γ/φ3 determination with B D0(*)K(*) Dalitz analysis ВД в эксперименте по измерению масс 25 мая 2002 φ3/γ with Dalitz analysis γ/φ3 determination with B D0(*)K(*) Dalitz analysis A. Poluektov Budker Institute of Nuclear Physics Novosibirsk, Russia November 27, 2007 А. Полуэктов

φ3/γ with Dalitz analysis B+ D0K+ decay Need to use the decay where Vub contribution interferes with another weak vertex. B– D0K–: B– D0K– : If D0 and D0 decay into the same final state, Relative phase: (B– DK–), (B+ DK+) includes weak (γ/φ3) and strong (δ) phase. Amplitude ratio: November 27, 2007

Dalitz analysis method φ3/γ with Dalitz analysis Dalitz analysis method A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003) A. Bondar, Proc. of Belle Dalitz analysis meeting, 24-26 Sep 2002. Using 3-body final state, identical for D0 and D0: Ksπ+π-. Dalitz distribution density: (assuming СР-conservation in D0 decays) If is known, parameters are obtained from the fit to Dalitz distributions of D Ksπ+π– from B±DK± decays November 27, 2007

φ3/γ with Dalitz analysis D0  Ksπ+π– decay Statistical sensitivity of the method depends on the properties of the 3-body decay involved. Close relation to charm physics Large variations of D0 decay strong phase are essential Currently, use the model-dependent fit to experimental data from flavor-tagged D*± D0π± sample. Model is described by the set of two-body amplitudes + flat non-resonant term. As a result, model uncertainty in the γ/φ3 measurement. November 27, 2007

D0  Ksπ+π– amplitude fit (Belle) φ3/γ with Dalitz analysis D0  Ksπ+π– amplitude fit (Belle) Intermediate state Amplitude Phase, ° Fit fraction KS σ1 KS ρ(770) KS ω KS f0(980) KS σ2 KS f2(1270) KS f0(1370) KS ρ(1450) K* (892)+π– K*(892)–π+ K*(1410)+π– K*(1410)–π+ K*0(1430)+π– K*0(1430)–π+ K*2(1430)+π– K*2(1430)–π+ K*(1680)+π– K*(1680)–π+ Nonresonant 1.43±0.07 1 (fixed) 0.0314±0.0008 0.365±0.006 0.23±0.02 1.32±0.04 1.44±0.10 0.66±0.07 1.644±0.010 0.144±0.004 0.61±0.06 0.45±0.04 2.15±0.04 0.47±0.04 0.88±0.03 0.25±0.02 1.39±0.27 1.2±0.2 3.0±0.3 212±4 0 (fixed) 110.8±1.6 201.9±1.9 237±11 348±2 82±6 9±8 132.1±0.5 320.3±1.5 113±4 254±5 353.6±1.2 88±4 318.7±1.9 265±6 103±12 118±11 164±5 9.8% 21.6% 0.4% 4.9% 0.6% 1.5% 1.1% 61.2% 0.55% 0.05% 0.14% 7.4% 0.43% 2.2% 0.09% 0.36% 0.11% 9.7% M (GeV 2 ) Ksπ – 2 σ1(M=520±15 MeV, Γ=466±31 MeV) σ2(M=1059±6 MeV, Γ=59±10 MeV) November 27, 2007

Dalitz model: ππ S-wave K-matrix (BaBar) φ3/γ with Dalitz analysis Dalitz model: ππ S-wave K-matrix (BaBar) Goal: keep unitarity of the amplitude in the presence of overlapping resonances. Avoid σ states. [Anisovich & Sarantev, Eur. Phys. Jour. A16, 229 (2003)] pp S-wave CA K*p DCS K*p pp P,D-waves m2p+p-(GeV2/c4) c2/dof 1.2 dominated by Kp P-wave November 27, 2007

Signal parameterization Fit experimental Dalitz plot of D0 distribution from B±DK± decays with the probability density: No CPV or mixing effects in D decays are included. (no problem to include them if needed) If no CPV in D decay Cartesian fit parameters: Polar coordinates are bad: rB positive-definite (biased, non-Gaussian), φ3 precision is inversely proportional to rB November 27, 2007

Event selection (Belle) φ3/γ with Dalitz analysis Event selection (Belle) Belle result (357 fb-1) [hep-ex/0604054, PRD 73, 112009 (2006)] BD*K BDK* BDK 331±17 events 81±8 events 54±8 events B- B+ B- B+ B- B+ November 27, 2007

(x±,y±) fit results (Belle) φ3/γ with Dalitz analysis (x±,y±) fit results (Belle) Fit parameters are x= rB cos(φ3+δ) and y= rB sin(φ3+δ) Unbinned maximum likelihood fit with event-by-event background treatment (ΔE-Mbc included into likelihood) BD*K BDK* BDK x–= 0.025-0.080 y–= 0.170-0.117 x+= –0.135-0.070 y+= –0.085-0.086 +0.072 x-= –0.128-0.146 y-= –0.339-0.158 x+= 0.032-0.116 y+= 0.008-0.136 x–= –0.784-0.295 y–= –0.281-0.335 x+= –0.105-0.167 y+= –0.004-0.156 +0.167 +0.249 +0.093 +0.172 +0.440 +0.069 +0.120 +0.177 +0.090 +0.137 +0.164 November 27, 2007

B– D(*)0K–, D0K*– signal (BaBar) φ3/γ with Dalitz analysis B– D(*)0K–, D0K*– signal (BaBar) [F. Martinez-Vidal, talk at CKM2006; hep-ex/0607104, hep-ex/0507101] D*0K, D*0 D0p0 97±13 Signal Dp BB qq D*0K, D*0D0g 93±12 D0K 398±23 347x106 BB D0K* 42±8 B-DK- B+  DK+ 227x106 BB November 27, 2007

(x±,y±) fit results (BaBar) D0K D0K* D*0K B+ B- B+ B+ B- B- Dalitz model systematic error November 27, 2007

φ3/γ with Dalitz analysis Statistical issues Measure Cartesian parameters x= rB cos(φ3+δ) and y= rB sin(φ3+δ) 4 parameters z=(x , y)  3 parameters μ=(φ3, rB, δ) for one mode 12 parameters z=(x , y)DK, D*K, DK*  7 parameters μ=(φ3, (rB, δ)DK, D*K, DK*) for 3 modes Use frequentist treatment to obtain μ CL for measurement result z0. Use toy MC to obtain p(z|μ) Not Gaussian (tails), systematic bias Number of “true” parameters < number of fit parameters. Classical Neyman ordering is not correct, especially far from physical region rB+=rB-. [B. Yabsley, hep-ex/0604055] Use Feldman-Cousins: November 27, 2007

φ3/γ with Dalitz analysis Model uncertainty Variation of fit model give an estimate of model uncertainty: ~10° Fit model (Δr)max (Δφ3)max (Δδ)max Formfactors = 1 0.01 3.1 3.3 Γ(q2)=Const 0.02 4.7 9.0 Reduced num. of resonances 0.05 8.5 22.9 No σ scalar 2.6 4.3 CLEO set of resonances 5.7 8.7 At the statistics of >1 ab-1, this uncertainty starts to affect the precision. Use charm data. [See next talk by A. Bondar.] Validate the model Model-independent measurement November 27, 2007

φ3/γ with Dalitz analysis φ3 constraints BDK only: φ3=66 -20 °(stat) +19 BDK , BD*K , BDK* combined: φ3=53°+15 3° (syst)9° (model) rDK =0.159+0.054 0.012(syst)0.049(model) rD*K=0.175+0.108 0.013(syst)0.049(model) rDK*=0.564+0.216 0.041(syst)0.084(model) -18 -0.050 -0.099 -0.155 2s 1s BDK and BD*K combined: γ=92°±41°±11°(syst)±12°(model) rDK<0.142 (<0.198) 0.016<rD*K <0.206 (<0.282) November 27, 2007

BaBar and Belle: HFAG comparison φ3/γ with Dalitz analysis BaBar and Belle: HFAG comparison BaBar has better precision on (x±,y±) Belle has better separation between B+ and B– regions  better φ3 precision. As statistics increases (σ(rB)<< rB) distributions become more Gaussian but hard to extrapolate the sensitivity since rB is unknown. November 27, 2007

Other possibilities: D0π+π–π0 (BaBar) φ3/γ with Dalitz analysis Other possibilities: D0π+π–π0 (BaBar) [BaBar collaboration, hep-ex/0703037] Modified likelihood to account for Br difference of B+ and B–: No significant constraint on γ yet. D KsK+K–: more promising? November 27, 2007

Other possibilities: B0D0K*0 (BaBar) φ3/γ with Dalitz analysis Other possibilities: B0D0K*0 (BaBar) [V. Sordini, talk at CKM2006; hep-ph/0703292] Both amplitudes are color-suppressed, rB larger: Self-tagging decay: K*0K+π– Estimated signal yield with 350 fb-1: 45 events. With that low statistics, toy MC shows significant bias in (x,y). November 27, 2007

φ3/γ with Dalitz analysis Summary Dalitz analysis of Ksπ+π- final state allowed to obtain first constraints on γ/φ3, but the significance is still low. When γ/φ3 will actually be measured, depends not only on statistics, but also on rB value. If rB~0.1, the evidence for CPV can be obtained in the nearest time. So far, only B  D(*)K, D  Ksπ+π–, provided significant constraint. However, many other possibilities exist: Other B meson decays: (B0D0K*0, larger rB~0.4) Other 3-body D decays: D  KsK+K–, D  π0π+π–, D  K–π+π0. 4-body D decays: DK+K–π+π– [Rademacker, Wilkinson, hep-ph/0611272] In all cases, the input from charm data is essential. For precision γ/φ3 measurement, charm factory is necessary. November 27, 2007