A number of approaches are being used in ATLAS reconstruction software, aiming to improve electron momentum measurement by taking into account the effects due to bremsstrahlung at various stages. One of them, designed and implemented in ATLAS, is covered in this talk. The method applies Dynamic Noise Adjustment (DNA) during the track fitting process based on the Kalman filter, and is both fast and efficien

Bouhova-Thacker, Evelina

Kartvelishvili, V

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PoS(ACAT)046Electron bremsstrahlung recovery in ATLAStracking using Dynamic Noise AdjustmentEvelina Bouhova-Thacker, Vakhtang Kartvelishvili∗Lancaster University, UK (on behalf of ATLAS collaboration)E-mail: vakhtang.kartvelishvili@cern.chA number of approaches are being used in ATLAS reconstruction software, aiming to improveelectron momentum measurement by taking into account the effects due to bremsstrahlung atvarious stages. One of them, designed and implemented in ATLAS, is covered in this talk. Themethod applies Dynamic Noise Adjustment (DNA) during the track fitting process based on theKalman filter, and is both fast and efficient.XI International Workshop on Advanced Computing and Analysis Techniques in Physics ResearchApril 23-27 2007Amsterdam, the Netherlands∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(ACAT)046Bremsstrahlung recovery with DNA Vakhtang Kartvelishvili1. IntroductionVarious physics channels to be used for physics studies by the ATLAS collaboration at theLHC — Higgs and supersymmetry searches, B-hadron and quarkonium physics and many oth-ers — require efficient detection and precise measurement of electrons and positrons produced inproton-proton collisions. High precision silicon detectors, transition radiation detectors and elec-tromagnetic calorimeters are used for this purpose in the ATLAS detector (see fig. 1 and ref. [1]for details).Figure 1: Schematic view of the ATLAS Inner Detector.However, the amount of material being traversed by the electrons propagating through theATLAS inner detector (ID), shown in fig. 2, is not negligible. In particular, particles emergingFigure 2: Material budget of ATLAS ID. The amount of material traversed by the electrons varies withpseudorapidity η from about 0.5 to about 1.5 radiation lengths.2PoS(ACAT)046Bremsstrahlung recovery with DNA Vakhtang Kartvelishvilifrom the interaction point in the pseudorapidity range |η | < 0.8 (“barrel region”) will go throughthe beam pipe, 3 layers of Pixel detectors, 4 layers of Semi-Conductor Tracker detectors (SCT),and 73 layers of Transition Radiation Detector (TRT) before reaching the calorimetry. Even in thebarrel region, every layer of the high precision silicon detectors (Pixel and SCT) contributes 2 to 6percent of X0. This results in a high probability of significant bremsstrahlung radiation by electronsand positrons, influencing the quality of their track reconstruction and measurement.2. BremsstrahlungThe “brem-ray” image of the ATLAS Inner detector (fig. 3), which shows R−Z coordinatesFigure 3: The R−Z coordinates of simulated bremsstrahlung points, showing that the denser parts of theinner detector account for more frequent brems, with more energy radiated.of simulated bremsstrahlung points, highlights the fact that denser parts of the detector account formore frequent brems, with more energy radiated. Early brems — in pixel and lower silicon layers— make electron momentum measurement ever more difficult.00.511.522.533.540 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Bethe-Heitlerf(z)=(−ln z)c−1/ Γ(c)c=0.25c=0.10c=0.02c = thickness(X0) / ln2zFigure 4: Bethe-Heitler distribution of the fraction z of energy retained by the radiating electron.3PoS(ACAT)046Bremsstrahlung recovery with DNA Vakhtang KartvelishviliAccording to the description of the bremsstrahlung process [2], the electron retains its directionof propagation and a fraction z of its energy, with the probability density given by the Bethe-Heitlerdistribution (fig.4). This probability density f (z) depends on the amount of traversed material andis highly asymmetric, with a singularity at z→ 1 and a long tail extending to very small z.Fig. 5 shows a radiating track in the magnetic field. If an electron suffers an act of bremsstrahlungat point C, its track will have a smaller radius of curvature after that point, hitting layer S5 at pointF instead of point G (while the photon follows the tangent C–E–H). A tracking algorithm whichS1 S2 S3 S4 S5AB C ED GFHFigure 5: A track changing its curvature at point C due to bremsstrahlung. This track has lost 35% of itsmomentum at that point.does not take the possibility of such changes into account will, in such cases, return a track with anunderestimated momentum value and unacceptable fit quality.3. Kalman FilteringThe default track reconstruction method in ATLAS [3] uses a Kalman filter (KF) [4, 5]. Thisis an iterative procedure used to determine the vector of track parameters, y, and its covariancematrix, C, taking into account the measurement m (and its respective covariance matrix V ) at eachdetector layer k. In a slightly simplified notation, the procedure includes three steps:1. Extrapolate y and C from layer k−1 to layer k:yk−1 → y−k , Ck−1 +Qk−1 →C−kHere Qk is the covariance matrix of the system noise at layer k, which can take into accountthings like multiple scattering and bremsstrahlung.2. Calculate Kalman gain K at layer k:Kk =C−kC−k +Vk3. Do measurement update:yk = y−k +Kk(mk− y−k ), Ck = (1−Kk)C−k4PoS(ACAT)046Bremsstrahlung recovery with DNA Vakhtang KartvelishviliIt can be shown (see e.g. [4] and references therein) that this procedure only works prop-erly if both measurement uncertainty V and the process noise Q are well described by gaussiandistributions. While this is usually the case for measurement errors and multiple scattering, it’s cer-tainly not true for bremsstrahlung, which causes problems during electron track reconstruction. Asmentioned above, when applied to a radiating electron track similar to the one shown in fig. 5, thedefault KF fit is likely to result in a bad fit quality with an underestimated reconstructed momentum.4. Gaussian Sum FilterIn the standard implementation, the Kalman filter can only view bremsstrahlung as anothersource of gaussian-distributed noise, which is clearly a very crude approximation to the Bethe-Heitler distribution (fig. 6). So, early attempts to replace the Bethe-Heitler distribution with aFigure 6: Comparison between the Bethe-Heitler distribution, a single gaussian distribution of equivalentmean and r.m.s., and a sum of several gaussians used by the Gaussian Sum Filter.single gaussian of equivalent mean and width did not work too well.The Gaussian Sum Filter (GSF) [4, 6] is a non-linear generalisation of the Kalman filter. GSFapproximates Bethe-Heitler distribution by a mixture of several gaussians, thus allowing to takeinto account the asymmetry and the low-energy tail of the distribution. After that, several Kalmanfilters run in parallel. In order to make things manageable and avoid exponential growth of compo-nents, component reduction has to be performed at each step. Even so, GSF may take 10 or even100 times longer than the default KF.GSF can be quite successful in bremsstrahlung recovery — e.g., the effective track momentumresolution for 10 GeV electrons in ATLAS improves from about 10% to 8%. However, the heftycomputing overhead is a major limiting factor in its use.5. Dynamic Noise AdjustmentAnother, quick and efficient method of dealing with electron tracks has been developed and5PoS(ACAT)046Bremsstrahlung recovery with DNA Vakhtang Kartvelishviliimplemented in ATLAS. It is based on the Dynamic Noise Adjustment (DNA) [7] during Kalmanfiltering.At each silicon layer, a simple single-parameter fit is performed to flag hits which may beassociated with bremsstrahlung. This fit tries to estimate the increase in curvature due to possiblebremsstrahlung at the current detector layer. If no bremsstrahlung was flagged, the track fitterreverts to the default Kalman filtering procedure. Otherwise, the result of the single parameter fit— the estimated fraction of energy retained by the electron, z — is used to calculate the additionaleffective “system noise” term, which is then fed to the Kalman filter.The effective “system noise” variance calculation is illustrated by fig. 7, which shows how theBethe-Heitler distribution is mapped onto the gaussian distribution of unit width. The deviation ∆zof the estimated z from the median z0 is mapped onto the gaussian to find the corresponding devia-tion ∆x. The effective noise σ is then calculated as σDNA(z) = ∆z/∆x. This procedure is equivalent00.511.522.533.540 0.2 0.4 0.6 0.8 1zBethe-Heitler,  f(z)median z0z00.10.20.30.40.50.6-2 0 2xGauss,  g(x)median∆x00.10.20.30.40.50.60.70.80.910 0.2 0.4 0.6 0.8 1zCumul. B-H,  F(z)∆z00.10.20.30.40.50.60.70.80.91-2 0 2xCumul.Gauss,  G(x)Figure 7: Mapping of the probability distributions used to calculate the variance of the effective noise term.to representing the random variable z, distributed according to the Bethe-Heitler probability den-sity, in the formz = z0 + xσDNA(z)where x is a random variable with gaussian probability distribution.So, in this approach bremsstrahlung is legitimately treated as a source of gaussian noise, butonly in those cases when bremsstrahlung-like behaviour of the track has been detected. The propergaussian probability distribution of this “system noise” is now guaranteed by construction.6PoS(ACAT)046Bremsstrahlung recovery with DNA Vakhtang KartvelishviliOf course, σDNA also depends on the thickness of material associated with the correspondinglayer, as illustrated by Fig.8.00.050.10.150.20.250.30.350.40.450.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1σ(z)c=0.25c=0.10c=0.02c = thickness(X0) / ln2zFigure 8: Effective σDNA(z) for various values of material thickness in the detector layer.The variance σ 2DNA is added to the appropriate term of the Kalman covariance matrix used dur-ing the fit, similarly to the treatment of any other source of system noise. However, this particularnoise term is adjusted dynamically according to the estimated z and the thickness of the layer, thusjustifying the name of the method.6. DNA fit in actionThe comparison between the results of the default Kalman Fit (labelled "DEFAULT", top row)and KF with DNA (labelled "DNA fit", bottom row), for a simulated sample of 20 GeV singleelectrons in the barrel region |η | < 0.8, is shown in Fig. 9. The left column shows the ratio ofmeasured to generated momentum, where one can see a marked reduction of the low momentumtail and a significant improvement in the average momentum measurement. The distribution ofestimated errors on measered momentum, returned by the fit (middle column), shows an increaseof the errors in cases where radiation has been flagged, which is quite natural and significantly in-creases the percentage of reliably measured electron tracks. This is illustrated by the improvementin the pull distribution (right column) with the gaussian core now showing a mean of −0.1 and awidth of 0.98 (as opposed to −0.6 and 1.09, respectively, for the default fit).When applied to heavier particles, the DNA fit did result in some deterioration of the fit qual-ity, and introduced some small biases, which we hope to reduce in the future. Investigation ofthe differences in the behaviour of the fitted momentum for electron and pion/muon tracks, withand without the DNA corrections, shows some interesting patterns, which open the possibility ofseparating “false positives” from true radiating electrons and may result in a useful tool for earlyidentification of electrons.7PoS(ACAT)046Bremsstrahlung recovery with DNA Vakhtang Kartvelishvilirec/(q/p)gen(q/p)0.6 0.8 1 1.2 1.40100200300400500600700DEFAULTp/p∆0 0.05 0.1 0.15 0.2020040060080010001200140016001800DEFAULTp∆)/gen-prec(p-6 -4 -2 0 2 4 6020406080100120140DEFAULTrec/(q/p)gen(q/p)0.6 0.8 1 1.2 1.40100200300400500600700DNA fitp/p∆0 0.05 0.1 0.15 0.20100200300400500600700800DNA fitp∆)/gen-prec(p-6 -4 -2 0 2 4 6020406080100120140160180200220240DNA fitFigure 9: Comparison of measured momentum, estimated error and pull distributions with default fit (toprow) and DNA fit (bottom row) for single electron simulations at 20 GeV in the barrel region.ATLASpreliminaryTable 1 shows the comparison of the numbers of simulated electron tracks in various selec-tions, for the default and DNA fits. Note that improved track measurement in the precision siliconlayers results in better matching between the silicon and TRT track segments. This, in turn, reducesthe fraction of electron tracks without TRT extensions from 20% to 8 %. This also means bet-ter extrapolation to the electromagnetic calorimeter (ECAL) and hence improved track-to-ECALmatching.Table 1: Fractions of electron tracks falling into various selections, for the default KF and the DNA fits.Selection Default KF with DNATotal reconstructed tracks 99.0% 99.4%Momentum within ±50% of true 93.4% 94.5%Momentum within ±20% of true 84.2% 86.4%Within gaussian core of q/p distr. 55.6% 65.5%Within gaussian core of pull distr. 51.3% 71.2%Tracks with TRT extensions 80% 92%8PoS(ACAT)046Bremsstrahlung recovery with DNA Vakhtang KartvelishviliDNA fit only works with precision hits from silicon layers, and hence cannot help in recoveringelectron tracks radiating in TRT. For very high energy electrons its effectiveness is also reduced,as the curvature radii become too large. However, the results of the DNA fit can be used as agood starting point for yet another method of bremsstrahlung recovery, being currently developedin ATLAS. The latter uses the information from the matched ECAL cluster to improve the track fit,and thus can address these problem areas.Remarkably, the computing overhead of the DNA fit is quite small, below 10% on top of thedefault fit. Better segment matching means fewer iterations of the Kalman fitter, thus sometimesmaking the DNA fit even faster than the default one. This opens the possibility of using the DNAfit during online processing in the high-level trigger, thus improving the electron trigger efficiency.First results on full simulation and reconstruction of J/ψ → e+e− in B decay events (fig. 10)show a clear improvement if DNA brem recovery is performed: the 15 MeV shift of the J/ψ massM(ee), GeV2.2 2.4 2.6 2.8 3 3.2 3.4N020406080100120140160 Brem.Rec.No Brem.Rec.Figure 10: Reconstructed invariant mass of e+e− in B→ J/ψ(→ e+e−)+X decay events, with (solid line)and without (dashed line) bremsstrahlung recovery using the DNA fit.ATLAS preliminaryvirtually disappears, invariant mass resolution is better by about 20%, and the J/ψ reconstructionefficiency is increased by 5%. It’s worth noting that more reliable error estimates returned by theDNA fit play an important role in improving the fit of the secondary vertex, necessary for thisanalysis.7. ConclusionBremsstrahlung recovery is extremely important in order to achieve the full range of physicsgoals in ATLAS. Higgs decays H → ZZ → e+e−e+e− and SUSY searches in multi-leptonic finalstates are good examples of processes to benefit from it. Hence the number of different approachesto bremsstrahlung recovery that have been developed, tried and implemented in ATLAS.9PoS(ACAT)046Bremsstrahlung recovery with DNA Vakhtang KartvelishviliThis presentation described the track fitting procedure which uses Dynamic Noise Adjustmentduring the Kalman filtering process, used in ATLAS tracking. DNA fit works well: significantimprovements in electron track reconstruction efficiency and quality have been achieved. Thanksto its speed, DNA fit can also be used online in high-level trigger to improve electron triggerefficiency.DNA fit is still in development, with further tests and potential improvements in progress. Forexample, in some cases “early” electron identification, based on silicon hits, may become possible.8. AcknowledgementsThe author is grateful to many ATLAS colleagues who contributed to this presentation oneway or another. Special thanks are due to Tom Atkinson, Anne-Catherine Le Bihan, Maria JoseCosta, Markus Elsing, Igor Gavrilenko, Jason Lee, Wolfgang Liebig, Darren Price and AndreasSalzburger.References[1] ATLAS Detector and Physics Performance TDR, CERN/LHCC 99-14, Geneva, May 1999.[2] H. Bethe, W. Heitler, Proc. Roy. Soc. Lond. A146 (1934) 83.[3] ATLAS tracking event data model. F. Akesson et al., ATL-SOFT-PUB-2006-004, CERN, Geneva,July 2006.[4] Branko Ristic, Sanjeev Arulampalam, and Neil Gordon, “Beyond the Kalman Filter: Particle Filtersfor Tracking Applications”, Artech House, 2004.[5] R. Frühwirth, Nucl. Instr. Meth. A262 (1987) 444.[6] R. Frühwirth, Comp. Phys. Comm. 100 (1997) 1.[7] V. Kartvelishvili, “Electron bremsstrahlung recovery in ATLAS”, talk given at IPRD06, 1–5 October2006, Siena, Italy.10

Electron bremstrahlung recovery in ATLAS tracking using Dynamic Noise Adjustment

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