1. 1 Ghost Trackers If there’s something strange (or charm or bottom) in your neighbourhood… Dave Jackson Oxford University / RAL LCFI Collaboration 28 th March 2006

2. 2 ZVRESZVKIN 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

3. 3 The straight ghost track is anchored at the IP, initially given a 25 μ m width then moved in θ and φ to minimise ∑ χ 2 (sum over jet tracks). Final ‘fitted’ width of ghost track (minimum 25μm ) calculated for ‘compatibility’ with jet tracks: each has χ 2 ≤ 1.0 with fitted ghost track SLD

4. 4 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

5. 5 Care with errors and χ 2 s important since vertex finding relies on probability of vertex fit calculation PROB(∑ χ 2,2N-3) For N tracks in jet from same MC B vertex (spike at zero due to non-Gaussian tails) PROB(∑ χ 2,2N-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

6. 6 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

7. 7 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

8. 8 BACKUP SLIDES…

9. 9 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

10. 10 Highly boosted B kinematics: IP→B→D straight to ~1% (for Z 0 ) B,D vertex locations are not independent in 3D space ‘Ghost Track Algorithm’ builds in this information from the beginning

11. 11 Stage 1: Pivot straight ghost track at IP, initially along jet axis direction Give ghost track a 25 μ m width and calculate χ 2 of ghost to each track in jet Swivel ghost track in θ and φ to minimise ∑ χ 2 (sum over jet tracks) Angle between true B flight and jet axis Angle between true B flight and ghost track Radians

12. 12 Stage 2: PROB(χ 2,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+1 1 2 3 N 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 PRISECTER

13. 13 The Topologies For a B decay to a single cascade charm D B IP True MC l B True MC l D Measured l B Measured l D cm lB lB lD lD

14. 14 Compare ‘ZVTOP’ with ‘Ghost Track Algorithm’ Number of Found Vertices ‘B Decay’ Invariant Mass GeV/c 2 ZVTOP GHOST

15. 15 Options The ‘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

16. 16 July 2003 World B S mixing sensitivity B 0 : b→c : D + or D 0