1. CBM meeting, Dubna 2008/10/14 L1 CA Track Finder Status Ivan Kisel (KIP, Uni-Heidelberg), Irina Rostovtseva (ITEP Moscow) Study of L1 CA track finder with new STS geometry and possibilities of parallel computing

2. CBM meeting, Dubna 2008/10/14 L1 CA Track Finder Status Adaptation to the New STS Geometry The STS geometry is changing Previously in each STS station the hits had the same Z hit == Z station. Now in the new geometry the sensors can have overlaps and are positioned at 8 different Z with ∆Z = Z hit – Z station ≤ 0.25cm. sts_Standard_s3055AAFK5.ExpE.geo → sts_Standard_s3055AAFK5.SecD.geo With the new geometry old L1TrackFinder lost ~20% efficiency. In future the value of max( ∆Z ) might change. => L1TrackFinder should be adapted to the new geometry. The tracking efficiency vs ∆Z should be studied.

3. CBM meeting, Dubna 2008/10/14 L1 CA Track Finder Status Extrapolation between hits from neighbour stations For the new STS geometry the most problematic part of the track finder is the extrapolation of tracks through the inhomogeneous magnetic field between neighbour stations L1/CPU trigger reco needs a fast and simple algorithm with well- controlled precision (both for trigger and off-line) The full extrapolation from each hit to each sensor would be too computationally expensive, therefore the task was split in two steps: – Extrapolation of the track to Z station – Extrapolation from Z station to Z hit Equation of motion in the magnetic field: For small extrapolation distances, one can assume: The solution is a parabolic function obtained using the Tailor expansion. For L1 track finder it is very important to investigate possibility to use only the linear part and neglect the quadratic term O(∆Z 2 )

4. CBM meeting, Dubna 2008/10/14 L1 CA Track Finder Status Estimate of the quadratic term ΔZΔZ ΔZΔZ Z station Z X ΔX–ΔX– ΔX+ R α ΔX+ = ΔZ·tanα + R(cosα - √1- (sinα - ΔZ/R) 2 ) ΔX – = -ΔZ·tanα + R(cosα - √1- (sinα + ΔZ/R) 2 ) The neglected quadratic term O(∆Z 2 ) ≤ ∆X + with R = p / k q B tan α =|p x / p z |, cos α =|p z / p|,... and ( sinα ≤ 1 – ΔZ/R )

5. CBM meeting, Dubna 2008/10/14 L1 CA Track Finder Status Study the validity of the linear extrapolation UrQMD MC central Au+Au 25AGeV Efficiency and fraction of killed tracks ok up to ∆Z = Z hit - Z station < ~0.2cm

6. CBM meeting, Dubna 2008/10/14 L1 CA Track Finder Status Modifications of the track finder Extrapolation through inhomogeneous magnetic field of the track candidate to the center of the station ( Z station ), ∆Z ~ 5cm Linear extrapolation of the track candidate to Z hit inside the station, ∆Z < ~0.25cm (neglecting dE/dx, mult. scattering, field variation and O( ∆Z 2 )) Use Z hit instead of Z station for tracklet construction and in the Kalman filter track fit => After the modifications the L1 CA track finder has the same high efficiency with the new STS geometry

7. CBM meeting, Dubna 2008/10/14 L1 CA Track Finder Status Creation of tracklets Pseudocode 01 void CATrackFinder(){ 02 for (step = 0; step <= 2; step++){ 03 if (step == 0) MinMom = 1.0; else MinMom = 0.2; 04 if (step <= 1) TargetConstrHit(ht); else NoTargetConstrHit(ht); 05 for (sta = NStation-2; sta >= 0; sta--){ // --- loop over stations 06 L = sta; M = sta + 1; 07 Duplets_LM = CreateDuplets(); 08 if (sta == NStation-1){ 09 Duplets_MR = Duplets_LM; // --- Overwrite doublets 10 continue; 11 } 12 Triplets_LM = CreateTriplets(Duplets_LM, Duplets_MR); 13 vTriplets.Add(Triplets_LM); 14 Duplets_MR = Duplets_LM; // --- Overwrite doublets 15... 16 } // --- end of loop over stations 17 } Duplet - track segment in 2 adjacent stations Triplet - duplets of 3 consecutive stations which share a common hit Duplets and triplets were constructed sequentially from station 8 to station 1 On each step the duplets from the previous pair of stations were overwritten

8. CBM meeting, Dubna 2008/10/14 L1 CA Track Finder Status Pseudocode modified for parallelization Creation of triplets can be separated from creation of duplets because duplets use no information about triplets Creation of duplets in each pair of stations does not depend on the previously created duplets and also allows parallelization 01 void CATrackFinder(){ 02 for (step = 0; step <= 2; step++){ 03 if (step == 0) MinMom = 1.0; else MinMom = 0.2; 04 if (step <= 1) TargetConstrHit(ht); else NoTargetConstrHit(ht); 05 for (sta = NStation-2; sta >= 0; sta--){ // --- 1st loop over stations 06 L = sta; M = sta + 1; 07 Duplets_LM = CreateDuplets(); 08 Duplets_LM_safe[sta] = Duplets_LM; // --- save the doublets 09 } // --- end of 1st loop over stations... 10 for (sta = NStation-3; sta >= 0; sta--){ // --- 2nd loop over stations 11 Duplets_LM = Duplets_LM_safe[sta ]; 12 Duplets_MR = Duplets_LM_safe[sta+1]; 13 Triplets_LM = CreateTriplets(Duplets_LM, Duplets_MR); 14 vTriplets.Add(Triplets_LM); 15... 16 } // --- end of 2nd loop over stations 17...

9. CBM meeting, Dubna 2008/10/14 L1 CA Track Finder Status Creation of tracklets modified for future parallelization Possibility to recover duplets (and even tracks in some extreme cases!) 12345678 Same tracking efficiency Same computation time Increase of memory for intermediate storage of duplets in all stations Storing all duplets might even further increase the efficiency (recovery in case of triplets lost due to dead channels)

10. CBM meeting, Dubna 2008/10/14 L1 CA Track Finder Status Summary and Plans Track finder was modified to allow for the STS geometry with overlapping sensors at different Z The full efficiency (~97%) was recovered and the updated L1TrackFinder has been included in the STSDevelopment version (thanks Radek!) Efficiency vs. ∆Z = Z hit – Z station has been studied: linear extrapolation looks valid up to ∆Z < ~0.2cm The algorithm was further modified to enable parallel construction of tracklets in future Adaptation to the realistic STS detector response (with realistic digitization and clusterization) Continue work on parallelization