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Dalitz analysis of the decay * B + →π + π - π +

Dalitz analysis of the decay * B + →π + π - π +. * charged conjugate states implied throughout talk. Richard Kass for the BaBar Collaboration. Outline of Talk *Introduction *Analysis technique *Results *Summary & Conclusions. Why study charmless 3-body B decays?.

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Dalitz analysis of the decay * B + →π + π - π +

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  1. Dalitz analysis of the decay* B+→π+π-π+ * charged conjugate states implied throughout talk Richard Kass for the BaBar Collaboration Outline of Talk *Introduction *Analysis technique *Results *Summary & Conclusions Richard Kass

  2. Why study charmless 3-body B decays? B+→π+π-π+is a charmless 3-body B decay Richard Kass Interference from both penguin & tree amplitudes can give direct CP violation. Time-dependent measurements & interferences between intermediate states can allow measurement of all three CKM angles. Can search for signs of new physics such as enhanced branching fractions or CP asymmetries – new physics particles can enter in the loop diagrams Can improve understanding of the nature of some intermediate resonances, i.e. hadronic physics.

  3. Dalitz-plot Analysis Dalitz plot is a representation of e.g. the B→PPP phase space. In our case P=pseudoscalar=charged pion. The invariant masses are constrained by mB2+mi2+mj2+mk2=mij2+mik2+mjk2 Make a 2D scatter plot in mij2 and mjk2 Our case: mij=low mass π+π-combo, mjk=high mass π+π-combo Structure in the DP gives information on resonance masses, widths and spins, relative phases, interference etc. Model each contribution to the DP as a separate amplitude with a complex coefficient (isobar model). example mhi2 Red points show a spin 0 resonance Green points show spin 1 resonance Purple points show spin 2 resonance Each of these has a different mass, width & composition. mlow2 Richard Kass

  4. Dalitz-plot analysis ofB+→π+π-π+ Richard Kass In principle can extract the CKM angle g from the interference between B+→cc0p+ & other modes such as B+→r0p+ This mode also provides important information to improve the DP model in B0→p+p-p0, which is used to measure the CKM angle a BF & ACP measurements used to test factorisation and other effective theories Light meson spectroscopy aided by information from as many different final states as possible

  5. Previous BaBar Results PRD 72, 052002 (2005) used 232x106BB events (~half of this analysis) Prominent ρ(770) and 3σ evidence for f2(1270) Richard Kass

  6. PEP-II at SLAC asymmetric e+e− collider: 9 GeV (e-)/3.1 GeV (e+) PEP-II Peak Luminosity 1.2 x 1034 cm-2s-1 BaBar recorded 424 fb-1 at Y(4S) 4.65 x 108 U(4S)→BB events Richard Kass

  7. BaBar Detector 1.5 T Solenoid Electromagnetic Calorimeter (EMC) Detector of Internally Recflected Cherenkov Light (DIRC) e+ (3.1 GeV) e- (9 GeV) Drift Chamber (DCH) Instrumented Flux Return (IFR) Silicon Vertex Tracker (SVT) SVT, DCH: charged particle tracking: vertex & mom. resolution, K0s/Λ EMC: electromagnetic calorimeter: g/e/π0/η DIRC, IFR, DCH: charged particle ID:π/μ/K/p Highly efficient trigger for B mesons Richard Kass

  8. Analysis Technique Threshold kinematics: we know the initial energy (E*beam) of the Y(4S) system Therefore we know the energy & magnitude of momentum of each B meson Event topology Signal Signal (spherical) Background Background (jet-structure) Also, use neural networks + unbinned maximum likelihood fits Richard Kass

  9. Backgrounds B Mesons Explicitly veto 2-body states that can mimic B+→π+π-π+ B+→D0π+ with D0→π+π- and/or mis-ID’s D0→π+K-/K+K- B+→Ksπ+ with Ks→π+π- B+→[J/Ψ, Ψ(2S)]π+ with Ψ→l+l- with mis-ID’s l’s as π’s Estimate background due to other B meson decays Number of events estimated from MC and used in ML fit I) 2-body with extra track: B0→π+π- plus π+ (11 events) II) 3-body with mis-ID track(s): B+→K+π-π+ (199 events) III) B0→π+π-π0 with π- substituted for π0 (120 events) IV) B combinatorial backgrounds (495 events) Continuum: e+e-→uu, dd, ss, cc modeled using MC and below-Y(4S) data Richard Kass

  10. Amplitude Formalism-I The total signal amplitudes for B+ and B- decays are: The nominal model includes: ρ(770), ρ(1450), f2(1270), f0(1370) + non-resonant The F’s contain the strong force dynamics: Fj=Fj Fj(m2max, m2min)ºRj(m)Xj(p*)Xj(q)Tj(m) j=spin of resonance, m=mass of resonance q=momentum of daughter in rest frame of resonance p*=momentum of bachelor pion in B rest frame Xj= Blatt-Weisskopf barrier form factors Rj(m)= resonance line shapes ρ’s use Gounaris-Sakurai parameterization, others relativistic BWs Tj(m)=angular distribution (use Zemach tensor formulism) The c’s contain the weak force dynamics: cj=(xj+Δxj)+i(yj+Δyj) & cj=(xj-Δxj)+i(yj-Δyj) Δxj & Δyj are CP violating components PDG ML fit Richard Kass

  11. Amplitude Formalism-II The fit fraction for an individual amplitude is: note: sum of fit fractions can be <1 or >1 due to interference The CP asymmetry for a contributing resonance is: The nominal model includes ρ(770), ρ(1450), f2(1270), f0(1370) + non-resonant BUT additional resonance added too, e.g. f0(980). Richard Kass

  12. Maximum Likelihood Fit Event yields are extracted using an unbinned extended maximum likelihood fit. our fit has 20 free parameters N=∑NK with Nk= event yield for category k. signal, qq, B meson backgrounds (number fixed from MC) Ne= total number of events in data sample qB= charge of the B meson Pk=PDF for category k: P=P(mES)xP(∆E)xP(Dalitz) The signal reconstruction efficiencies are determined as a function of location in Dalitz plot (m2max, m2min) for B+ and B- separately using MC. Procedure is extensively tested with Monte Carlo toy MCs and embedded MCs Richard Kass

  13. Fit to Data signal signal qq qq We calculate a chisq between a model & data: Number of events in a bin vs predicted number The best model is the one with the lowest chisq/dof PRD 79, 072006 (2009) 4335 B± candidates yields 1219±50 signal events __ ML fit __ ML fit __ ML fit __ ML fit “sPlots” NIM A 555 (2005) 356 Richard Kass

  14. Systematic Errors Many sources of systematic errors considered allow BB backgrounds to float vary the PDF parameters compare with data/MC control samples: B-→ D0π-, D0→K-π+ tracking efficiency & particle ID modeling of Neural Network Dalitz plot model (composition of model & values of masses, widths, etc) Richard Kass

  15. Branching Fraction Results PDG: (16.2±1.5)x10-6 stat syst model “Best Fit Solution” The decay is dominated by B+→ ρ(770)0π+ and 3π non-resonant The χc0, χc2, & f0(980) components not statistically significant determined from ML fit f0(1370) mass=1400±50 MeV/c2 f0(1370) width=300±80 MeV Richard Kass

  16. CP Asymmetry Results 2nd best best “Best Fit Solution” All CP asymmetries are consistent with zero. Large variation in the ACP’s between best & 2nd best fit: χ2best/dof =82/84 χ22nd/dof= 86/84 Richard Kass

  17. B+→π+π-π+ Conclusions ●This analysis uses the full BaBar data set Published: PRD 79, 072006 (2009) ●Decay is dominated by ρ(770)π& 3π non-resonant No evidence for χc0, χc2, & f0(980) BFs in good agreement with PDG & theories Li and Yang, PRD 73, 114027 (2006), Chiang and Zhou, J. HEP. 03 (2009) 055. ●All CP asymmetries consistent with zero Lack of χc0 & χc2 implies this mode is not useful for CKM angle γ measurement with present data samples. ●These results will help other analyses Reduce model related errors in determination of CKM angle α from time dependent Dalitz analysis of B0→π+π-π0 Richard Kass

  18. Extra slides Richard Kass

  19. BaBar K/p ID D*+ → D0p+ D0→ K+ p- BaBar DIRC Richard Kass

  20. D0 J/Ψ & Ψ(2S) Dalitz Plot, Data Background subtracted Dalitz plot exclude charm and charmonia regions Richard Kass

  21. Best & 2nd Best Fit Results Richard Kass

  22. Model Parameterization Blatt-Weisskopf Barrier Form Factors: rBW=4.0±1.0 (GeV/c)-1 Breit-Wigner line shape: q0=q(m0) Zemach Tensors: Gounaris-Sakurai parameterization Non-resonant: αnr=0.28±0.06(GeV/c2)-2 Richard Kass

  23. Predictions Li and Yang, PRD 73, 114027 (2006). Chiang and Zhou, J High Energy Phys. 03 (2009) 055. Scheme A2 Scheme B2 Richard Kass

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