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B +/-  K S π +/- π 0 Dalitz Plot Analysis

B +/-  K S π +/- π 0 Dalitz Plot Analysis. Jennifer Prendki LPNHE, Universités Paris 6 & 7 Journées Jeunes Chercheurs 2008, Saint-Flour. Outline. SLAC and the BABAR detector Motivation Principle of a Dalitz Plot Analysis Components in the Selected Sample The Fit Parameterisation

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B +/-  K S π +/- π 0 Dalitz Plot Analysis

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  1. B+/- KSπ+/-π0Dalitz Plot Analysis Jennifer Prendki LPNHE, Universités Paris 6&7 Journées Jeunes Chercheurs 2008, Saint-Flour

  2. Outline • SLAC and the BABAR detector • Motivation • Principle of a Dalitz Plot Analysis • Components in the Selected Sample • The Fit • Parameterisation • Validation of the Fitter • Why did we miss ICHEP 2008 ? • Future Plans and Summary Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  3. ON Υ(4S) peak √s = 10.58 GeV OFF peak √s = 10.54 GeV PEP-II B-Factory and the BaBar Detector (1) • We collide e+ and e- at the Y(4S) resonance energy (10.58 GeV)• Y(4S) then decays into BBbar On-Peak : √s at Υ(4S) energy Off-Peak : √s 40 MeV below Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  4. PEP-II B-Factory and the BaBar Detector (2) • Y(4S) data taking has ended at the end of 2007 at SLAC • No data taking at all since April, 2008 But BaBar parts will be used in future detectors (SuperB) Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  5. (,)     (0,0) (1,0)  Motivations Vub*Vud + Vcb*Vcd + Vtb*Vtd = 0 First Dalitz Plot Analysis of B+/- KSπ+/-π0 Constraints on the γ angle of the unitarity triangle M. Ciuchini, M.Perini and L.Silvestrini, Phys.Rev. D 74 (2006) 051301 M. Gronau, D. Pirjol, A. Soni and J. Zupan, Phys.Rev. D 75 (2007) 014002 New Physics in penguin diagrams ? Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  6. 3 body decays described in a 2D plot B+/- KSπ+/-π0Dalitz Plot Analysis (1) 3 pseudo-vectors  12 Signal model :  mass constraints - 3  conservation laws - 4  free rotation in space - 3 remaining constraints  2 remaining constraints  5 remaining constraints  9 remaining constraints  12 square DP : transformation to magnify corners, where interference occur nominal DP m2Ksπ0 cos(θ’Ksπ0) m’Ksπ0 m2Ksπ+ Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  7. B+/- KSπ+/-π0Dalitz Plot Analysis (2) Invariant amplitude : For each resonance :  one amplitude  one phase one spin  one lineshape decay rate given by : • Interference of Q2B modes • DP analysis sensitive to relative phases Interferences = constraints on the γ CKM angle CPS phase θ’ m’ Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  8. mKsπ02 mKsπ+2 Analysis Method • Event selection • Kinematics, geometry, shape • The selected sample contains signal and background : • Fitting • We use well measured (TM) and mismeasured (SCF) events • Unbinned maximum likelihood to determine and and, from that : Signal efficiency map CP averaged Branching Fraction : CP asymmetry : Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  9. Kinematic Discriminating Variables • Common BaBar reconstructed B kinematic variables • Energy substituted mass (mES) • Difference between beam and reconstructed B energy (ΔE) Signal : peaks in mB Continuum background  DP dependence handled in cuts and fit for signal Signal : peaks in 0 Continuum background Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  10. Truth-Matched and Self-Cross-Feed Signal (1) particle taken from wrong B What is Truth-Matched (TM) ? Correctly reconstructed events θ’Ksπ0 Υ(4S) m2Ksπ0 B1 B2 m2Ksπ+ m’Ksπ0 Ks π+ π0 X X X Ks π+ π0 π0 reconstructed from random γ pairs What is Self-Cross-Feed (SCF) ? π0 misreconstructed Υ(4S) Υ(4S) Misreconstructed events • Migrating events : not reconstructed in the right position in DP B1 B2 B1 B2 Ks π0 π+ X π+ π0 Ks π+ Ks Ks π+ π+ π0 γ X ‘particle from other B • Expected fraction of SCF ~21% γ γ π0 Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  11. Truth-Matched and Self-Cross-Feed Signal (2) How far do SCF events migrate in DP ? Fraction of SCF varies across the Dalitz Soft particles corners = higher fraction of SCF θ’Ksπ0 migration in m’ m’Ksπ0 θ’Ksπ0 Expanded corners migration in θ’ m’Ksπ0 Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  12. Continuum Background • Real B’s at rest in center of mass referential  Spherical events • Continuum background = qqbar (q lighter than b)  Jet-like events • Continuum/signal discriminative power strong for shape variables • Used variables for building of NN : shape variables + tagging information Signal Continuum BBkg B decays Continuum NN Cut chosen : wider one to make the fit work Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  13. B-Backgrounds (1) • B-Backgrounds : real B’s decaying to other channels, mistaken as signal • Classification of B-Backgrounds Done per « mistake » type  Emphasize the discriminative power  Avoid dependence on implemented BR in generic Monte Carlo Mode discussed in next section - Same final state as expected signal- Treated as B-Background in the fit because D0 flies and does not interfere Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  14. B-Backgrounds (2) : More Details on Strategy ‘SCF (1)’ Bbkg ‘TM’ Bbkg Υ(4S) Υ(4S) B1 B2 B1 B2 ‘SCF (2)’ Bbkg Υ(4S) Ks Ks π0 π0 Ks Ks π+ π+ π0 π0 X X X X π+ π+ X X X B1 B1 B2 Ks π+ X π0 Ks π+ γ X γ π0 γ Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  15. ( ) B-Backgrounds (3) : B+/- D0( KSπ0) π+/- • 2875 expected events in the data ~ 2 x expected yield of signal • We do not want to apply a veto to remove the D0  can provide a constraint on the PDF parameters for signal  measure of the exclusive channel from a Dalitz analysis • Expected problems : • Can bring biases in the fit • The D0 width depends on the position in the Dalitz plot θ’Ksπ0 m’Ksπ0 m’Ksπ0 m’Ksπ0 Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  16. The Fit - We use a maximal extended likelihood fit method - The likelihood function : Signal events Continuum B-Backgrounds - Variable used in the fit : mES, ΔE’,NN, DP variables Red shades stand for DP correlation - The fit is blind - 32 floating parameters Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  17. PDF Parameterisation see slide 18 see slide 20 see slide 43 see slide 19 G : Gaussian GG : Double Gaussian BG : Bifurcated Gaussian Pn : polynom of nth order SH : smoothed histogram see slide 44 Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  18. m2Ksπ0 m2Ksπ+ ΔE’ PDF for Truth-Matched Signal • ΔE’ PDF for TM parameterized as the sum of a gaussian and a bifurcated gaussian • ΔE’ depends on π0 momentum i.e. mKsπ+2 Mean value of ΔE map Dependence of :mean of bifurcated gaussian (left) mean of gaussian (right) m2Ksπ+ m2Ksπ+ Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  19. Dalitz Plot PDF for D0 Events m’ distribution wider for low momentum π0’s m’ parameterized as the sum of 2 gaussians which parameters depend on θ’ θ’ for TM D0 events Same feature for SCF D0 events m’ for TM D0 events Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  20. 3 samples can be used  Offpeak data  Onpeak sideband (data without « signal box »)  Monte Carlo qqbar Adapt the smoothing coefficient accordingly to the DP structures PDF « multizone » PDF« simple » Continuum Dalitz PDF Is know to be « wrong » Smoothing coefficient depending on the Dalitz 1,2,3 and 4 are the zones to be used in the new PDF : they are all smoothed with different smoothing coefficient Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  21. Toy Studies or How do we test the fitter ? (1) • One toy = one «data-sized» sample  Poissonized generation of the number of events for each species • Randomization of the values of the discriminatives variables on the PDFs • Each sample is fitted several times • Randomization of the starting point of the fit • Why fit those samples since we know what was generated ? Choice of initial parameters  Obtain the biases due to the fitter • Procedure repeated several times to : • Obtain the central values and the errors on the fitted parameters • Study the stability of the fit Toy Studies = simplified simulations done with the fitter One toy signal only Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  22. phTK*(892)0 bar phTK*(892)0 phTK*(1430)- phTK*(1430)+ phTK*(1430)0 bar phTK*(1430)0 phTρ(770)- phTρ(770)+ phTN.R bar. phTN.R. Toy Studies or How do we test the fitter ? (2) Fitted phases for the B- Fitted phases for the B+ Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  23. High Stat Scans (1) : Method Likelihood scans =- generate one high stat toy - fix all the parameters but one to generation value - draw likelihood vs floating parameter curve Likelihood scan of the K*(892)0, all other parameters fixed to generation values Local minima value selected for this toy Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  24. High Stat Scans (2) : 2-Resonance Models Model = {K*(892)+/-, ρ(770)+/-} Model = {K*(892)+/-, K*(892)0(bar)} Model = {K*(892)0, ρ(770)+/-} TM+SCF TM only Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  25. High Stat Scans (3) : {K*(892)+ + K*(892)0 + ρ(770)+} Adding the ρ to {K*(892)+,K*(892)0} model  fit finds wrong solution Adding the K*(892)+ to the {K*(892)0,ρ(770+} model barely improves the results Adding the K*(892)0 to {K*(892)+ + ρ(770)+} spoils the results, but the situation is still not too bad K*0 scan, ρ GS ρ+ scan, ρ GS Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  26. High Stat Scans (4) : {6-resonance model} Using a 6-resonance model works (other points in phase space tried as well) K*(892)0 scan K*(1430)0 scan N.R. scan ρ(770)+ scan K*(1430)+ scan Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  27. Validation and Embedded Fits : Conclusions • Scans result :6-resonance model don’t show any degeneracies(other points of phase space tried as well) • Problematic situation of the soft π0 corner recovered by the use of other resonances • No problem either when adding backgrounds to the scans • Toys result :Convincing Validation, no major bias with the new NN cut • Embedded fits result :Only one bias observed on the NR amplitude, around -1σ Fits on samples where : - Signal = MC- Background generated by the fitter Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  28. Fits on Full MC, Blind/Unblind • Full datasize MC = sample {signal, continuum, BBkg} built from MC in the anticipated proportions in the data fit on Full MC : test of the fitter in « almost real » conditions • Unblind fit « à la 3-body charmless » = fit on the data assuming that CP is conserved. we look at the yields Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  29. Full MC Study (1) : mES and ΔE’ Signal enriched mES Signal enriched ΔE’ Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  30. Full MC Study (2) : Dalitz Plot Variables Signal enriched mKsπ+ Signal enriched mKsπ0 Signal enriched mπ+π0 Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  31. Blind Fit (1) : Projection plots of mES and ΔE’ Signal enriched mES Signal enriched ΔE’ problem ! Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  32. problem ! Blind Fit (2) : Dalitz Plot Variables mKsπ+ Signal enriched mKsπ0 Signal enriched mπ+π0 Signal enriched Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  33. Unblinding or «Why Did We Miss ICHEP ?» (1) : mES et ΔE’ Signal enriched mES problem ! ΔE’ problem ! Signal enriched Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  34. Unblinding or «Why Did We Miss ICHEP ?» (2) : Dalitz mKsπ+ Signal enriched mKsπ0 Signal enriched mπ+π0 Signal enriched Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  35. New Strategy Diagnostic of the July failure : PDF Bbkgs from the generic Too many Bbkg events Dalitz plot continuum K*+ hard to modelise SOLUTION SOLUTION SOLUTION Stricter Cut on ΔE Detailed Study of the Dalitz qq Specific MC, more statistics Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  36. Cut on ΔE (1) : A Risky Bet • Wide Cut on ΔE : • Why ? Keep enough SCF : • Facilitate the parameterization of the Dalitz PDF of SCF • Keep maximum signal in the interference zones • Keep more B-Background : • Facilitate the modelization and the classification • To solve : • Explosion of the continuum events number • Lots of B-Background (in GeV²) reduce the yield and/or optimize the parameterization Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  37. Cut on ΔE (2) : New Efficiencies Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  38. Résumé and « To-Do’s List » • The new selection have been decided and frozen • All PDFs are ready, excepted :    - the continuum Dalitz - the B-Background : new classification in progress • Validation to be done again • Fit on Full MC, blind and unblinded fits • Interpretation of all Kππ analyses results Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  39. Back-Up Slides

  40. Event Selection • Total efficiency : 20.7% with additional NN cut : 16.1% • Number of candidates per event ~1.1 • Best candidate chosen from χ2 calculated from mKs and mπ0 increase the TM fraction Event selection done on kinematical and geometric criteria Examples of cuts applied on some variables Expected yields for all components (including already NN cut, discussed later) Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  41. Event Selection : Detailed Cuts Examples of cuts applied on some variables Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  42. θ’ mKsπ02 m’ mKsπ+2 Event Selection : Efficiencies • Total efficiency : 20.7% (with additional NN cut :16.1%) • Number of candidates per event ~1.1 • Best candidate chosen from χ2 calculated from mKs and mπ0 increase the TM fraction • Efficiency significantly varies across the Dalitz plot Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  43. mES and ΔE’ PDF for TM D0 1 2 mES ΔE’ Same PDF used for mES parameterisation for TM signal and TM D0 Same PDF used for ΔE’ it has been checked that ΔE’ for TM D0 and for TM signal in D0 band were coinciding 1 2 Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

  44. PDFs for some B-Backgrounds Classes mES ΔE’ squared DP BBkg 1 : TM events, D0 correctly reco, nb particles ≥ 3 BBkg 2 : Hybrid class, contains all events with a D+ (reco or not) BBkg 6 : SCF events, nb particles ≥ 2 Status of the B+ KSπ+π0 Dalitz AnalysisJennifer Prendki, BABAR team, LPNHE

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