The paper describes the track reconstruction in the system of VELO and TT detectors. Two separate algorithms for off-line and on-line approaches were merged. The single algorithm consists of the common code for pattern recognition and two parts specific to off-line and on-line functionalities. The note presents the performance in terms of track reconstruction efficiency and ghost rate

Callot, O

Kucharczyk, M

Witek, M

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LHCb/2007-010TRACKINGApril 23, 2007VELO-TT track reconstructionOlivier CallotLaboratoire de l’Acce´le´rateur Line´aire, Orsay, FranceMarcin Kucharczyk, Mariusz WitekInstitute of Nuclear Physics PAN, Cracow, PolandAbstractThe paper describes the track reconstruction in the system of VELO andTT detectors. Two separate algorithms for off-line and on-line approacheswere merged. The single algorithm consists of the common code for patternrecognition and two parts specific to off-line and on-line functionalities. Thenote presents the performance in terms of track reconstruction efficiency andghost rate.Contents1 Introduction 22 Pattern recognition 23 Simplified VELO-TT fit 54 The tuning for on-line reconstruction 65 The tuning for off-line reconstruction 76 Future development 811 IntroductionThe reconstruction of short tracks in detectors situated before the magnet is of aspecific nature. In the off-line environment the short tracks are searched for torecover the low momentum tracks which do not reach the T stations or are notreconstructed by the long track finding algorithms due to various reasons. The lowmomentum tracks are used in the method of global particle identification and mayserve for flavour tagging, in particular if they are identified as kaons. It is possiblethat these short tracks can be used in the future for selecting some B decay channels.The momentum range concerned is 0.5-3 GeV/c.In the trigger system, the main purpose of the VELO-TT reconstruction is tofind high pT tracks. The high pT combined with the high impact parameter is thesignature of B-decay products and can be used as a powerful tool to suppress the rateof minimum bias events coming from L0. The momentum range of tracks consideredin the trigger is above 3 GeV/c.So far two separate algorithms were employed: for the off-line [1] and on-line [2,3]. Although the two algorithms refer to different momentum ranges and workwithin different environments and timing constraints, a single algorithm for bothcases has been developed and is the subject matter of this note. A large part ofthe algorithm is the same for both cases. In particular, they both have an identicalpattern recognition phase. The only difference is the tuning of steering parametersto fulfil the requirements of different momentum ranges. The following parts concernthe selection of a unique track candidate, the determination of momentum and therequirements related to the track quality.2 Pattern recognitionThe input for pattern recognition is a collection of VELO tracks and a set of TThits. The TT hits are created from the light clusters which are read out from theraw buffer. Every hit contains the information about the central point of the cluster(the barycenter of the TT cluster), readout strip length (the TT readout scheme isdescribed in [4]) and the error on the coordinate perpendicular to strip orientation.The track finding makes use of two windows which are presented in Fig. 1. The firstone is the Search Window, Wsearch, opened around the straight line extrapolationof the VELO track at zttmid, the z coordinate in the middle of TT. This window isused to collect TT hits which might correspond to a given VELO track. The size ofWsearch depends on the minimum momentum of the track. The deflection from thestraight line extrapolation, calculated at zttmid as a function of inverse momentum, isshown in Fig. 2. Based on the hits falling into the search window the combinationsof hits coming from a VELO track under consideration are constructed. The ∆x iscalculated for each layer as a difference between the x coordinate of the hit and the xcoordinate of the straight line extrapolation of the VELO track. ∆x is then rescaledto the zttmid and is indicated by ∆xnorm. To obtain a perfect VELO track, in theabsence of multiple scattering, the correct hits should have the same value of ∆xnorm2Figure 1: The idea of the pattern recognition in TT.∆x vs 1/p 1/p [1/GeV]∆x [mm]010203040500 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Figure 2: The expected deflection from the straight line in the magnetic field ∆x, calcu-lated in the middle of TT as a function of inverse momentum.3for the four TT layers. In a real situation a spread of these distances around somecentral value is expected. The Tolerance Window, Wtol, shown in Fig. 1 is employedto set the maximum allowed difference between the values of ∆xnorm coming fromdifferent TT layers. The example distribution of the difference between the first andthird TT layers, ∆xnorm1− ∆xnorm3, is illustrated in Fig. 3 for the two momentumranges. According to the expectations, a much wider spread is observed for the lowmomenta due to a greater influence of multiple scattering. It is clear that the fixedvalue of the absolute difference ∆xnormi −∆xnormj (i, j denote the TT layers, i 6= j)cannot be used for the whole momentum range. However, the relative valueSrel = (∆xnormi −∆xnormj )/∆xnormionly weakly depends on the momentum of the track (Fig. 3). Thus the tolerancewindow can be expressed by the linear dependence valid for all the momenta:Wtol = W0tol + Srel ∗∆xnorm,where W 0tol is the constant reflecting the spatial resolution within the limit of infinitemomentum, while Srel embraces effects of multiple scattering, increasing for lowmomenta. To speed up the procedure, the hits are sorted in the ascending orderAbsoluteIDRMS            702  2.166∆xn1-∆xn3 [mm]a)p < GeVAbsoluteIDRMS            712 0.6895∆xn1-∆xn3 [mm]b)p > 3 GeV05001000150020002500300035004000-10 -8 -6 -4 -2 0 2 4 6 8 10025005000750010000125001500017500200002250025000-10 -8 -6 -4 -2 0 2 4 6 8 10RelativeIDRMS            602 0.7936E-01(∆xn1-∆xn3)/∆xnmeanc)p < 3 GeVrelativeIDRMS            612 0.1136(∆xn1-∆xn3)/∆xnmeand)p > 3 GeV010002000300040005000-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.501000200030004000500060007000-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5Figure 3: Distributions of absolute difference of normalized deflections ∆xnorm betweentwo TT layers on different stations for a) p < 3 GeV and b) p > 3 GeV. Distributions ofa relative difference are shown for c) p < 3 GeV and d) p > 3 GeV. The width of relativedistributions depends weakly on the momentum and can be used to fix the size of thetolerance window for all momenta.according to their ∆xnorm, from the smallest negative value to the largest positiveone. The search for the combinations of TT hits is performed in turn for every4hit. Other hits are added to the combination if they are found within the tolerancewindow. The best combination has to be selected from the list of all of them. Thereare two different procedures for on-line and off-line cases, where the simple leastsquare fit is an important element.3 Simplified VELO-TT fitThe main reason behind the simplified VELO-TT fit is the limitation of the executiontime. The Kalman fit based on the Transport Service could not be used in theenvironment of High Level Trigger. A dedicated least square fit was developed todetermine the track momentum. The corresponding pseudo χ2 can be used to selectthe best solution from the combinations of TT hits1 found.It is assumed that the track segments in VELO and TT can be approximatedby straight lines which converge at one point. This condition is fulfilled in the caseof VELO trajectory where the magnetic field is negligible. In the region of TT theapproximation is still reasonable for the momenta above 3 GeV, i.e. for the rangeof concern for the HLT. In the case of lower momenta a bias is expected, due toa significant deviation from linearity which occurs in the increasing magnetic fieldin the TT region. However, this low momentum region is important for the off-lineanalysis and may be duly considered in the final stage by the Kalman fit. The twolinear track segments in VELO and TT are supposed to meet at a point (xbdl, zbdl)in the XZ projection. The zbdl indicates the z coordinate corresponding to a half ofthe Bdl integral (the middle of the effective magnet). Since there is no deflection inthe Y Z projection, the y slope in TT, stty , is assumed to be the same as sveloy . Thetotal pseudo χ2 consists of two elements:χ2tot = χ2velo + χ2tt,whereχ2velo =(∆tveloxσtvelox)2= f1(xbdl)andχ2tt =n∑i=1(∆xiσxi)2= f2(xbdl, tttx ).The first component χ2velo comes from the uncertainty on the track slope mea-sured in VELO. The second component is the χ2 of the straight line in TT. Asindicated above, the χ2tot is a function of two unknown parameters, xbdl and sttx .The minimum of this two-dimensional function can be determined by solving thefollowing system of equations:∂χ2tot∂xbdl= 0,∂χ2tot∂tttx= 0.1Since the errors used in the simplified fit do not include contribution from the multiple scat-tering, the χ2 used for minimization is not statistically correct and therefore it is called pseudoχ2.5Since the solution can be expressed analytically, the execution of the algorithm isfast. The product of the inverse momentum and the charge of the track can bedetermined in the XZ projection according to:Qpxz= 3.3356 ∗ (sinθtt − sinθvelo)/∫Bdl,where θtt and θvelo indicate angles of the track in the XY projection in TT andVELO, respectively. The pseudo χ2 coming from the minimization will be denotedas χ2pseudo.The total momentum can be found using the slope of the track in the Y Z pro-jection.p = pxy ∗√1 + (stty )2.4 The tuning for on-line reconstructionAs was explained in the note [5], the quality of the reconstruction is crucial for theperformance of the generic bb¯ trigger2. The optimal working point is a compromisebetween good high pT tracks efficiency (important for signal selection efficiency) anda low rate of low pT tracks wrongly assigned to high pT ones (reduction of minimumbias events).Typically tracks with pT > 1 GeV, are responsible for the trigger decision. Sincep = pT /sinθ, the momentum range of tracks with pT ≥ 1 GeV starts from ∼ 3 GeVfor highest θ measurable in LHCb and quickly goes up with decreasing θ angle. Ascan be seen in Fig. 2, the width of the search window used to reconstruct tracks withmomenta above 3 GeV is around 10 mm. In the algorithm, the minimum momentumof the searched tracks is specified and then translated to the width of the Wsearch.The constant size, W 0tol, is set to 0.8 mm. This value was set by analysing thedistribution of the ∆xnorm for correct TT hits. It turned out that the momentumdependent term Srel ∗∆xnorm could be neglected since the reconstruction efficiencyof high momentum tracks shows no significant improvement.There might be a number of combinations of TT hits for a single VELO-TTtrack. A solution is chosen on the basis of the number of activated TT layers. Thesolution with more layers is favoured (4 layers vs 3 layers). In the case of equalnumber of layers the solution with smaller χ2pseudo is preferred3.The performance of the reconstruction is illustrated in Fig. 4. The two curves,for the signal efficiency and ghost rate as a function of momentum, correspond tothe cut on maximum χ2pseudo/NDF < 256. For tracks with p > 5 GeV the averageefficiency and ghost rate are 84.5 % and 4.8 % respectively.2The trigger performance is defined as the signal efficiency at a fixed level of retention forminimum bias events.3Usually, it involves selection of a higher momentum track.6efficiency and ghosts 1/p (1/GeV)eff/ghosts00.10.20.30.40.50.60.70.80.910 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4Figure 4: Track reconstruction efficiency (solid line) and ghost rate (dashed line) after theon-line tuning.5 The tuning for off-line reconstructionIn the case of off-line reconstruction the selection of unique combination of TT hitsassociated to a given VELO track is based on the χ2 of the Kalman fit. This enablesa correct comparison of the track quality over the whole range of track momenta.One disadvantage is the large CPU time needed to fit all VELO-TT track candidates.For VELO tracks pointing to regions of high hit density the number of candidates tobe considered can be large. Therefore a preselection of combinations based on theχ2pseudo coming from the simple fit (Sec. 3) is performed. The three track candidateshaving smallest χ2pseudo are kept for the Kalman fit. The single combination withthe lowest χ2/NDF is kept. The removal of VELO-TT track candidates sharingthe same TT hits is done in the same way as in on-line mode4. The distributions ofχ2/NDF from the the Kalman fit for correctly and wrongly matched TT hits areshown in Fig 5. Tracks with χ2/NDF > 5 are removed.The performance for the reconstruction in off-line mode is shown in Fig 6. Theefficiency and ghost rate curves correspond to pattern recognition starting from allVELO tracks and all TT hits. For tracks with p > 1 GeV the average efficiency andghost rate are 85.6 % and 15.5 % respectively.For the sequence of reconstruction algorithms in the Brunel the VELO-TT trackfinding is executed at the end of tracking. Many VELO tracks are already convertedto long tracks and their momenta are precisely measured. Therefore, the VELO-4The real χ2 is used instead of χ2pseudo.70204060801001200 1 2 3 4 5 6 7 8 9 10Kalman χ2/NDFFigure 5: The distribution of the χ2 after the fit for correct (solid line) and wrong (dashedline) Velo-TT matching. The distributions are normalized to the same area.TT reconstruction needs only to be performed for the VELO tracks which were notreconstructed by other tracking algorithms. In addition only the TT hits which werenot associated to any track should be used. The efficiency and ghost rate for suchinitial conditions are presented in Fig 7 as a function of momentum. One can seethat the ghost rate becomes very high for momenta below 1 GeV. Since multiplescattering washes out the difference between correct and incorrect track candidatesthe reconstruction quality cannot be significantly improved.6 Future developmentThe current version of VELO-TT reconstruction, described in this note, is used intwo applications: Brunel (off-line tuning) and HLT (on-line tuning). There is stillroom for modifications. In the off-line case two improvements have to be imple-mented. The track state at the end of VELO has to be used, rather than the stateclosest to the beam.It is necessary to use the Kalman fit for all TT combinations in order to select thebest solution. This will be possible when the new fast Transport Service is avail-able. In the case of the on-line version, a major technical rebuild of the algorithmis foreseen5. The current algorithm for pattern recognition, track fit and momen-tum determination will be split into three parts: the common code will be put into5It will affect the off-line version too.8efficiency and ghosts 1/p (1/GeV)eff/ghosts00.10.20.30.40.50.60.70.80.910 0.25 0.5 0.75 1 1.25 1.5 1.75 2Figure 6: Track reconstruction efficiency (solid line) and ghost rate (dashed line) as afunction of inverse momentum after the off-line tuning.00.10.20.30.40.50.60.70.80.910 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5efficiency and ghosts p (GeV)eff/ghostsFigure 7: Track reconstruction efficiency (solid line) and ghost rate (dashed line) as afunction of momentum for the tracks that are not reconstructed in the T stations.9the Gaudi tool and specific short algorithms will be created for off-line and on-lineapplications.Such a modification will not affect the performance described in the present note.However, it will allow for the introduction of a better structure of the HLT algorithmwhere the different treatment of selected tracks has to be considered within the newtrigger structure which is based on the idea of alleys.At the same time a modification of the pattern recognition to run with no mag-netic field is being implemented.10References[1] Short track reconstruction with VELO and TT, Y. Xie, Note LHCb-2003-100.[2] VELO-TT matching and momentum determination at Level-1 trigger,M. Witek, Note LHCb-2003-060.[3] Online Pattern Recognition, O. Callot, Note LHCb 2004-094.[4] Channel Numbering and Readout partitioning for the Silicon Tracker, M. Need-ham, Note LHCb-2006-033.[5] The relevance of the magnetic field in the Level-1 trigger, H. Dijkstra, J. A.Hernando, T. Schietinger, M. Witek, Note LHCb-2003-110.11

VELO-TT track reconstruction

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