ and K L ππ Introduction Data K L -K S Binned Analysis Conclusion K S and K L can be expressed: CF DCS A(D 0 →K S ππ) = K* - (CF) + K* + (DCS) + f 0 + ρ 0 + … A(D 0 →K L ππ) = K* - (CF) - K* + (DCS) + (1-2re i? )f 0 + (1-2re i? )ρ 0 + … Define r as the magnitude of DCS/CF ratio r is small (~ 0.06), but is the phase known? By varying each unknown phase and recalculating c i, we can determine a measure of the systematic uncertainty for K L ππ Value of c i is in general different for K L ππ and K S ππ, but can be related through U-spin symmetry

August 6, Charm 2007 Eric White, University of Illinois 13 Binned Analysis s i can be determined from c i → s i = ±√1 – c i 2 Provided fluctuations of phase difference δ D across bins are small Variation of δ D phase can be minimized by choosing a more intelligent, model-inspired binning: We use N = 8 bins in this analysis Δδ D = 0 Δδ D = π m+2m+2 m-2m-2 Belle Collaboration, A. Poluektov et al. Phys. Rev. D73, (2006) Bondar, Poluektov hep-ph/ v1 (2007) Introduction Data K L -K S Binned Analysis Conclusion

August 6, Charm 2007 Eric White, University of Illinois 14 Comparing c i for K S,L π + π -  Obtain K L ππ model by changing sign of DCS terms → K* + (892), K* + (1410)…  Calculate c i from K S ππ and K L ππ models  Vary phase for each resonance, keep largest difference in c i K S ππ K L ππ c i calculated from model c i difference model 398 pb -1  Systematic uncertainty from K L ππ is small compared to c i difference  Good agreement of c i difference in data Introduction Data K L -K S Binned Analysis Conclusion

August 6, Charm 2007 Eric White, University of Illinois 15 Sensitivity to c i  We combine K L ππ, K S ππ Dalitz plots into an improved overall measurement of c i  Scale statistical uncertainty up to full 750 pb -1  Combine with K L ππ systematic uncertainty to determine overall expected sensitivity from CLEO-c measurement Introduction Data K L -K S Binned Analysis Conclusion c i calculated from model Error bars represent expected uncertainty, as projected from current data sample

August 6, Charm 2007 Eric White, University of Illinois 16 Conclusion Introduction Data K L -K S Binned Analysis Conclusion  K L ππ, K S ππ samples can be combined  Good sensitivity to c i  Total D CP expected to be ~ 1,530 for 750 pb -1  Combined BaBar/Belle (2 ab -1 ) statistical uncertainty → ±6 o  CLEO-c can reduce model uncertainty from ±10 o down to ± 4 o in γ/φ 3 measurement

August 6, Charm 2007 Eric White, University of Illinois 17 Back up Following modes will also be used to measure c i and s i K S ππ vs. K S ππ (~ 480) K S ππ vs. K L ππ (~ 1240) } Expected yields (750 pb -1 )