φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov Measurement of φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov BINP, Novosibirsk, Russia Outline: • • • • • • • Introduction to the technique D0 model determination Signal selection Estimation of statistical errors with toy MC Estimation of systematic errors Combined B+→ D0K+ and B+→ D*0K+ fit Conclusion March 21-28, 2004 Recontres de Moriond, EW session 1 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov CKM matrix & unitarity triangle λ Vus Vub 1 − λ2 / 2 1 − λ2 / 2 −λ Vcs Vcb ≈ Vts Vtb Aλ3 (1 − ρ − iη ) − Aλ2 Vud Vij = Vcd V td B0 ππ B0 ρπ (ρ,η) * ub * cb V V ud V V cd B0 D(*)π B+ DK March 21-28, 2004 (α) (γ) V t*bV t d V c*bV c d (β) Recontres de Moriond, EW session Aλ3 ( ρ − iη ) 2 Aλ 1 = 0.2235I0.0033 A = 0.81I0.08 |-i| = 0.36I0.09 |1- -i | = 0.79I0.19 B0 J/ψ ψKs B0 φKs B0 D(*)D(*) 2 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D0K+ decay * M 1 ~ Vcb Vus ~ A λ3 M 2 ~Vub* Vcs ~Aλ 3(ρ + iη ) ~ e iφ3 If both D0 and D0 decay into the same final state, B+→ D0K+ and B+→ D0K+ ~ amplitudes interfere. Mixed state is produced: D 0 = D 0 + re iθ D 0 Phase θ is a sum of strong and weak phases: θ = φ3 + δ Use 3-body final state, identical for D0 and D0: Ksπ+π-. Dalitz plot density: d σ ( m | M ( m K2 sπ + , m K2 sπ − 2 K sπ + ) | 2 =| f ,m2 ) ∝| M K sπ − ( m K2 π + , m K2 π − s s |2 dm 2 )+ dm 2 − + K sπ K sπ re iθ f ( m K2 π − , m K2 π + s s ) |2 (assuming CP conservation in D0 decay) March 21-28, 2004 Recontres de Moriond, EW session 3 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D0K+ decay ~ D0 = D 0 + reiθ D0 If D0 decay model is known, parameters r and θ can be obtained by Dalitz plot analysis. For B-→ D0K- weak phase of color-suppressed amplitude changes sign: − iϕ 3 * 3 M 2 ∝ VubVcs ∝ A λ ( ρ − iη ) ∝ e Strong phase is not changed. Therefore, θ − = δ − ϕ 3 (r, φ3, δ) can be obtained with simultaneous fit of B+ and B- data. Use unbinned likelihood technique to fit Dalitz plots. r≈ * Vub Vcs * Vcb Vus × | a2 | = 0.09 / 0.22 × 0.35 ≈ 1 / 8 | fa1 + a2 | Factor |a2|/|fa1+a2|=0.35 related to color suppression can be estimated from the ratio of B0→ D0K0 and B+→ D0K+ branching fractions (measured by Belle) References: • A. Giri, Yu. Grossman, A. Soffer, J. Zupan, hep-ph/0303187 • Belle collaboration, hep-ex/0308043 (Contributed to LP2003) March 21-28, 2004 Recontres de Moriond, EW session 4 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov Effect of CPV and φ3 (MC) B→ D0K decays) s 2 MK π – (GeV 2 ) MC generated statistics (50000 M K2 π + (GeV 2 ) s Most sensitive regions of the Dalitz plot (r = 0.125, δ=0, φ3=70°) March 21-28, 2004 Recontres de Moriond, EW session 5 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov ER ) Belle detector TSUKUBA Area (Belle) RF WIGGLER OHO Area RF (L RF RF WIGGLER Lo fo w E rP n os erg itr y R on in g NIKKO Area ) ER (H KEKB Collider g n Ri gy er En tron gh c Hi r Ele fo HER LER Interaction Region LE c na Li RF RF FUJI Area - Positron /e Electron + R e HE R (TRISTAN Accumulation Ring) 3.5 GeV e+ & 8 GeV e– asymmetric Collider 3 km circumference, 11 mrad crossing angle L= 1.2 x 1034 cm–2s–1 (world record) ∫ L dt = 219 fb–1 @ (4S)+off(~10%) (140 fb-1: 1.52 x 108 BB pairs) March 21-28, 2004 ~350 scientists, 55 institutions Recontres de Moriond, EW session 6 A. Poluektov φ3 with B→D(*)0 K Dalitz analysis at Belle Analysis overview • Determination of D0 → Ksπ+π– decay model • Use flavor tagged sample of D0‘s from D*–→ D0π–, D0 → Ksπ+π– produced in continuum • Selection of B+→ D0K+ events • Selection of B+→ D*0K+, D*0→ D0π0 events • Unbinned maximum likelihood fit of the D0 Dalitz plots with free parameters (r, φ3, δ) • Fits to control samples without opposite flavor contributions: B+→ D0π+, B+→ D*0π+, B0→ D*+π• Evaluation of statistical errors using large number of toy MC pseudo-experiments • Evaluation of systematic and model errors • Combined φ3 measurement March 21-28, 2004 Recontres de Moriond, EW session 7 A. Poluektov φ3 with B→D(*)0 K Dalitz analysis at Belle D*–→ D0π–, D0 → Ksπ+π– selection MD (GeV) ∆M (GeV) 140 fb-1 statistics 101800 events 3.1% background • 144.6<MD*-MD<146.4 MeV • 1.856<MD<1.874 GeV (shape from ∆M sidebands) March 21-28, 2004 • PD*>2.7 GeV Recontres de Moriond, EW session 8 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov D0 → Ksπ+π– decay model Phase, ° Fit fraction σ1 Ks 1.66±0.11 218.0±3.8 11% ρ(770) KS 1 0 21% ω Ks (3.30±1.13)·10-2 114.3±2.3 0.4% f0(980) Ks 0.405±0.008 212.9±2.3 4.8% σ2 Ks 0.31±0.05 236±11 0.9% f2(1270) Ks 1.36±0.06 352±3 1.5% f0(1370) Ks 0.82±0.10 308±8 0.9% K* (892)-π+ 1.656±0.012 137.6±0.6 60% K*(892)+π - 0.149±0.007 325.2±2.2 0.5% K*0(1430) -π+ 1.96±0.04 357.3±1.5 5.8% K*0(1430)+π - 0.30±0.05 128±8 0.1% K*2(1430) -π+ 1.32±0.03 313.5±1.8 2.8% K*2(1430) +π - 0.21±0.03 281.5±9 0.07% K*(1680) +π - 2.56±0.22 70±6 0.4% K*(1680) -π + 1.02±0.22 102±11 0.07% Non resonant 6.1±0.3 146±3 24% March 21-28, 2004 Sum of two-body amplitudes: f = aK * e iϕ K* iϕ ρ [ FD FK * M J BW (mK2 π − )] + s J 2 π +π − aρ e [ FD Fρ M BW (m )] + ... 2 Amplitude MKsπ – (GeV 2 ) Our fit Resonance Recontres de Moriond, EW session M K2 π + (GeV2 ) s 9 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov s 2 MK π – (GeV 2 ) D*–→ D0π–, D0 → Ksπ+π– Dalitz plot Doubly Cabibbo suppressed K* M K2 π + (GeV 2 ) s M K2 π − (GeV 2 ) M K2 π − (GeV 2 ) s s ρ-ω interference M K2 π + (GeV 2 ) s March 21-28, 2004 M π2 +π − (GeV 2 ) Recontres de Moriond, EW session M π2+π − (GeV 2 ) 10 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B candidate selection Pairs of B mesons are produced in Υ(4S) decays (near BB mass threshold) ⇒ E B = Ecm / 2 , low p in CM frame CM energy difference: ∆E = ∑ Ei − ( Ecm / 2) B meson beam-constrained mass Mbc: M bc = ( Ecm / 2) 2 − (∑ pi ) 2 Continuum (e+e-→uu,dd,ss) background suppression: • Angle between B candidate thrust axis and thrust axis of the rest of the event • Fisher discriminant based on “virtual calorimeter” March 21-28, 2004 Recontres de Moriond, EW session 11 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D0K+ signal with 140 fb 1 D0K D0π misID ∆E (GeV) Mbc (GeV) 12% reconstruction efficiency 146 events 112±12 signal 36±3 background (25%) MD (GeV) •|∆E|<22 MeV •5.272<Mbc<5.288 GeV •|MD-1.86 GeV|<11 MeV •|cosΘthr|<0.8 •Fisher discriminant F>-0.7 •PID(K/π)>0.7 March 21-28, 2004 Recontres de Moriond, EW session 12 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D*0K+ signal with 140 fb- 1 D0K D0π misID ∆E (GeV) Mbc (GeV) MD (GeV) MD* -MD (GeV) 6.2% reconstruction efficiency •|∆E|<22 MeV 39 events •5.272<Mbc<5.288 GeV •|MD-1.86 GeV|<11 MeV 33.6±6.2 signal 4.6±1.1 background (12%) •140<MD*-MD<145 MeV •|cosΘthr|<0.8 •Fisher discriminant F>-0.7 •PID(K/π)>0.7 March 21-28, 2004 Recontres de Moriond, EW session 13 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D0K+, D0→Ksπ+π- Dalitz plot 73 events 2 2 73 events MKsπ + (GeV 2 ) MKsπ – (GeV 2 ) K*(892) bands M K2 π + (GeV 2 ) M K2 π − (GeV 2 ) s D0 from B+→ D0K+ March 21-28, 2004 s D0 from B-→ D0K(π+ and π - interchanged) Recontres de Moriond, EW session 14 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D*0K+, D0→Ksπ+π- Dalitz plot 19 events 2 2 20 events MKsπ + (GeV 2 ) MKsπ – (GeV 2 ) K*(892) bands M K2 π + (GeV 2 ) M K2 π − (GeV 2 ) s D0 from B+→ D*0K+ March 21-28, 2004 s D0 from B-→ D*0K(π+ and π - interchanged) Recontres de Moriond, EW session 15 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov Likelihood function Minimizing logarithmic likelihood: N − 2 logL = −2∑ log f (m+2,i , m−2,i ) + 2 log∫ f (m+2 , m−2 ) dm+2 dm−2 i=1 m+2,i , m−2,i are Dalitz plot points f (m+2 , m−2 ) =| M (m+2 , m−2 ) |2 ×ε (m+2 , m−2 ) ⊕ σ p (mπ2 +π − ) + b(m+2 , m−2 ) Matrix element M ( m +2 , m −2 ) = f ( m +2 , m −2 ) + re iθ f ( m −2 , m +2 ) Efficiency shape ε (m+2 , m−2 ) Momentum resolution σ p (mπ2 +π − ) - from phase-space MC Background March 21-28, 2004 - from phase-space MC b(m+2 , m−2 ) Recontres de Moriond, EW session 16 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D0K+ B+→ D*0K+ Im(reiθ) Im(reiθ) B+→ D(*)0K+ fit results Re(reiθ) Re(reiθ) r+=0.40±0.15, θ+=256±19° r- =0.21±0.15, θ- = 71±37° March 21-28, 2004 r+=0.29±0.19, θ+=353±38° r- =0.38±0.19, θ- =249±32° Recontres de Moriond, EW session 17 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov Test sample fits Re(reiθ) r+=0.065±0.029, θ+=232±24° r- =0.069±0.027, θ- =228±23° Bias in B0→ D*+π- (517 events) Im(reiθ) B+→ D*0π+ (351 events) Im(reiθ) Im(reiθ) B+→ D0π+ (1850 events) Re(reiθ) Re(reiθ) r+=0.041±0.069, θ+=164±100° r- =0.057±0.054, θ- = 340±65° r+=0.005±0.058, θ+=324±686° r- =0.052±0.053, θ- = 201±57° B+→ D0π+ sample (background, fluctuation?), however, no CP violation observed March 21-28, 2004 Recontres de Moriond, EW session 18 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D0K+ constraints 20% 97% + 97% 74% 20% + + + (φ3, δ) and (φ3+π, δ+π) ambiguity 74% r=0.28+0.09 -0.11 , φ3=86±20°, δ=168±20° — <68% CL interval from MC-based PDF 0.07<r<0.45, 37°<φ3<135°, 119°<δ<217° — <95% CL interval. CP violation significance: 94% (φ3≠0). r > 0 with 97% CL. March 21-28, 2004 Recontres de Moriond, EW session 19 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D*0K+ constraints 20% 97% 74% + 74% 20% + + + (φ3, δ) and (φ3+π, δ+π) ambiguity r<0.25, φ3=51±47°, δ=302±47° — <68% CL interval from MC-based PDF r<0.44, -31°<φ3<133°, 220°<δ<384° — <95% CL interval. CP violation significance: 38% (φ3≠0). March 21-28, 2004 Recontres de Moriond, EW session 20 A. Poluektov φ3 with B→D(*)0 K Dalitz analysis at Belle Estimation of systematic errors B+→ D0K+ B+→ D*0K+ Background shape Background fraction Efficiency shape Momentum resolution B+→ D0π+ test sample bias: Total March 21-28, 2004 4.6° 0.1° 3.5° 2.5° 11° 13° 1.3° 0.6° 0.8° 2.5° 11° 11° Recontres de Moriond, EW session 21 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov Model uncertainty D0 decay amplitude f = | f (m+2 , m−2 ) | | f (m+2 , m−2 ) |2 directly measured φ (m+2 , m−2 ) model-dependent e iφ ( m+2 ,m−2 ) Fit model K*, ρ, ω, f0 + non-resonant Meson formfactors Fr=FD=1 Constant BW width Γ(q2)=Const Non-resonant amplitude aNR=0 No σ(500) (∆φ3)max,° Total 11 March 21-28, 2004 9.9 3.1 4.7 0.4 0.7 Recontres de Moriond, EW session 22 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D0K+ and B+→ D*0K+ combined Multiply φ3 PDF’s for Combined fit B+→ D0K+ B+→ D0K+ and B+→ D*0K+ samples (r and δ left independent) B+→ D*0K+ Stat. confidence intervals: φ3=81±19° (68% CL) φ3=81±46° (95% CL) 68% March 21-28, 2004 95% Combined result: φ3=81 ±19°±13°(syst)±11°(model) Recontres de Moriond, EW session 23 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov Constraints on unitarity triangle η D0K Dalitz B→J/ψKs <95% CL regions B→ππ Indirect measurements ρ March 21-28, 2004 Recontres de Moriond, EW session 24 A. Poluektov φ3 with B→D(*)0 K Dalitz analysis at Belle Conclusion • B+→ D0K+ and B+→ D*0K+, D0 → Ksπ+π- samples analyzed with 140 fb-1 φ3=81°±19°±13°(syst)±11°(model) for combined fit 95% CL interval from combined fit: 35°<φ3<127° • Direct CP violation effect significance is 94%. • A new promising method to measure φ3 using Dalitz plot analysis of D0 from B→D(*)0K decay is applied to the data collected by Belle. • Advantages: • Higher statistical power than methods based on branching fractions • No absolute branching fractions involved ⇒ lower detector systematics • Model-independent approach exists based on the cτ-factory data. • The precision can be increased by adding other suitable modes (neutral B decays, other three- and four-body D0 decays) March 21-28, 2004 Recontres de Moriond, EW session 25 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov D0 → Ksπ+π- fit result (discussion) • Needed to introduce two scalars in π+π- channel: • σ1 with mass M=538±9 MeV, BW width Γ=452±15 MeV • σ2 with mass M=1048±8 MeV, BW width Γ=109±11 MeV • Large non-resonant amplitude observed. • Correlated with σ1 amplitude: • aNR=4.66±0.15 for aσ =0 (compared to 6.1±0.3) • aσ =0.78±0.05 for aNR=0 (compared to 1.65±0.10) • Probably indicates poor description of σ1. Consider as a systematic effect. • Use symmetric set of resonances, i.e. take doubly Cabibbo suppressed partners for all flavor-specific modes (K*(892)+π -, K*0(1430)+π-, K*0(1430)+π-, K*(1680) +π-). Otherwise systematic bias of opposite flavor admixture r. March 21-28, 2004 Recontres de Moriond, EW session 26 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D0K+ fit result Error estimation from the fit likelihood CL vs. (δ, φ3) CL vs. (r, φ3) -2 log L vs. φ3 r=0.31±0.11, φ3=86±17°, δ=168±17° or (φ3+π, δ+ π) March 21-28, 2004 Recontres de Moriond, EW session 27 φ3 with B→D(*)0 K Dalitz analysis at Belle A. Poluektov B+→ D*0K+ fit result Error estimation from the fit likelihood CL vs. (δ, φ3) CL vs. (r, φ3) -2 log L vs. φ3 r=0.34±0.14, φ3=51±25°, δ=302±25° or (φ3+π, δ+ π) March 21-28, 2004 Recontres de Moriond, EW session 28 A. Poluektov φ3 with B→D(*)0 K Dalitz analysis at Belle Parameterization of fit PDF PDF for the single Dalitz plot fit: 2 2 r r r r θ θ θ θ ( cos − cos ) + ( sin − sin ) d 2 P (r ,θ ) ∝ exp[− ]rdrdθ 2 2σ r ,θ - true values, r ,θ - reconstructed values PDF of reconstructed values values r , ϕ3 , δ r , ϕ3 , δ for a given set of true for combined fit of two Dalitz plots (B+ and B-): d 2P d 3P d 2P (r , ϕ 3 , δ ) ∝ (r , δ + ϕ 3 ) ⋅ (r , δ − ϕ 3 ) drdϕ 3dδ drdθ + drdθ − Can also obtain PDF of true values r , ϕ 3 , δ for a given set of reconstructed values r , ϕ 3 , δ with this parameterization. This PDF is used to obtain confidence intervals and significance. March 21-28, 2004 Recontres de Moriond, EW session 29 A. Poluektov φ3 with B→D(*)0 K Dalitz analysis at Belle Backgrounds • qq combinatorial (including real D0) B →D0 K B→D*0K 22.1% 9.0% 2.2% 2.1% 1.0% 0.6% 0.4% 0.4% <0.4% <0.4% – Fraction: from ∆E distribution – Dalitz plot: from continuum data • Other B decays – Fraction and Dalitz plot: from generic MC • “Wrong” particles in D0 decay – Fraction and Dalitz plot: from B→D0K MC • B→D0π with K/π misID – Fraction: from ∆E distribution – Dalitz plot: D0 • Flavor tagging K from combinatorics – Fraction from MC March 21-28, 2004 Recontres de Moriond, EW session 30 A. Poluektov φ3 with B→D(*)0 K Dalitz analysis at Belle Illustration of CP asymmetry Select regions on Dalitz plot with σ(B+)>σ(B-) or σ(B-)>σ(B+) by >20% Calculate the number of B+ and B- decays in each of the regions. CP asymmetry ⇒ difference in number of B+ and B- events March 21-28, 2004 Recontres de Moriond, EW session 31