1. STAR STAR VMC tracker V. Perevoztchikov Brookhaven National Laboratory,USA

2. STAR Victor Perevoztchikov, BNL STAR Tracking Review Why new tracker? More than 6 years in STAR was used ITTF(or Sti) tracker. It works rather good but there are some important limitations. Geometry is too limited and cannot be enough accurate. In result, energy loss and multiple scattering are not accounted with the needed precision; Geometry ordering, essential for Sti, does not fit well even for TPC and practically impossible for the new detectors; Only TPC like detectors are allowed. Sensitive planes must be oriented along Z axis. Other orientations are not allowed. Introducing of new detectors demands rather complicated job with a lot of additional coding; Magnetic field must be constant and along Z. 2

3. STAR Victor Perevoztchikov, BNL STAR Tracking Review The new tracker, with the provisional name Stv, has the main features: ROOT TGeo as the geometry description ; TGeo Stv extension keeps automatically created special tracking information; Geant VMC as a tracking engine; Automatisation of relationship between hits and detector elements. I.e. Geant id and blueprint numbering; Arbitrary magnetic field orientation; Multi keys hit map containers; Seed Finder list. Kalman fit in Dca Coordinate System; New TPC hit error parameterization; Track extension to other, not tracking detectors; All these features are not existing in ITTF/Sti : New tracker. Main features. 3

4. STAR Victor Perevoztchikov, BNL STAR Tracking Review ROOT TGeo is chosen as the geometry description. TGeo allows detailed description of the detector. Thus energy loss and multiple scattering would be accurate; The same geometry could be used for simulation and reconstruction; TGeo Stv extension Each TGeo volume has a proxy object which contains additional information. Most of information is automatically created during initialization stage; Description of sensitive detector element: orientation, type (plane, cylindrical, …), hit error functors, activity status etc… Hit container with hits associated with this detector element; Etc… : ROOT TGeo and extensions 4

5. STAR Victor Perevoztchikov, BNL STAR Tracking Review Geant VMC was selected as a tracking engine. The standard Geant machinery is used to do tracking thru the complicated geometry, accounting the magnetic field, energy loss and multiple scattering; When track is entering into a sensitive volume, then the according hit error functor, hit container and activity flag are accessible. Relationship of hits with detector elements also provided by Geant WhereIAm utility: Thus user does not need to define lookup tables connecting blueprint and Geant geometry numbers; Hence no recalculation of lookup tables after each modification blueprint or geometry. : Geant tracking engine 5

6. STAR Victor Perevoztchikov, BNL STAR Tracking Review Loading of hits is made maximally independent of the hit nature and origin. To add into Stv new detector there is no need to modify even one line of code. No more StiSsd, StiSvt, StiTpc, StiRnD and StiXXX classes. StiHitLoader does the following:  Iterate thru input hit container;  Adds hit into Stv;  Stv converts it into internal StvHit;  Ask Geant which sensitive volume contains or close to this hit;  Save hit into volume proxy object.  Update global lookup table with the hit id and Geant volume. Next time, when the new hit will come with the same id it will be immediately assigned to the according volume. It is faster, than to ask Geant again; : Hit detector element realtionship 6

7. STAR Victor Perevoztchikov, BNL STAR Tracking Review What should be done to add new detector?  Make geometry description of the detector;  Make StHit container in StEvent. If, by any reason, it is inconvenient, the special adaptor should be made;  Make hit errors definition. It could be done via StHit or as a functor inherited from StvHitErrCalculator;  If new detector can provide hit space points, job is done ;  If not, then new seed finder must be created with detector oriented code inherited from StvSeedFinder;  Job is done : Add New detector 7

8. STAR Victor Perevoztchikov, BNL STAR Tracking Review Geant allows tracking in arbitrary magnetic field. Stv uses Geant tracking engine, so tracking in Stv in arbitrary field as well. But trackingonly is not enough. To do fitting the error propagation is also needed. Right now error propagation is implemented for Z magnetic field only. Implementation of it in arbitrary field is not very complicated. : Arbitrary magnetic field orientation 8

9. STAR Victor Perevoztchikov, BNL STAR Tracking Review Typical problem in any reconstruction is searching of the hits in small region around the given point. There are many ways to do it. No one is the perfect. In Stv was developed multi key map container. It is a binary tree, where on each level different key is used to split objects. By this way set of objects is sorted by multiple keys. On the input we have volume definition, xmin,xmax, ymin,ymax, … Due to sorting, only small amount of objects need to be tested to find all the objects inside of the given volume. This approach is used in seed finder and in fitting, to find the nearest hit.. : Multi key hit map 9

10. STAR Victor Perevoztchikov, BNL STAR Tracking Review StvDefaultSeedFinder uses similar to Sti algorithm. The difference only in hit container mentioned above. But way of using of seed finders is different.  Stv allows list of seed finders called one after another;  Each seed finder could be called several times;  At the end default seed finder is called repetitively up to no more tracks is founded. Right now we have StvDefaultSeedFinder, StvTpcCASeedFinder and StvFgtSeedFinder(in progress) : Stv Seed Finders 10

11. STAR Victor Perevoztchikov, BNL STAR Tracking Review Non standard seed finders are needed in two cases: 1. Increase performance for concrete detector; 2. Non standard detector, for which default seed finder does not work; The typical example of point 2. is Fgt. Fgt hits are elongated. Some hits define only Z and Rxy, others Z and Phi. In addition, there are amplitudes. StvFgtSeedFinder is supposed to solve this problem using close cooperation between Stv and Fgt information. There is no implementation yet, but we have some ideas how to do it. In future, we will try to create more general seed finder for all detectors similar to Fgt. : Add new seed finder 11

12. STAR Victor Perevoztchikov, BNL STAR Tracking Review Modified Kalman fit Stv used modified Kalman fit. More precise, not a Kalman fit was modified but the system of coordinates is different. Standard Kalman fit: Let consider simplified, 2d case. Hitting plane along Y axis, track crossed Y axis with angle α wrt X axis. So :  global track parameter α projected into local Y and proportional to tan(α).  then δY ~ δ α *(1+ tan(α) * (δα) /2)/  when α << 1, then cos(α ) =1, tan(α) = α, second term is very small and projection from global to local system is linear.  Projections of error matrix is also linear. In local frame fit is linear. Transformation to global of fitted parameters and errors is linear too. So life is good. But when α >1, cos(α ) ~0, life is bad. Linearization is wrong, linear fit is wrong, Backward transformation into global is also wrong. All times, when I saw unstable fit in Sti, it was α >1 12

13. STAR Victor Perevoztchikov, BNL STAR Tracking Review Fit continue Could we do something with bad fit when α > 1? Yes, we can! Why we fit in local frame? There are only two reasons:  We know that track is crossing our hit plane;  We know the errors in this frame; Let invent another local frame, where linearization is always working. The evident candidate is Dca frame. Dca frame is a track coordinate system where origin is in Dca point to hit. In this frame plane perpendicular to the track and crossing the hit point is a Dca plane. Look the following picture. 13

14. STAR Victor Perevoztchikov, BNL STAR Tracking Review Dca Frame α α δdδd D δDδD d δα 14 hit plane hit Dca plane Fitted track Y

15. STAR Victor Perevoztchikov, BNL STAR Tracking Review Picture caption  Vertical bold line: Hit Plane;  Green star: Hit on hit plane;  Red star: Dca point of track wrt hit (green star). Arrow is a predicted track with the parameters in Dca point.  Blue star is a new position of track with the modified parameters in this point;  α is a crossing angle of the predicted track;  δα is an angle between predicted track and fitted one;  α+β is a crossing angle of the fitted track;  D is the distance between hit and crossing point of the predicted track;  D+δD is the distance between hit and crossing point of the fitted track; 15

16. STAR Victor Perevoztchikov, BNL STAR Tracking Review Picture caption continue  d is the distance between hit and Dca point of the predicted track;  d+δd is the distance between hit and fitted track point in Dca plane; 16

17. STAR Victor Perevoztchikov, BNL STAR Tracking Review Fit in Dca frame What is the difference between classic Kalman fit and Kalman fit in Dca frame?Classic fit: 1. Propagate 5 track parameters and error matrix onto hit plane; 2. Transform 5 parameters and matrix into local frame; 3. Fitting 4. Transform 5 fitted parameters and matrix into global frame Dca frame fit: 1. Propagate track 5 parameters and error matrix onto Dca plane; 2. Transform 2 hit parameters and matrix into Dca frame; 3. Fitting Classic fit needs 4 stages and two transformation of matrix. Fit in Dca need 3 stages and only one transformation matrix and 2 hit parameters 17

18. STAR Victor Perevoztchikov, BNL STAR Tracking Review Track extensions Stv should provide track extensions to other detectors, like TOF or EMC. Stv can do tracking in arbitrary magnetic field. Hence to make this extensions we need only to define simple interface to point out detectors to which these extensions are needed, It is not yet implemented, but could be done fast. However we must check the accuracy of magnetic field we know, outside TPC. 18

19. STAR Victor Perevoztchikov, BNL STAR Tracking Review Shortly what is the benefit from new Stv features: ROOT TGeo as the geometry description: accurate account of energy loss and multiple scattering; TGeo Stv extension: automatisation of adding new detectors, arbitrary orientation of sensitive surfaces; Geant tracking: passing thru multiple detectors with arbitrary magnetic field; providing hits detector elements relationship; track extension to other, not tracking detectors; Multi keys hit map: speed up and simplification of hit search; Seed Finder list: adding non standard seed finders; Dca Kalman fit: increase accuracy and number of hits per track New TPC hit error parameterization; Summary. 19

20. STAR Victor Perevoztchikov, BNL STAR Tracking Review Conclusion  Version of Stv is available and ready for evaluation;  There is ten features implemented, which are not existing in Sti;  In the same time two features of Sti was not implemented: l Refit iterations. In Sti it was related mostly for non linearity of the fit. I expect it is not needed for Stv. Should be checked; l Tree hit search. It was not profitable in Sti.  Performance must be improved. In current implementation only quality was taken into account;  An additional tuning is needed, which follows from Tpt/Sti/Stv comparing 20