1. Some mediation on fast track reconstruction of BESIII Wang Dayong Mar 10,2004

2. – Purpose, status in the system  For background reduction in L3 trigger(see figures below)  For event classification  Real time data quality check and detector monitoring  To enable physicists’ fast analysis in a few hours after data taking A clear and definite top-level design and decision together with the online system is needed badly Z0 distrib. of triggered events (Left:Babar Right: Belle)

3. Requirements for fast track reconstruction compulsory requirements (whatever the top level design)  System must be completely automated and operable within the Online System  Fast reconstruction system must incur no deadtime  Complete reconstruction for 100% of all events  System must be fault tolerant Optional requirements: ( according to different top level design)  Detailed quality monitoring data for feedback to detector operators, thus  Low latency (nominally within 2 hours of data acquisition)  Event tagging based upon analysis of fully reconstructed events  Dynamic calculation of traditionally “offline” constants to be used in subsequent reconstruction jobs  Dynamic calculation of alignment corrections  Quality monitoring results must integrate into run summary  Alarms must be recorded and handled properly

4. Limiting factors, present conditions  it must be performed on online farms  information from hardware triggers could be utilized  the software framework should be identical with at least similar to the final offline reconstruction  clear and flexible event data model accommodating different implementation and later updating  use mature,fast and stable algorithms  if possible,make use of the ready-to-wear core codes due to lack of tracking experts (Babar,Belle,BesII, STAR…)

5. Different track fitting methods(model)  explicit track model (helix tracking)  variational method  spline approximation  multidimensional function parameterization  Predictor-corrector methods

6. Different track finding methods A.Local methods  Track following  Track roads  Kalman filter  Track element B. Global methods  Global Kalman filter  Hough transform ( histogram)  Hopfield network  Template matching  Minimum spanning tree

7. Performance of Babar and Belle fast track reconstruction  Babar AlgorithmsAlgorithms L1 trigger rates ~1000Hz L3 trigger rates CPU time per track:  Belle AlgorithmsAlgorithms L1 trigger rates 200-300Hz CPU time per track: L4 track finder:5.0 ms/event/CPU of UltraSPAC 167Mhz compared to offline: 2.7s/event/CPU( total,half from tracking)

8. BesIII MDC hardware triggers 1.Track Segment Finding ： Method of look-up table 2.Track Finding: the same method as TSF Use SL-5 as pivot to find : Long track: TSF also found in SL-10 Short track: TSF only found in SL-5 3.Inner layer z trigger(? Still in study) only for backgrounds suppression without complete z hits information as Belle Pivot layer

9. Some possibilities of BesIII fast track recon.  Track fitting scheme: surely the simple helix model! a. Rewrite the helix fitting of BesII fortran codes with C++ or make it reusable in BOSS as fortran codes(but how to deal with COMMONs?) b. learn from the related Babar or Belle packages  Track finding scheme: full event data and L1 hits as input a. r-phi track finding with TSF hits and s-z track finding with full event data from stereo wires,then track fitting with full event data to get better resolution (fast,but maybe online only) b. using full event data for track finding then fitting with L1 output as a guidance to set regions of interest for track candidates ( could have multiple uses both online and offline, but speed requirements online?)

10. Possible track finding algorithm  algorithms of histogram class in conjugation with conformal transformation are both simple and fast, which fulfill requirements of BESIII  Possible choices: I. R-Phi track finding a)Nose-following with track extension and fitting in conformal plane b)Phi histogramming in conformal plane and circle fit in the plane II. S-z track finding and fitting III. Helix fitting

11. About Event Data Model  be general enough to accommodate different implementations  Data should be independent of the algorithms that produce them  Really OO-styled hierarchy of abstract classes for codes update  A well-defined format of hits  “Hits” conversion from the raw data should be provided by framework  Modularization design for more effective debugging

12. Babar Dch L1 trigger scheme 1.Track segment finder: time information has been considered : Utilize the 267ns sampling over max ~600ns drift time 0.8mm spatial resolution for a segment ~1.5cm σ Z for stereo layers. 2.Binary link tracker: Share the algorithm of CLEO-II start from the innermost superlayer, and moves radially outward to link them into complete tracks 3.PT discriminator Using TSF fine-phi data to find high Pt tracks within Pt envelope.

13. Babar L3 fast track reconstruction algorithm L3Dch starts with the track segments from the TSF system and improves the resolution by making use of the actual DCH information.  t 0 determination t 0 values for each segment are binned and the mean produced from the values in the most populated bin is used as the estimated event t 0. resolution ~1.8-3.8ns  pattern recognition L3Dch searches a look-up-table for matches to segments found by the TSFs,allowing for up to two missing TSF segments per track  track fitting algorithm with both the track segments found and the individual hits, adding segments close to the initially fitted track, and dropping hits with large residuals. The final fit does not demand that the track originate from the IP.

14. Belle CDC L1 trigger scheme 1. r– trigger : from axial superlayers  Anode wires grouped into track segment finder (TSF)  hit pattern in each cell is examined by a memory look-up (MLU) to find track segment  TSF-cell outputs to form track finder (TF) wedges 2. z- trigger : axial and stereo superlayers

15. Belle L3 fast track reconstruction algorithm Input: summarized hit signals from hardware trigger 1. R- Track finding : based on the memory lookup method a. search for fired TSF in the outermost super-layer b. search for inner hit TSF signals in the limited region c. logical-AND of the obtained pattern and stored patterns 2. Track fitting a. conformal transformation b. fit the line in the conformal space c. get PT from the distance from the origin to the line 3. R-z Track Reconstruction a. get z-hit patterns for the r- segment from r-z trigger b. Fill histogram as a function of the polar angle to get Pz

16. Belle fast track reconstruction in software trigger L4 trigger track finding and fitting :

17. Algorithms of L4 fast track reconstruction 1.Track segment finding 2. R- phi track building 3.r-phi track fitting 3 track parameters out of 5 determined (dr, phi0, κ ) 4.Event time correction 5. 3D track building 6. s-z track fitting linear fit to determine the other 2 track parameters(dz,tanλ)