Measurement of Relative Fragmentation Fractions of BHadrons at CDF

1
Measurement of Relative Fragmentation Fractions
of B Hadrons at CDF

• Karen Gibson
• Carnegie Mellon University
• Fermilab Wine and Cheese
• April 28, 2006
• Arbor Day

2
Recent B Physics Results
3
Outline

• B fragmentation overview
• Semileptonic signal reconstruction
• Semileptonic sample composition
• Reconstruction efficiencies
• Fit for fragmentation fractions
• Fragmentation fraction results
• Outlook

4
Outline

• B fragmentation overview
• Semileptonic signal reconstruction
• Semileptonic sample composition
• Reconstruction efficiencies
• Fit for fragmentation fractions
• Fragmentation fraction results
• Outlook

5
B Physics at Tevatron

• Reconstruct all flavors of B hadrons
• Bd0, Bu, Bs0, Bc, ?b0
• Contrast to B factories, ?(4S) ?(5S)
• Bd0, Bu Bs0
• Large dataset of B hadrons
• 1 fb-1 data available for B measurements
• Very large production cross-section makes
  Tevatron competitive w/B factories
• Make exciting new measurements
• Bs mixing (1 fb-1)
• Refine older measurements
• B fragmentation fractions (360 pb-1)

6
B Fragmentation

• Probability of b quark hadronizing with an
  anti-quark or a di-quark pair
• fq ? B(b ? Bq)
• Many models for heavy flavor fragmentation
• Petersen, Lund,
• B fragmentation fractions inherently empirical
  quantity
• Include B, B in fragmentation fractions

7
Why Fragmentation Fractions?

• Search for Bs?µµ-
• B(Bs?µµ-) fu/fs?B(B?J/yK)?
• Improvement in limit _at_95 CL if
• Reduce uncertainty on fs/fd
• fs/fd at Tevatron is higher than world average

8
Fragmentation Fraction Status

• Measured many times before
• LEP (ALEPH, DELPHI, OPAL)
• fu, fd, fs, fb-baryon
• ee- collisions
• pT(b) 40 GeV/c
• fs/(fufd) 0.109 0.026
• Tevatron
• fu/fd, fs/(fufd), f?b/(fufd)
• pp collisions
• pT(b) 10-15 GeV/c
• CDF Run I fs/(fufd) 0.213 0.038

2004 PDG, dominated by LEP
Average between two CDF Run I results
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B Fragmentation Intrigue

• Other 2.5 sigma discrepancies observed between
  LEP and CDF Run I
• c fdcd fscs
• 0.118 0.005 average measured at LEP
• 0.152 0.013 measured at CDF Run I (110 pb-1)
• The discrepancies could be due to
• New physics present in pp collisions
• OR fs is simply higher at Tevatron
• OR just fluctuations, etc

10
B Frag. Fractions in Run II

• Use method similar to Run I measurement
• Reconstruct five semileptonic B signals
• l-D, l-D0, l-D(?D0?), l-Ds, l-?c (le,µ)
• Relate to parent B hadrons
• Bd0, Bu-, Bs0, ?b0
• Cross-talk from excited charm states makes life
  complicated!

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Outline

• B fragmentation overview
• Semileptonic signal reconstruction
• Semileptonic sample composition
• Reconstruction efficiencies
• Fit for fragmentation fractions
• Fragmentation fraction results
• Outlook

12
CDF Detector

• Tracking chamber
• Seven layers of silicon
• Precision detection of displaced tracks
• Drift Chamber
• dE/dx
• Lepton Identification
• Electromagnetic Calorimeter
• Hadronic Calorimeter
• Muon chambers

Thanks to the Tevatron for the great work
delivering a record luminosity!
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SVT

• Hardware trigger
• Can trigger on displaced tracks in Run II
• Allows for accumulation of large sample of B
  events
• Uses information from
• Drift chamber (XFT)
• Silicon detector

14
Semileptonic B Trigger

• New lSVT trigger in Run II
• pT(l) gt 4 GeV/c
• pT(SVT) gt 2 GeV/c
• 120 µm lt d0(SVT) lt 1 mm
• m(l,SVT) lt 5 GeV/c2
• Run I trigger
• pT(l) gt 8 GeV/c

15
lCharm Reconstruction

• Reconstruct 5 charm signals
• D ? K-pp
• D0 ? K-p
• D ? D0p
• Ds ? fp, f ? K-K
• ?c ? pK-p
• Require one of charm tracks be SVT track
• Require a trigger lepton in vicinity
• Vertex charm hadron with trigger lepton

16
Signal Selection

• Cut on quantities which distinguish B decays
• ct(lD) Lxy(P.V.? lD)m(B)/pT(lD) gt 200 µm
• Inconsistent with being prompt
• Lxy(P.V. ? D)
• pT(tracks)
• Probability of vertex fits to bottom and charm
  hadrons

17
Reflection Backgrounds
CDF Run II Monte Carlo
Ds?KK-p

• Combinatorial backgrounds present beneath all
  signals
• Significant reflection backgrounds present in two
  signals
• D signal contaminated by Ds?KK-p
• Include reflection in fit to signal
• ?c signal contaminated by D?K-pp, Ds?KK-p
• Use dE/dx cut on proton in ?c? pK-p

18
Ds Reflection in D Signal

• Use MC to determine reflection shape
• Fit number of Ds?jp observed in data
• Scale efficiency of Ds?jp to generic Ds?K-Kp
• Measure NDs  13.4  0.8  relative to D yield
  in m?1.78,1.95

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µCharm Meson Signals
20
µ?c Signal
With dE/dx cut on proton
No dE/dx cut
21
Semileptonic B Yields
360 pb-1

• Run I yields used in fragmentation fraction
  measurement
• N(e-Ds) 59 10
• N(e-?c) 79 17

More than 50 times the yield in Run II compared
to Run I!
22
Outline

• B fragmentation overview
• Semileptonic signal reconstruction
• Semileptonic sample composition
• Reconstruction efficiencies
• Fit for fragmentation fractions
• Fragmentation fraction results
• Outlook

23
Sample Composition

• Need to disentangle parent B hadrons from
  lepton-charm signals
• Missing neutrino prevents fully reconstructing
  decay at CDF
• Allows excited charm states to contribute to
  reconstructed charm signals
• Cross-talk between signals
• B0, B-, Bs0 contribute to l-D, l-D0, l-D,
  l-Ds
• ?b0 contributes to l-?c
• Meson ? baryon cross talk small

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Simple Sample Composition

• Simple parameterization of semileptonic B0, B
  decays into D0 and D-

25
Full Sample Composition
Consider all significant decays to semileptonic
charm signals, including sequential semileptonic
decays.
Physics backgrounds e.g. B0?D(?K-pp)D-(?l-X)
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Parameterization

• Simple example w/only ground state
• N(lD-)
• N(B0)B(B0?l?D-)B(D-?Kp-p-)
• e(B0?l?D-,D-?Kp-p-)
• N(b)fd?(B0)G(B0?l?D-)B(D-?Kp-p-)
  e(B0?lnD-,D-?Kp-p-)
• Extend this to all mesons
• Generalize notation
• N(lDi)Sjd,u,s N(b) fj ?(Bj)
  SkGkBijk(Djk?Di)eijk
• Di D-, D0, D- , and Ds
• Gk G, G, G

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Branching Ratios

• Need model for semileptonic decays
• G(B? l?D(,)) 1/?(B) x B(B? l?D(,))
• Use spectator model for meson decays
• G(B0? l?D-) G(B? l?D0) G(Bs? l?Ds) G
• G(B0? l?D-) G(B? l?D0) G(Bs? l?Ds) G
• G(B0? l?D-) G(B? l?D0) G(Bs? l?Ds)
  G
• Assume G G G Gsl(B? l?X)
• Use fixed sample composition for ?b?ln?cX
• Use PDG 2004 for known branching ratios
• Use theoretical predictions and symmetry
  principles for unmeasured BR

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Outline

• B fragmentation overview
• Semileptonic signal reconstruction
• Semileptonic sample composition
• Reconstruction efficiencies
• Fit for fragmentation fractions
• Fragmentation fraction results
• Outlook

29
Acceptances and Efficiencies

• Need relative acceptances and efficiencies of
  individual lcharm decays
• Fit to relative fractions
• Use MC to determine acceptances
• Detector geometry
• Kinematic differences between lepton-charm
  signals
• Use data to determine remaining efficiencies
  which are different between charm channels

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Monte Carlo

• Monte Carlo is good for most kinematic
  differences between lepton-charm signals
• ct(D), pT(tracks), etc
• Generate single B hadron directly
• Use input pT spectrum measured from data
• Inclusive pT(b?J/yX) spectrum
• Separate set of Monte Carlo generated for each
  decay in sample composition
• Separate sets of Monte Carlo for e, µ
• Validate with inclusive Monte Carlo samples by
  comparing data and Monte Carlo
• e.g. B?lnDX

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Reconstruction Efficiencies

• Measure some efficiencies from data
• Single track efficiency
• D0?K-p vs. D? K-pp
• XFT trigger efficiencies for p, K, p
• dE/dx efficiency for cut on proton
• ?c?pK-p
• Use to re-weight Monte Carlo for total efficiency

32
Single Track Efficiency

• Efficiency to add an additional track depends on
  environment in detector
• Monte Carlo only generates B hadron
• Reconstruct D0?K-pp-p
• Measure efficiency relative to D0?K-p in data
  and Monte Carlo
• Efficiency to add two additional tracks
• Measure
• etrk 87.8 2.1-1.2 (stat.sys.)

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XFT Efficiencies

• Differences in tracking p, K, p in drift chamber
• Differences in efficiencies between reconstructed
  charm states
• Only applies to SVT trigger track
• Varying drift chamber performance not optimally
  described by Monte Carlo
• Again measure from data
• Re-weight Monte Carlo
• Measure in separate run ranges

34
XFT Efficiencies
35
Comparison of Data and MC
c2/NDF11.9/8.0
c2/NDF24.3/27.0
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B Meson pT Spectra

• Choice of pT spectrum used is important for
  determination of efficiencies
• Use inclusive pT(b?J/yX) spectrum measured in Run
  II for meson signals
• Good agreement with data

37
?b pT Spectra

• Inclusive pT(b?J/yX) spectrum does not describe
  the l?c data
• Observe softer spectrum in data than the MC
• Tune the l?c Monte Carlo spectrum to match the
  l?c data

38
Outline

• B fragmentation overview
• Semileptonic signal reconstruction
• Semileptonic sample composition
• Reconstruction efficiencies
• Fit for fragmentation fractions
• Fragmentation fraction results
• Outlook

39
General Idea of Fit

• Express each term of sample composition in terms
  of B0
• Fit for relative production
• Npred(lDi) N(B0) Sjd,u,s fj/fd ?(Bj)
• SkGk Bijk(Djk?Di)eijk
• Npred(l?c) N(B0) f?b/(fufd)(1fu/fd)
• (SkBk (?b ?l??c,k? ?c))ek
• ?² fit to 5 lepton charm channels
• fu/fd, fs/(fufd), f?b/(fufd)
• fs/fd fs/ (fufd) (1fu/fd)
• N(B0)
• Parameter for fit, not physical number of B0s

40
Implementation of Fit

• Fit looks like
• ?² Si1..5 (Npred(lDi) -Nmeas(lDi))²/smeas,i²
• (G-GPDG)²/sGPDG²
• (G-GPDG)²/sGPDG²
• (G-GPDG)²/sGPDG²
• Gaussian constraints for G, G, G
• Test with high statistics toy Monte Carlo

41
Fit Results
f?b higher than previously measured!

• Statistical errors ONLY
• Fit eSVT and µSVT separately
• Cancel lepton ID efficiencies
• Statistically independent samples
• Results are consistent- very nice!
• Results are consistent if fu/fd fixed to unity

42
Outline

• B fragmentation overview
• Semileptonic signal reconstruction
• Semileptonic sample composition
• Reconstruction efficiencies
• Fit for fragmentation fractions
• Fragmentation fraction results
• Outlook

43
Systematic Uncertainties

• Measurement is dominated by systematic
  uncertainties
• Largest come from unknown branching ratios,
  particularly ground state charm
• Other source of systematic uncertainty arise from
  determination of efficiencies, counting yields,
  and false lepton backgrounds
• Knowledge of the Bs0 and ?b0 pT spectrum
• Residual false lepton contamination

44
?b pT Spectrum Uncertainty

• Vary tuned l?c spectrum to match agree with
  inclusive J/y spectrum
• Produces large uncertainty 0.049
• Estimate conservatively
• True ?b0 spectrum isnt known

45
Systematic Uncertainties
0.062 -0.074
0.058 -0.035
0.141 -0.103
46
pT Threshold for Measurement
CDF Run II Monte Carlo
CDF Run II Monte Carlo

• Choose to quote pT threshold for all
  fragmentation fractions
• pT(B) gt 7 GeV/c determined from Monte Carlo

47
Final Results

• Weighted average between eSVT and µSVT samples
• Statistical error is very small!
• Error on fs/(fufd) is dominated by PDG 2004
• B(Ds?j?)   (3.6  0.9)
• Sheldon Stones estimate of CLEO-c measurement
  (FPCP06)
• B(Ds?j?)   (3.73  0.42)

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Comparison with PDG
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Comparisons with Other Results
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Outline

• B fragmentation overview
• Semileptonic signal reconstruction
• Semileptonic sample composition
• Reconstruction efficiencies
• Fit for fragmentation fractions
• Fragmentation fraction results
• Outlook

51
Prospects

• New fragmentation fraction measurement at CDF
  will be improved with expected new CLEO-c
  branching ratios
• Measurements of B pT spectra at CDF in fully
  reconstructed modes limit uncertainty
• Improved statistics are always helpful!!

52
Arbor Day Poem
This is the state of man today he puts forth
The tender leaves of hope tomorrow blossoms,
And bears his blushing honors thick upon him
The third day comes a frost, a killing frost
And when he thinks, good, easy man, full surely
His greatness is a-ripening-nips his roots, And
then he falls, as I do. --Shakespeare, Henry
VIII Excerpt taken from Indiana Division of
Forestry Arbor Day website www.in.gov/dnr/forestry
/education/arborday/adpoems.html
53
Arbor Day Poem
This is the state of man today he puts forth
The tender leaves of hope tomorrow blossoms,
And bears his blushing honors thick upon him
The third day comes a frost, a killing frost
And when he thinks, good, easy man, full surely
His greatness is a-ripening-nips his roots, And
then he falls, as I do. --Shakespeare, Henry
VIII Excerpt taken from Indiana Division of
Forestry Arbor Day website www.in.gov/dnr/forestr
y/education/arborday/adpoems.html