1 track reconstruction and physics analysis in lhcb outline introduction to the lhcb experiment...
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Track reconstruction and physics analysis in LHCb
Outline• Introduction to the LHCb experiment• Track reconstruction
→ finding and fitting• Physics analysis
→ event selection and sensitivity study
• More details in my thesis: Track simulation and reconstruction in LHCb
Seminar: Particle and AstrophysicsU Zürich, Physik Institut
07 December 2005, Jeroen van Tilburg, NIKHEF
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Reminder: CP violation
tbtstd
cbcscd
ubusud
VVV
VVV
VVVCKM matrix
Complex phases in matrix elements → CP violation
CKM matrix connects the quark mass eigenstates with the weak interaction eigenstates
~ e-iβ~ eiχ
~ e-iγ
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The LHC tunnel
The LHCb detector
CERN, Geneva
The Large Hadron Collider
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The LHCb detector
~1.41.3 m2
~65 m2
VELO
21 stationsR and φ sensors
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Different track types, different algorithms
Velo tracks: used to find primary vertex.Long tracks: used for most physics studies: B decay products.T tracks: improve RICH2 performance.
Downstream tracks: enhance KS finding.Upstream tracks: improve RICH1 performance, moderate p estimate
Track types
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Track event display
VELOTT
T2 T3T1
Outer tracker station
Average # of tracks in b-events: 34 VELO,
33 long, 19 T tracks, 6 upstream, 14 downstream +
Total 106 reconstructed tracks
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Example: Matching algorithm
Matches T tracks with VELO tracks to find long tracks:→ estimate momentum of T track→ extrapolate T track through magnet to the VELO→ find best match (based on χ2 cut).→ add TT hits
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Matching algorithm: estimate p
zmagnetVELO T stations T seedzc
p-kick
p-kick method
Estimate momentum of the T track with p-kick method:→ Magnetic field is ~ an instant kick at focal plane z=zmagnet.→ Assume track originates from interaction point.→ Re-evaluate center of magnet (zc).
δp/p=0.7%
Bdl ~ 4.2 Tm
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Matching χ2
Efficiency = 91.2%Wrong combinations = 4.8%
p > 5 GeV
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Adding TT hits for matched tracks
→ Extrapolate matched tracks to TT stations.→ Group the hits depending on distance to track.→ Find best group of TT hits.
Group the hits:Distance d to track < 10 mmΔd in same station < 1 mmΔd in other station < 2 mmGroup has at least 3 hitsHit can belong > 1 group
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Adding TT hits
Select the group with the lowest q2.
Tune wspread
q2 = d2 + w2spread sd
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Average distance of groupDistance deviation of group
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Long track performance
Average number of hits: 12.7 VELO,
3.0 TT, 2.4 IT, 17.5 OT +
Total 35.6
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Long track performance
efficiency ghost rate
ε = 94.3% (p>5 GeV) g = 7.7% (p>5 GeV)
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Tracking robustness
Tracking is robust against number of interactions
relative multiplicity
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Track fit
The Kalman Fit properties:• Adds measurements recursively.• Mathematically equivalent to least χ2 method.• Multiple scattering and energy loss can be naturally included.
The tracks are fitted using the Kalman Filter.
prediction stepfilter step
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Outlier removal
Outliers (hits with high χ2 contribution) can be removed.→ requires a refit→ remove only 1 hit per iteration
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Outlier removal (long tracks)
Improves χ2 distribution
Number of iterations
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Fit quality (long tracks)
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Momentum resolution
LHCb provides an excellent momentum estimate at the vertex.
Note: Fitted with single Gaussian in each bin.
Reconstructed tracks
Ideal tracks
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Impact parameter @ vertex
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Physics analysis
Two benchmark decay channels of LHCb:1. Bs → Ds π measures Δms (Bs oscillation frequency)2. Bs → Ds K measures γ-2χ (CP violation)
For my thesis I studied the• event selection for these decays, and the• final sensitivity on Δms and γ-2χ
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Branching fractions
Decay channel Branching fraction Annual productionBs → Ds
± π± 1.2 * 10-4 26 M eventsBs → Ds
± K± 1.0 * 10-5 2.1 M events
Event topology
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Bs → Ds* K and Bs → Ds K*
Event topology
Included two similar channels:
K*± → K0 π± (67%) → half decays to Ks0
K± π0 (33%)Ds
*± → Ds± γ (94%)
Bs → Ds* K and Bs → Ds K*
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Selection strategy
1. Preselection to reduce background → using standard LHCb applications (DaVinci and LoKi)
2. Remove specific backgrounds → using a single cut
3. Tune remaining cuts against generic background→ using an optimisation tool
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1. Preselection
Loose
cuts
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2. Specific background
Bs→Dsπ background in Bs→DsK selection
→ cut on RICH likelihood
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2. Specific background
For instance, cut at ΔlnLKπ=3 gives:
Fit both mass distributions simultaneously to find the number of signal events (S) and its error (σS).
±50 MeV
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2. Specific background
Vary ΔlnLKπ cut to find the optimum with respect to the statistical significance of the signal:
S
S
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3. Generic background
Optimisation tool:• Optimise remaining cuts simultaneously• Divide each selection variable into equidistant bins.• Scan the total selection space.• Find the combination of cuts for which
is maximal.S
S S
S B
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Final selection cuts
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Efficiencies and yield
Low yield
Need to cut harder due to high background
Lower detection efficiency
Efficiencies quoted in %.
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Decay time resolution and pull
Pull distributionResolution
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Acceptance function
After selection and trigger
Selection and trigger cuts reduce efficiency at zero decay time
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Sensitivity study
Matter Antimatter
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Sensitivity study
Use Toy Monte Carlo and Fitting Program:• Generate events according to expected annual yield and with realistic time errors from full simulation.• Account for acceptance function.• Perform an unbinned likelihood fit to “observed” decay time distribution.• Fit both Bs→Dsπ and Bs→DsK events simultaneously.
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“Observed” decay times
Bs→DsK3 years
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Default parameters
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Computing power
0
500
1000
1500
2000
2500
Submitted ~10k jobs (=experiments) on the DataGrid:
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Oscillation frequency
Sensitivity on Δms
Δms deviation for 100 “experiments”: Amplitude method:
After 1 year
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Sensitivity on weak phase
Sensitivity for 100 “experiments” after 3 years.
Weak phase: γ-2χ
Error bars represent RMS fluctuation.
1 year: σ = 15.2º
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Conclusions
• Different track reconstruction algorithms developed for the different track types (e.g. the matching algorithm).• The LHCb experiment provides an efficient track reconstruction of 94% with a ghost rate of 8% (p>5 GeV).• LHCb has an excellent spatial (42 um) and momentum resolutions (0.35%) at the interaction point.• Three-step event selection for Bs→Dsπ and Bs→DsK provides a sufficient background reduction.• After 1 year of running LHCb can measure Δms up to 88 ps-1 and γ-2χ with an error of 15.2º.