Updates on the P0D reconstruction LE PHUOC TRUNG SUNY@STONY BROOK Track fitting using Kalman filter Extrapolation tracks from the TPC T2K US-ND280 meeting, June 24, 2008

Track fitting overview Warning: not P0D actual scintillator plane layout! Particle trajectory Scintillator plane Recon. position + direction Before fitting: only a set of hits, no track parameters Calculate the best estimates of position and direction of the particle trajectory at each scintillator plane. After fitting: track parameters: position and direction

The Kalman filter System matrix Process noise State to be estimated A linear discrete-time system: System matrix Process noise State to be estimated Measurements Measurement noise Measurement matrix State notation: State estimate BEFORE using measurement k The key element in the Kalman filter is the Kalman filter gain. State estimate AFTER using measurement k Iterative formula: Prediction step: Kalman filter gain Update step: Contain new information

Kalman filter for track fitting State: Dynamic system: zero-mean Gaussian Mention deltaz, Random, small direction change Measurement:

Forward-backward smoothing Measurement: charge-weighted position Forward filtering Backward filtering Forward/backward direction is not important, just pick a direction. Kalman filter update step uses measurements up to and including measurement k, we want to use as much information as possible in the estimation => smooth Smoothing Calculated from forward, backward cov. matrices

Fitting results Evaluate performance: Use muon MC with small step length, 1mm  Save more trajectory points At each plane, calculate the x,y deviations of the recon. position from the true position The true position is the true GEANT4 track point that is z closest to the recon. point. mm mm

TPC track extrapolation Motivation: improve 0 purity P0D TPC Muon track obscured by showers P0D TPC 0 sample after all 0 selection cuts Muon track obscured by showers A CC event passing all 0 selection cuts

Extrapolation procedure and result Extrapolate using Kalman filter: 4cm gate TPC k k-1 scintillator planes Need to mention that fact that extrapolation is fully 3D Hits within the gate are used as new position measurement. Measurement update the filter. If the gate is empty, stop extrapolating. Note: 3D extrapolation, alternate x,y scintillator planes A TPC track successfully extrapolated into the P0D

Summary and to-do list Summary: To do: Track fitting using Kalman filter Extrapolation TPC tracks To do: Full-spill reconstruction  Through-and-through muon tracking  Muon decay tagging  Improve 0 reconstruction

Forward-backward smoothing Forward filtering Backward filtering Smoothing Forward/backward direction is not important, just pick a direction

Fitting results Angle (degrees) Delta z(mm)

Charge-weighted position Original hits Charge weighted position MC hits and weighted positions