Hadronic Moments in Semileptonic B Decays

1
Hadronic Moments in Semileptonic B Decays

• Ramon Miquel
• Lawrence Berkeley National Laboratory
• (for the CDF II Collaboration)

2
Motivation (I)
Most precise determination of Vcb comes from Gsl
(inclusive determination)
U(4S), LEP/SLD, CDF measurements.
Experimental ?Vcb1
Theory with pert. and non-pert. corrections.
?Vcb2.5
Ftheory evaluated using OPE in HQET expansion
in as and 1/mB powers O(1/mB) ? 1 parameter
? (Bauer et al., PRD
67 (2003) 071301) O(1/mB2) ? 2 more parameters
?1, ?2 O(1/mB3) ? 6 more parameters ?1, ?2,
T1-4
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Motivation (II)
Many inclusive observables can be written using
the same expansion (same non-perturbative
parameters) the spectral moments

• Photonic moments Photon energy in b ? s ?

(CLEO)

• Leptonic moments B?Xcl?, lepton E in B rest
  frame

(CLEO, DELPHI, BABAR)

• Hadronic moments B?Xcl?, recoil mass M(Xc)

(CLEO, DELPHI, BABAR, CDFII)
Constrain the unknown non-pert. parameters and
reduce Vcb uncertainty. With enough
measurements test of underlying assumptions
(duality).
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What is Xc?
Higher mass states D
Semi-leptonic widths (PDG 03)
Br ()
B ? Xc l ? 10.89 ? 0.26
B ? D l ? 6.00 ? 0.24
B ? D l ? 2.23 ? 0.15
(b/B/B0 combination, b?u subtracted)

• 25 of semi-leptonic width
• is poorly known

• Possible D?D() p p contributions neglected
• No experimental evidence so far
• DELPHI limit
• We assume no D contribution
  in our sample

5
Analysis Strategy
Typical mass spectrum M(X0c) (Monte Carlo)

• D0 and D0 well-known
• ? measure only f
• ? only shape needed

1) Measure f(sH) 2) Correct for
background, acceptances, bias ? moments of
D 3) Add D and D ? M1,M2 4) Extract ?, ?1
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Channels

• Must reconstruct all channels to get all the D
  states.
• However CDF has limited capability for neutrals

• B0?D- l ? always leads to neutral particles ?
  ignore it
• B-? D0 l- ? better, use isospin for missing
  channels

• D0 ? D ?- OK
• D0 ? D0 ?0 Not reconstructed. Half the rate
  of D ?-
• D0 ? D ?-
• D ? D0 ? OK
• D ? D ?0 Not reconstructed. Feed-down to D
  ?-
• D0 ? D0 ?0 Not reconstructed. Half the rate
  of D ?-

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Event Topology
Exclusive reconstruction of D

• D0 D ?-
• D0 ? (Br67.7)
• K- ? (Br3.8)
• K- ? ?- ?
  (Br7.5)
• K- ? ?0
  (Br13.1)

• D0 D ?-
• K- ? ? (Br9.1)

D
D
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Backgrounds
Physics background B?D()Ds-, D(s)?Xl? ? MC,
subtracted
Combinatorial background under the D() peaks ?
sideband subtraction

• Feed-down in signal
• D0 ?D(? Dp0)p-
• irreducible background to
• D0 ?Dp-.
• subtracted using data
• shape from D0?- in
• D0 ?D(? D0p)p-
• rate
• ½ (isospin) x eff. x BR

• Prompt pions faking ?
• fragmentation
• underlying event
• separate B and primary vertices
• (kills also prompt charm)
• ? use impact parameters to discriminate
• ? model wrong-sign p ?- combinations

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Lepton D() Reconstruction

• Data Sample
• e/? displaced track
• 180 pb-1
• (? Sept 2003)

• Lepton D()
• D vertex
• 3D
• lD(?) vertex (B)
• 3D
• Lxy(B) gt 500 ?m
• M(B) lt 5.3 GeV

• Track Selection
• e/? pT gt 4 GeV
• other pT gt 0.4 GeV

Total 28000 events
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? Selection

• Based on topology
• impact parameter significances w.r.t. primary, B
  and D vertices

Cuts are optimized using MC and background data
Additional cuts only for D

• pT gt 0.4 GeV
• ?R lt 1.0

• d0PV/? gt 3.0
• d0BV/? lt 2.5

d0DV/? gt 0.8 Lxy B?D gt 500?m
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Raw m Distribution
Measured in Dm, shifted by M(D()), side-band
subtracted.
D1,D1,D2
D2,D0
Feed-down
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Efficiency Corrections

• 1) Correct the raw mass for any dependence of
  ?reco on M(D)
• Possible dependence on the D species (spin).
• Monte-Carlo for all D (Goity-Roberts for
  non-resonant), cross-checked with pure
• phase space decays.
• 2) Cut on lepton energy in B rest frame
• Theoretical predictions need well-defined pl
  cut.
• We cant measure pl, but we can correct our
  measurement to a given cut
• ? pl gt 700 MeV/c.

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Corrected Mass and D Moments
Procedure
Results

• Unbinned procedure using weighted events.
• Assign negative weights to background samples.
• Propagate efficiency corrections to weights.
• Take care of the D / D relative
  normalization.
• Compute mean and sigma of distribution.

No Fit !
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Final Results
0.61
0.69
Pole mass scheme
1S mass scheme
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Systematic Errors
?m1 (GeV2) ?m2 (GeV4) ?M1 (GeV2) ?M2 (GeV4) ?? (GeV) ??1 (GeV2)
Stat. 0.16 0.69 0.037 0.25 0.075 0.055
Syst. 0.08 0.20 0.065 0.12 0.090 0.082
Mass resolution 0.02 0.13 0.005 0.04 0.012 0.009
Eff. Corr. (data) 0.03 0.13 0.006 0.05 0.014 0.011
Eff. Corr. (MC) 0.06 0.05 0.016 0.03 0.017 0.006
Bkgd. (scale) 0.01 0.03 0.002 0.01 0.003 0.002
Physics bkgd. 0.01 0.02 0.002 0.01 0.004 0.002
D / D BR 0.01 0.02 0.002 0.01 0.004 0.002
D / D Eff. 0.02 0.03 0.004 0.01 0.005 0.002
Semileptonic BRs 0.062 0.10 0.064 0.022
?1 0.041 0.069
Ti 0.032 0.031
?s 0.018 0.007
mb, mc 0.001 0.008
Choice of pl cut 0.019 0.009
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Comparison with Previous Measurements
Pole mass scheme
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Summary

• First measurement of hadronic moments in
  semileptonic B decays performed at a hadron
  collider.
• Good agreement with HQET and previous
  determinations.
• Competitive with other experiments. Little model
  dependency. No assumptions on shape or rate of
  D components.
• Increased statistics and improved tracking will
  lead to substantially more precise results in the
  near future.

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BACK-UP SLIDES
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CKM and Vcb
Vcb A?2 (defines the scale of UT)
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Vcb measurements

• Vcb from exclusive B decays
• Large statistics on Bd0?D()?-? available and
  new measurements are coming
• Present precision (5) is systematics limited
• Experiments D states, Ds BR
• Theory form factor extrapolation,
  corrections to F(1)1
  can be reduced in the future

Vcbexcl(42.1 ?1.1exp ?1.9theo) ?10-3
(PDG 2002, Vcb review)

• Vcb from inclusive B decays
• Experiment large statistics on BR(B?Xc?-?) and
  tB and small systematics

Vcbincl (40.4 0.5exp 0.5?,? 0.8theo)
?10-3
(PDG 2002, Vcb review)
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Lepton D Reconstruction

• Data Sample
• e/? displaced track
• 180 pb-1
• (? Sept 2003)

• Lepton D()
• D vertex
• 3D
• lD(?) vertex (B)
• 3D
• Lxy(B) gt 500 ?m
• Lxy(D/B) gt -200 ?m
• m(B) lt 5.3 GeV

• Track Selection
• e/? pT gt 4 GeV
• other pT gt 0.4 GeV

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D Reconstruction and Yields
D channels Dm ? M(D0?) M(D0)
D() l- (cc) yields
28000 events
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Monte-Carlo Validation (I)
MC vs. semileptonic sample
67 74 23
43 69 87
Matching ?2 probability for those plots
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Monte-Carlo Validation (II)
Relative yield prediction K3?/K? (cross-check)
Rdata 0.770.02 Rpred 0.800.04 Rpred/Rdata
1.040.06
? efficiency for adding tracks understood
Relative yield prediction K2?/K? (needed for
D/D normalization)
Two methods (a,b) to derive this BR
PDG BR MC efficiency ratios
Rdata Rpred Rpred/Rdata
3.710.08 3.310.58 0.890.16
3.710.08 3.230.29 0.870.08

1. Based on inclusive b?D()l?
2. Based on exclusive B?D()l?, Dl?

• uncertainties in Br (incl.) and D spectroscopy
  (excl.) compromise prediction
• 1. 0.87 13 used as systematics

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Impact Parameters in MC
Comparison data/MC for IP (worst case)

• Residual corrections
• derived from data
• ?
• non-SVT D daughters (pT gt 1.5 GeV)
• corrections from double ratios
• in pT
• in m

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Background Subtraction

• Use mass side-bands to subtract combinatorial
  background.
• Use D D0pp- to subtract feed-down from
  D Dp0p- to Dp-.
• Use wrong-sign p l- combinations to subtract
  prompt background to p.
• Possible charge asymmetry of prompt background
  studied with fully reconstructed Bs 4
  contribution at most.
• Possible D D() p p contributions neglected
• No experimental evidence so far.
• DELPHI limit
• We assume no D contribution in our
  sample

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Combination with D0, D0

• Take M(D0), M(D0), Gsl, G0, G from PDG 2003
• Gsl, G0, G are obtained combining BRs for B-,
  B0 and admixture, assuming the widths are
  identical (not the BRs themselves), and using
  
• f- / f0 1.04 0.08
• t(B-) / t(B0) 1.085 0.017
• Results
• BR(B X0c l nl) 0.1089 0.0026
• BR(B D0 l nl) 0.0223 0.0015
• BR(B D0 l nl) 0.0600 0.0024

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Main Systematics

• Semileptonic branching ratios when combining D
  with D and D
• Efficiency corrections from data
• Use data-corrected efficiency. vs. pure MC
  efficiency
• Efficiency corrections from D Monte-Carlo
• D states NR Goity-Roberts vs. pure
  phase-space
• Mass resolution
• Dominated by satellite 60 MeV
• Prompt background scale
• Charge correlations WS / RS 4
• Other D/D normalization, physics, pl cut,
  theory