TOOLS FOR DATA ANALYSIS INVOLVING

Transcription

1 TOOLS FOR DATA ANALYSIS INVOLVING µ-vertex DETECTORS KalmanFitter package : Primary vertex fit Secondary vertex fit Decay chain TMVA package : Multivariate analysis 1 J. Bouchet Kent State University cτ = 124μm

2 WHAT IS KALMANFITTER PACKAGE? Package to allow the reconstruction of vertices and decayed particles based on Kalman Fitter machinery. We use the I. Kisel et al. implementation [1,2,3], used in CBM and ALICE experiments [4]. The main object, describing all particles, i.e. mother and daughter particles, is a state vector, defined as : r =(x,y,z,px,py,pz,e,s=l/p) Produc2on vertex L = pathlength Decay vertex Parameters do not depend on a specific track or geometry model. Uses track parameters and their associate covariance matrix to obtain the parameters of the decayed particle using a Kalman Fitter procedure. [1]S. Gorbunov and I. Kisel, Secondary vertex fit based on the Kalman filter. CBM-SOFT-note , 14 September [2]S. Gorbunov and I. Kisel, Reconstruction of decayed particles based on the Kalman filter. CBM-SOFT-note , 7 May [3]S. Gorbunov, I. Kisel and I. Vassiliev, Analysis of D 0 meson detection in Au+Au collisions at 25 AGeV. CBM-PHYS-note , 23 June [4]S. Gorbunov: Reconstruction of vertices and decayed particle with the ALiKFParticle package 2

3 RECONSTRUCTION OF DECAYED PARTICLE : CONCEPT Initial conditions : r 0,C 0 Decay point : r =(x,y,z,px,py,pz,e) C : covariance matrix of r- vector r 0,C 0 Several iterations to get robust and optimal estimation Transport of a k-th daughter particle Filtering a daughter particle using KalmanFitter techniques n-daughters Fitted parameters : r, C..... r, C Decay point : r =(x,y,z,px,py,pz,e,s) 3

4 KFPARTICLE IN STAR Adapted to STAR software by Y. Fisyak. Interface with the class StDcaGeometry that contains the full covariance matrix of track : It is needed to propagate the tracks errors to the primary vertex Example for a 3 bodies decay. KFPar2cle par2cle[5];// vertex + track1 + track2 + track3 + mother const KFPar2cle pvertex = par2cle[0]; int NDaughters = 3; const KFPar2cle *vdaughters[3] = {&par2cle[1],&par2cle[2],&par2cle[3]}; KFPar2cle DP; DP.Construct(vDaughters,NDaughters,&pVertex,- 1,0); DP.SetProduc2onVertex(pVertex) par2cle[1].setproduc2onvertex(dp) par2cle[2].setproduc2onvertex(dp) par2cle[3].setproduc2onvertex(dp) Definition of the decay system : primary vertex + 3 daughters + secondary vertex at the decay vertex Definition and reconstruction of the mother particle Mother particle is transported from the decay point to the production point Daughters are fully refitted to the decay point KFPar2cle also provides easily, via Get() methods, the proper2es of the reconstructed par2cle. DTree.KFZ[cand] = DP.GetX(); DTree.KFMass[cand] = DP.GetMass(); DTree.KFDecayLength[cand] = DP.GetDecayLength(); DTree.KFErrDecayLength[cand] = DP.GetErrDecayLength();; Get the X position of secondary vertex Get the mass, decay length. 4

5 STDCAGEOMETRY (NEW) Pt GLOB Pt DcaGeo vs. Pt GLOB Track info used to be saved at first hit/last hit Tracks are moved inside the beam pipe vacuum, its center (x,y)= (0,0). This full track/error information is saved as DcaGeometry. It accounts for the multiple Coulomb scattering (MCS) as the tracks pass through the detector layers. Also in vacuum helix model hypothesis is exact. 5

6 EXAMPLE : D 0 RECONSTRUCTION S L >0 S L >5 6

7 TOOLKIT FOR MULTIVARIATE ANALYSIS [5] TMVA is a package provided by ROOT which includes several classification methods and scripts/codes for training, testing. Goal : in HEP, analysis often requires to discriminate signal from background between many variables. example : within these 2 variables, what cuts are the best to optimize the signal/background? Many methods are included : Rectangular cuts Likelihood Neural network Decision tree Vector machine [5] : A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhhag, E.von Toerne, and H. Voss, TMVA - Toolkit for Multivariate Data Analysis, arxiv:physics/

8 ANALYSIS FLOW SIGNAL SAMPLE Data to analyze TMVA BACKGROUND SAMPLE Reader : xml files Analysis (selection of a type of events, regression) based on the classifier output 1. Training Phase : a) Signal and background input : (X 1,X 2. X N variables) b) Mapping (X 1,X 2 X N ) MVA output is written to weight files for each classifier. 2. Application Phase : a) Classification based on a cut of MVA output. 8

9 CORRELATION BETWEEN VARIABLES The package also provides the correlation matrices between variables. Removing these correlations also improves the results for some classifiers. 9

10 QUANTIFICATION OF A METHOD The quality of a method uses the probability density function y(x) of the signal and background, where X= {x 1,x 2 x N } variables } It can be evaluated by looking at the Receiver Operation Characteristics (ROC) curve : shows the signal efficiency (x-axis) vs. the background rejection (y-axis) the larger area for a classifier will give better performances, ( ) Changing y(x)>cut moves the working point (efficiency vs. purity) along the ROC curve. PDF B (y) PDF B (y) 10

11 CHOICE OF THE WORKING POINT Measurement of signal/cross section maximum of S/ sqrt(s+b) Discovery of new signal maximum of S/sqrtB Precision measurement high purity Trigger selection high efficiency 11

12 EXAMPLE OF TMVA ANALYSIS Identification of charmed particle : D 0 Kpi Simulation ; using STAR silicon vertex run 7. Next will be HFT case. Classifier distribution (Kpi) invariant mass 12

13 SUMMARY KFParticle : adapted to take into account measurements of pixel detector : precise pointing resolution for direct charm identification using secondary vertex reconstruction. TMVA : powerful technique to identify signal within large combinatorial background. Both techniques are heavily used in recent experiments (ALICE, ATLAS, CBM) [ref CHEP2012] 13

14 TMVA CLASSIFIERS PERFORMANCES 14 [6]:A. Hoecker, Workshop on advanced methods in Statistical data analysis,2009

15 KALMAN FITTER In KFparticle, the state vector representing a track is defined as : r =(x,y,z,px,py,pz,e,s=l/p) Goal : find the optimum estimation r of an unknown r according to the measurements m k, where k=1..n of the r vector. The kalman fitter is an iterative procedure to reconstruct the track from its outerpoint to the origin, picking up measurements and noise (multiple coulomb scaterring and loss energy dedx measurement). Main equation : r k t = A k r t k-1 + v k,where A k = linear operator, V k : noise process btw (k-1)-th and k-th measurement Measurement m k linearly depends on the state vector with : m k = H k r t k + η k, with η k the measurement error. Main steps are : Initialization : choose an approximation (large) of vector r 0 Filtering : estimation of the present state vector k, based upon on the k-1 past measurements Prediction : estimation of the state vector at a future time KFParticle uses an extended Kalman fitter, in the sense that the track propagator A k are not linear. (eg: track propagator in magnetic field) 15

16 TMVA : CHECKS Check that the simulation samples are agree with real data Track point resolution [microns] vs. momentum for tracks with 4 silicon hits Check that the output of the classification gives the expected result Line : classifier distribution after the training phase. Symbols : classifier distribution after the application phase, where whether the same background (signal) as in the training phase is used as input. 16