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Ghost Trackers

If there’s something strange (or charm or bottom) in your

neighbourhood…

Dave Jackson

Oxford University / RAL

LCFI Collaboration

28th March 2006

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ZVRES ZVKIN

In the conventional ZVTOP algorithm secondary vertices

are found first. The linearity of the B->D decay chain is then

used for ‘L/D’ track attachment

In the Ghost Track algorithm the ‘straight’ IP->B->D

topology is exploited first, to estimate the B/D flight direction before vertex

finding

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The straight ghost track is anchored at the IP, initially given a 25μm width then moved in θ and φ to minimise ∑ χ2 (sum over jet tracks).

Final ‘fitted’ width of ghost track (minimum 25μm) calculated for ‘compatibility’ with jet tracks: each has χ2 ≤ 1.0 with fitted ghost track

SLD

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The SLD Ghost Track used straight Gaussian tubes for fast analytic

track fits – this required

reparametrising the track near a vertex

location.

This should not be so much of an issue for the LCFI C++ code in

which the approximation is not

made

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Care with errors and χ2s important since vertex finding relies on probability of vertex fit calculation

PROB(∑χ2,2N-3)

For N tracks in jet from same MC B vertex (spike at zero due to non-Gaussian

tails)

PROB(∑χ2,2N-4)

Where N now includes the Ghost Track in the fit – so

less ‘free’ than the jet tracks alone.

Probability is now a measure of a good

secondary vertex fit AND compatibility with the B direction (ghost track).

SLD

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The algorithm proceeds to build

vertices according to the highest Probability;

while Prob>1%.

So this distribution needs to be fairly flat for genuine vertices; and to be flat for a

range of track multiplicity (shown

here), decay length, etc.

The pre-requisite for this is a fitter that has the right properties for

jet tracks alone.

Probability of ghost + B tracks fit

SLD

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At SLD the B’s came in back-to-back pairs. The

EVENT would be tagged with ZVRES

before running ZVKIN for analysis of each jet

For LCFI generally would like to consider

each jet independently; design flavour/charge tagger

for each jet with ZVTOP3 in C++

SLD

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BACKUP SLIDES…

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L/D for non-Seed tracks passing T < 1mm

Monte Carlo Track

Origin

D Decay

IP

B Decay

VXD2 b-jets

Cut at L/D > 0.3 to attach tracks from B decay chain to Seed

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Highly boosted B kinematics: IP→B→D straight to ~1% (for Z0)

B,D vertex locations are not independent in 3D space

‘Ghost Track Algorithm’ builds in this information from the beginning

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Stage 1:

Pivot straight ghost track at IP, initially along jet axis direction

Give ghost track a 25μm width and calculate χ2 of ghost to each track in jet

Swivel ghost track in θ and φ to minimise ∑ χ2

(sum over jet tracks)Angle between true B flight and jet axis

Angle between true B flight and ghost track

Radians

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Stage 2:PROB(χ2,ndof) for jet track(s) to be consistent with each other and with the ghost track or IP ellipsoid is constructed

For jet with N tracks, initially N+1 candidate vertices:

IP

N+11 2

3N

Ghost

Calculate fit probability for all pairs of objects (if IP is not included, then ghost track is added)

If maximim PROB > PCUT (typically 1%) then: combine the two objects and iterate

Else: vertex reconstruction is complete:

Allows reconstruction of ‘1-prong’ vertices

PRI SEC TER

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The Topologies

For a B decay to a single cascade charm

D

B

IP • • • •

True MC lB True MC lD

Mea

sure

d lB

Mea

sure

d lD

cm cm

lB

lD

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Compare ‘ZVTOP’ with ‘Ghost Track Algorithm’

Number of Found Vertices

‘B Decay’ Invariant Mass GeV/c2

ZVTOP

ZVTOP

GHOST

GHOST

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OptionsThe ‘Tidy’ cuts:For SLD ~20% of jets contained ≥ 1 high impact parameter track from Ks, Λ, detector interaction etc.

Tidy cuts are applied first to prevent the Ghost Track direction being distorted (~half background tracks removed at SLD)

For each algorithm ~4 tunable parameters that effect efficiency vrs purity of vertex reconstruction

also:ZVTOP – can guide vertex finding with V(r) weighting

Ghost Track – can force the topology to find fixed number of vertices – Momentum factor

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July 2003

World BS mixing sensitivity

B0 : b→c : D+ or D0