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

B0 Lifetime and Mixing with partially reconstructed D*lν and Lepton Tag

IHBD Meeting May 9, 2003

M.Margoni, F.Simonetto

Analysis Strategy

* Fit to ∆z distribution to determine simultaneously ∆m, τ and dilution constrained to the inclusive fraction of mixed events χd Signal Vertex: Tag Vertex: lπ* + beam spot (x,y) l (Elbatag) + beam spot (x,y) l+

Signal Side Tag Side

π∗− l−

data B

• ther

B+ combinatoric continuum data B0

• ther

B+ combinatoric continuum data B0

• ther

B+ combinatoric continuum

2002 mν

2

2000 2001

Lepton Tag Sample

The Signal PDF

Tagging Lepton Sample: b−> l b−>c−>l D0 −> l

{

From tag B From decay B

Resulting PDF:

f±(∆t;τB;∆m;...)= ΓB/2 exp (−ΓB |∆t|) * (1−α)/2 *[ Fb−>l (1±Db−>l cos(∆m∆t)) + + Fb−>c−>l(1±Db−>c−>l cos(∆m∆t))] + ΓD/2 exp (−ΓD |∆t|) * { α(1−ρ) αρ

Tag Side Composition 1

Lepton from D0 (Signal Vertex) affects the Tag−Side l+

Signal Side Tag Side

π∗− l−

D0−>l+ lπ* Flavour=D0 Flavour Time independent dilution D0 leptons mostly populate unmixed sample τD

effective free parameter

in the PDF ∆z meas <∆z true

2000

B

0 Btag→lept

B

0 D0→lept

B+ Btag

→lept B+ D0→lept combinatoric continuum 52.84 / 48 A0 0.9966

B0

tag

D0

tag

Combinatorial Continuum

ID Entries

Mean RMS 166 50 0.8064 0.1927 33.25 / 17 P1

• 0.7244E-02

0.2218E-02 P2

0.1696 0.2208E-01 P3

• 0.8108

0.6423E-01 P4 1.101 0.5261E-01 ID Entries Mean RMS 453 50

• 0.1354

0.5666 16.10 / 20 P1 0.2516 0.5440E-01 P2

• 0.1550

0.6423E-01

D0

tag

Cosθ π*−l Cosθ π*−l

α ρ

Tag Side Composition 2

α ( )=ΝDtag/NTag ρ ( ) =(NMixed/Ntot)Dtag Expressed in terms of Cosθπ*−l to disentagle Btag from Dtag components Cosθ π*−l Cosθ π*−l Cosθ π*−l

Signal Vertex: D0 l Description

Dtag PDF: τ ⊗ 2G

Free parameters: effective τD0 , bias τD0 = 0.316

0.022 ps bias = −0.233

0.019 ps MC 2000

Unmixed Mixed

Tag Vertex: b l / b c l Description

∆z = Zreco − Ztag Lepton π* ∆z true ∆z meas. If ∆z > 0: ∆zmeas < ∆ztrue Lepton Tag l Tag l ∆z true ∆z meas. π* If ∆z < 0: |∆zmeas | > |∆ztrue| Btag c Btag c

Separate treatment of the prompt and cascade lepton samples: same pulls, different biases (~ 0 for b l ) and dilutions.

Cascade fraction (~ 7%) from external fit to Lepton Momentum (up to now fixed from MC ) MC 2000

Unmixed Mixed

Prompt Cascade

Fit to resonant B+

PDF pure lifetime term ⊗ resolution resolution: same as for signal B0,

with separate biases for

narrow and wide gaussians Free parameters: − two biases α+,ρ+ vs cosθ taken from MC

Unmixed Mixed 2000 MC

Fit to signal B0 + resonant B+

Unmixed Mixed b−>l b−>c−>l B+ DTAG B0 − B+ lifetime fixed to 1.65ps − B+ fraction constraied (σ=50%) to MC estimation −α+, ρ+ vs cosθ calculated from MC Free parameters: − signal B0 resolution function params − two biases in B+ resolution function, same pulls as for B0 resolution

Results τB = 1.5379±0.0069 ps ∆md = 0.4683±0.0050 ps−1 Db−>l = 0.9823±0.0032 Db−>c−>l = −0.663±0.087 τD

= 0.423±0.061 ps

fB+ = 0.74±0.32 χd = 0.171±0.003

2000 MC 2000 MC

Combinatorial background

B0 + B+ combinatorial (MC) side band, right charge fit

Unmixed Mixed

B0 + B+ combinatorial (MC) mass band, right charge Side band fit

Compatible shapes

2000 MC 2000 MC

Combinatorial PDF

Empirical parametrization: − combinatorial B0 − combinatorial B+ − B0 and B+ fractions are free parameters in the fit fBKG = fBKG

B0(1−αBKG B+) + fBKG B+αBKG B+(1−ρBKG B+)

fBKG

B0 = fBKG B(1−αBKG) +αBKG fBKG D(1−ρBKG)

fBKG

B+ = fBKG +(1−αBKG +) +αBKG +f+ D(1−ρBKG +)

Unmixed: Free parameters

B0: B+:

fBKG

B : (oscill + lifetime) ⊗ 3G

fBKG

D : lifetime ⊗ 2G (same bias)

2 lifetimes (τunmix, τmix) fBKG

+ : lifetime ⊗ 3G (same resolution params

as in fBKG

B)

fD

+ : lifetime ⊗ 2G (same resolution params

as in fBKG

D)

1 lifetime only

Signal + background MC fit

Unmixed Mixed

Signal B0 Combinatorial Resonant B+

τΒ = 1.5447±0.0086 ps ∆md = 0.4661±0.0063 ps−1 to be compared with the pure−signal fit result: τΒ = 1.5379±0.0069 ps ∆md = 0.4683±0.0050 ps−1

2000 MC

∆(τB) = 0.0068±0.0051 ps ∆(∆md) = −0.0022±0.0038 ps−1 Combinatorial parameters fixed from side−band fit

New approach: Systematics from combinatorial BKG absorbed

in the statistical error by means of a simultaneous side−band fit Statistical errors significantly lowered due to strong anticorrelations arising between signal/BKG parameters τΒ = 1.5426±0.0058 ps ∆md = 0.4657±0.0042 ps−1 χd = 0.170±0.002 to be compared with the

• ld−approach result:

τΒ = 1.5447±0.0086 ps ∆md = 0.4661±0.0063 ps−1 χd = 0.171±0.004 Preliminary

Unmixed Mixed Asimmetry

∆msig τsig (ρij) = ∆mBKG .03 −.23 τBKG . 13 −.55

2000 MC

Conclusions and Next Steps

* MC fit finalized: − Separate description of prompt and cascade leptons − Dtag fraction from cosθπ∗−l fit − Dtag PDF described in terms of an effective τD − B+ PDF described by a pure lifetime term − B+ fraction constrained to m2ν fit result − Combinatorial PDF from simultaneous fit to the side−band right charge sample − χd constraint from the fraction of mixed events * Given the available luminosity (Run1+Run2) we expect: σstat(τΒ)~0.005 ps σstat(∆m)~0.004 ps−1 ∆m: −0.005 ps−1 ( Boost Approximation Bias ) *Next Steps: −Year by year stability −Real Data Analysis