# Presentation: 528874

## Measurement of Relative Fragmentation Fractions of  B Hadrons at CDF

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

## Recent B Physics Results

## Outline

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

## Outline

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

## B Physics at Tevatron

- Reconstruct all flavors of B hadrons
- Bd0, Bu+, Bs0, Bc+, Λb0
- Contrast to B factories, Υ(4S) [Υ(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)

## 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

## Why Fragmentation Fractions?

- Search for Bs→μ+μ
- B(Bs→μ+μ) = fu/fsB(B+J/K+)...
- Improvement in limit @95% CL if
-  Reduce uncertainty on fs/fd
-  fs/fd at Tevatron is higher than world average...

## Fragmentation Fraction Status

- Measured many times before
- LEP (ALEPH, DELPHI, OPAL)
-  fu, fd, fs, fb-baryon
-  e+e collisions
-  pT(b) ~ 40 GeV/c
-  fs/(fu+fd) = 0.109 ± 0.026
- Tevatron
-  fu/fd, fs/(fu+fd), fΛb/(fu+fd)
-  pp collisions
-  pT(b) ~ 10-15 GeV/c
-  CDF Run I: fs/(fu+fd) = 0.213 ± 0.038

- 2004 PDG,
- dominated by LEP

- Average between two CDF Run I results

## B Fragmentation Intrigue

- Other ~2.5 sigma discrepancies observed between LEP and CDF Run I
- = fdd + fss
-  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...

## 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Λc+ (l=e,μ)
- Relate to parent B hadrons
- Bd0, Bu, Bs0, Λb0
- Cross-talk from excited charm states makes life  complicated!

## Outline

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

## 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!

## 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

## Semileptonic B Trigger

- New l+SVT trigger in Run II
- pT(l)  4 GeV/c
- pT(SVT)  2 GeV/c
- 120 μm  d0(SVT)  1 mm
- m(l,SVT)  5 GeV/c2
- Run I trigger
- pT(l)  8 GeV/c

## l+Charm Reconstruction

- Reconstruct 5 charm signals
- D+  K++
- D0  K+
- D*+  D0+
- Ds+  φ+, φ KK+
- Λc+  pK+
- Require one of charm tracks be SVT track
- Require a trigger lepton in vicinity
- Vertex charm hadron with trigger lepton

## Signal Selection

- Cut on quantities which distinguish B decays
- ct*(lD) = Lxy(P.V.→ lD)∙m(B)/pT(lD)  200 μm
-  Inconsistent with being prompt
- Lxy(P.V. → D)
- pT(tracks)
- Probability of vertex fits to bottom and charm hadrons

## Reflection Backgrounds

- Combinatorial backgrounds present beneath all signals
- Significant reflection backgrounds present in two signals
- D+ signal contaminated by Ds+→K+K+
-  Include reflection in fit to signal
- Λc+ signal contaminated by D+→K++, Ds+→K+K+
-  Use dE/dx cut on proton in Λc+→ pK+

**CDF Run II Monte Carlo**

- Ds→K+K+

## Ds+ Reflection in D+ Signal

- Use MC to determine reflection shape
- Fit number of Ds+→+ observed in data
- Scale efficiency of Ds+→+ to generic Ds+→KK++
- Measure NDs = 13.4 ± 0.8 % relative to D+ yield in m[1.78,1.95]

## μ+Charm Meson Signals

## μ+Λc Signal

- No dE/dx cut

- With dE/dx cut on proton

## Semileptonic B Yields

| Signature | Yield |
| --- | --- |
| lD | 46,848 ± 275 |
| lD* | 8,490 ± 95 |
| lD+ | 31,015 ± 262 |
| lDs+ | 3,081 ± 95    |
| lΛc+ | 4,739 ± 168 |

- Run I yields used in fragmentation fraction measurement
- N(eDs+) = 59 ± 10
- N(eΛc+) = 79 ± 17

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

- 360 pb-1

## Outline

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

## 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+
- Λb0 contributes to lΛc+
-  Meson  baryon cross talk small

## Simple Sample Composition

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

## Full Sample Composition

- Consider all significant decays to semileptonic charm signals, including sequential semileptonic decays.

- “Physics backgrounds”
*e.g.* B0→D+(→K++)D(→lX)

## Parameterization

- Simple example w/only ground state
- N(l*+*D)
-      =N(B0)×B(B0*→*l*+*D−)×B(D*−**→*K+)
- 		       ×ε(B0→l+D−*,*D−→K+)
-  =N(b)×fd×(B0)×Γ*(*B0*→*l+D−)×B(D*−**→*K+)          	             	       ×ε(B0*→*l+D−*,*D−→K+)
- Extend this to all mesons
- Generalize notation
- N(*l*Di)=Σj=d,u,s N(b) × fj × (Bj) ×ΣkΓk×Bijk(Djk→Di)×εijk
- Di = D−, D0, D*− , and Ds
- Γk = Γ, Γ*, Γ**

## Branching Ratios

- Need model for semileptonic decays
- Γ(B→ lD(*,**)) = 1/(B) x B(B→ lD(*,**))
- Use spectator model for meson decays
-  Γ(B0→ lD) = Γ(B+→ lD0) = Γ(Bs→ lDs) ≡ Γ
-  Γ(B0→ lD*−) = Γ(B+→ lD*0) = Γ(Bs→ lDs*) ≡ Γ*
-  Γ(B0→ lD**−) = Γ(B+→ lD**0) = Γ(Bs→ lDs**) ≡ Γ**
- Assume Γ+ Γ*+ Γ**= Γsl(B→ lX)
- Use fixed sample composition for Λb→lΛcX
- Use PDG 2004 for known branching ratios
- Use theoretical predictions and symmetry principles for unmeasured BR

## Outline

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

## Acceptances and Efficiencies

- Need relative acceptances and efficiencies of individual l+charm 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

## 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/X) 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→lDX

## Reconstruction Efficiencies

- Measure some efficiencies from data
- Single track efficiency
-  D0→K+ vs. D+→ K++
- XFT trigger efficiencies for p, K, 
- dE/dx efficiency for cut on proton
-  Λc+→pK+
- Use to re-weight Monte Carlo for total efficiency

## Single Track Efficiency

- Efficiency to add an additional track depends on environment in detector
-  Monte Carlo only generates B hadron
- Reconstruct D0→K++
-  Measure efficiency relative to D0→K+ in data and Monte Carlo
-  Efficiency to add two additional tracks
- Measure
- trk = 87.8 +2.1-1.2 (stat.+sys.)%

## XFT Efficiencies

- Differences in tracking p, K,  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

## XFT Efficiencies

## Comparison of Data and MC

******2****/NDF=24.3/27.0**

******2****/NDF=11.9/8.0**

## B Meson pT Spectra

- Choice of pT spectrum used is important for determination of efficiencies
- Use inclusive pT(b→J/X) spectrum measured in Run II for meson signals
- Good agreement with data

## Λb pT Spectra

- Inclusive pT(b→J/X) spectrum does not describe the lΛc data
- Observe softer spectrum in data than the MC
- Tune the lΛc Monte Carlo spectrum to match the lΛc data

## Outline

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

## General Idea of Fit

- Express each term of sample composition in terms of B0
- Fit for relative production
- Npred(lDi)= N(B0) Σj=d,u,s  fj/fd  × (Bj)
- 				×ΣkΓk ×Bijk(Djk→Di)×εijk
- 		Npred(lΛc)= N(B0) × [fΛb/(fu+fd)](1+fu/fd)
- 				×[(ΣkBk (Λb →lΛc,k→ Λc))×εk]
- 2 fit to 5 lepton charm channels
- fu/fd, fs/(fu+fd), fΛb/(fu+fd)
- fs/fd = [fs/ (fu+fd)] ×(1+fu/fd)
- N(B0)
- Parameter for fit, not physical number of B0’s

## Implementation of Fit

- Fit looks like
- 	2 = Σi=1..5 (Npred(lDi) −Nmeas(lDi))2/σmeas,i2
-          		+ (Γ−ΓPDG)2/σΓPDG2
- 				+ (Γ*−Γ*PDG)2/σΓ*PDG2
-              		+ (Γ**−Γ**PDG)2/σΓ**PDG2
- Gaussian constraints for Γ, Γ*, Γ**
- Test with high statistics toy Monte Carlo

## Fit Results

- Statistical errors ONLY
- Fit e+SVT and μ+SVT separately
- Cancel lepton ID efficiencies
- Statistically independent samples
-  Results are consistent- very nice!
- Results are consistent if fu/fd fixed to unity

- fΛb higher than previously measured!

## Outline

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

## 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 Λb0 pT spectrum
-  Residual false lepton contamination

## Λb pT Spectrum Uncertainty 

- Vary tuned lΛc spectrum to match agree with inclusive J/ spectrum
- Produces large uncertainty: ±0.049
- Estimate conservatively
- True Λb0 spectrum isn’t known

## Systematic Uncertainties

- +0.062 -0.074

- +0.058 -0.035

- +0.141 -0.103

## pT Threshold for Measurement

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

**CDF Run II Monte Carlo**

**CDF Run II Monte Carlo**

## Final Results

- Weighted average between e+SVT and μ+SVT samples
- Statistical error is very small!
- Error on fs/(fu+fd) is dominated by PDG 2004
-  B(Ds+→+)  = (3.6 ± 0.9)%
- Sheldon Stone’s estimate of CLEO-c measurement (FPCP06)
-  B(Ds+→+) =  (3.73 ± 0.42)%

## Comparison with PDG

## Comparisons with Other Results

## Outline

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

## 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!!

## 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

## 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