B 0 Lifetime and Mixing with partially reconstructed D*l and Lepton - PowerPoint PPT Presentation

B 0 Lifetime and Mixing with partially reconstructed D*l ν and Lepton Tag IHBD Meeting May 9, 2003 M.Margoni, F.Simonetto

Analysis Strategy l π * + beam spot (x,y) Signal Vertex: l (Elbatag) + beam spot (x,y) Tag Vertex: Signal Side Tag Side l + l − π∗− * Fit to ∆ z distribution to determine simultaneously ∆ m, τ and dilution constrained to the inclusive fraction of mixed events χ d

� Lepton Tag Sample 2002 2000 2001 data data data B 0 B 0 0 B other other other B + B + B + combinatoric combinatoric combinatoric continuum continuum continuum 2 m ν

The Signal PDF b−> l { From tag B Tagging Lepton Sample: b−>c−>l D0 −> l From decay B Resulting PDF: f ±(∆ t ;τ B ;∆ m ;...)= Γ B /2 exp (− Γ B | ∆ t|) * (1− α )/2 *[ F b−>l (1 ± D b−>l cos( ∆ m ∆ t)) + + F b−>c−>l (1 ± D b−>c−>l cos( ∆ m ∆ t))] α(1−ρ) + Γ D /2 exp (− Γ D | ∆ t|) * { αρ

Tag Side Composition 1 Lepton from D 0 (Signal Vertex) affects the Tag−Side Signal Side Tag Side l + l − D 0 −>l + ∆ z meas < ∆ z true π∗− l π * Flavour=D 0 Flavour τ D effective free parameter Time independent dilution in the PDF D0 leptons mostly populate unmixed sample

☎ ✂ ✁ ☎ ✁ ✄ Tag Side Composition 2 2000 B 0 Continuum D 0 tag Combinatorial ID 166 Entries 50 tag α Mean 0.8064 RMS 0.1927 D 0 33.25 / 17 0 B tag → lept B 0 D 0 → lept P1 -0.7244E-02 0.2218E-02 B B + B tag → lept P2 0.1696 0.2208E-01 B + D 0 → lept tag P3 -0.8108 0.6423E-01 combinatoric P4 1.101 0.5261E-01 continuum 52.84 / 48 A0 0.9966 Cos θ π *−l ID 453 Entries 50 ρ Mean -0.1354 RMS 0.5666 16.10 / 20 P1 0.2516 0.5440E-01 P2 -0.1550 0.6423E-01 Cos θ π *−l α ( )=Ν Dtag/NTag Cos θ π *−l ρ ( ) =( NMixed/Ntot) Dtag Cos θ π *−l Expressed in terms of Cos θ π *−l to disentagle Cos θ π *−l Btag from Dtag components

✆ ✆ ✝ ✝ Signal Vertex: D 0 l Description Dtag PDF: τ ⊗ 2 G Free parameters: effective τ D0 , bias Mixed Unmixed MC 2000 τ D0 = 0.316 0.022 ps bias = −0.233 0.019 ps

✆ ✆ Tag Vertex: b l / b c l Description MC 2000 Unmixed Mixed Separate treatment of the prompt and Prompt cascade lepton samples: same pulls, Cascade different biases (~ 0 for b l ) and dilutions. Cascade fraction (~ 7%) from external fit to Lepton Momentum (up to now fixed from MC ) ∆ z = Z reco − Z tag Lepton Tag l Lepton B tag c B tag c Tag l π * π * ∆ z meas. ∆ z meas. ∆ z true ∆ z true If ∆ z > 0: ∆ z meas < ∆ z true If ∆ z < 0: | ∆ z meas | > | ∆ z true |

Fit to resonant B + 2000 MC PDF Unmixed pure lifetime term ⊗ resolution resolution: same as for signal B 0 , with separate biases for narrow and wide gaussians Free parameters: α + , ρ + vs cos θ Mixed − two biases taken from MC

Fit to signal B 0 + resonant B + 2000 MC − B + lifetime fixed to 1.65ps − B + fraction constraied ( σ =50%) to MC estimation − α + , ρ + vs cos θ calculated from MC Unmixed Free parameters: − signal B 0 resolution function params − two biases in B + resolution function, same pulls as for B 0 resolution b−>l Mixed 2000 MC b−>c−>l Results τ B = 1.5379 ± 0.0069 ps D TAG B 0 ∆ m d = 0.4683 ± 0.0050 ps −1 B + D b−>l = 0.9823 ± 0.0032 D b−>c−>l = −0.663 ± 0.087 τ D = 0.423 ± 0.061 ps f B+ = 0.74 ±0.32 χ d = 0.171 ± 0.003

Combinatorial background B 0 + B + combinatorial (MC) side band, right charge Unmixed fit B 0 + B + combinatorial (MC) mass band, right charge 2000 MC 2000 MC Mixed Side band fit Compatible shapes

Combinatorial PDF B : (oscill + lifetime) ⊗ 3G f BKG D : lifetime ⊗ 2G (same bias) Empirical parametrization: f BKG − combinatorial B 0 2 lifetimes ( τ unmix , τ mix ) − combinatorial B + + : lifetime ⊗ 3G (same resolution params f BKG − B 0 and B + fractions are free B ) as in f BKG parameters in the fit + : lifetime ⊗ 2G (same resolution params f D D ) as in f BKG 1 lifetime only Free parameters Unmixed: B0 (1− α BKG B+ α BKG B+ (1− ρ BKG B+ ) + f BKG B+ ) f BKG = f BKG B (1− α BKG ) + α BKG f BKG D (1− ρ BKG ) B0 = f BKG B 0 : f BKG + (1− α BKG + ) + α BKG D (1− ρ BKG B+ = f BKG + f + + ) B + : f BKG

Signal + background MC fit Combinatorial parameters fixed τ Β = 1.5447 ± 0.0086 ps from side−band fit ∆ m d = 0.4661 ± 0.0063 ps −1 Unmixed Signal B 0 to be compared with the Combinatorial pure−signal fit result: Resonant B + 2000 MC τ Β = 1.5379 ± 0.0069 ps ∆ m d = 0.4683 ± 0.0050 ps −1 Mixed ∆(τ B ) = 0.0068 ± 0.0051 ps ∆(∆ m d ) = −0.0022 ±0.0038 ps −1

New approach: Systematics from combinatorial BKG absorbed in the statistical error by means of a simultaneous side−band fit Preliminary 2000 MC τ Β = 1.5426 ± 0.0058 ps Unmixed ∆ m d = 0.4657 ± 0.0042 ps −1 χ d = 0.170 ± 0.002 to be compared with the Mixed old−approach result: τ Β = 1.5447 ± 0.0086 ps ∆ m d = 0.4661 ± 0.0063 ps −1 Asimmetry χ d = 0.171 ± 0.004 ∆ m sig τ sig Statistical errors significantly lowered due to strong (ρ ij ) = ∆ m BKG .03 −.23 anticorrelations arising between τ BKG . 13 −.55 signal/BKG parameters

Conclusions and Next Steps * MC fit finalized: − Separate description of prompt and cascade leptons − Dtag fraction from cos θ π∗− l fit − Dtag PDF described in terms of an effective τ D − B + PDF described by a pure lifetime term − B + fraction constrained to m 2 ν fit result − Combinatorial PDF from simultaneous fit to the side−band right charge sample − χ d constraint from the fraction of mixed events * Given the available luminosity (Run1+Run2) we expect: σ stat (τ Β )~0.005 ps σ stat (∆ m)~0.004 ps −1 ∆ m: −0.005 ps −1 ( Boost Approximation Bias ) *Next Steps: −Year by year stability −Real Data Analysis