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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.