Updates on the P0D reconstruction

LE PHUOC TRUNG

SUNY@STONY BROOK

T2K US-ND280 meeting, June 24, 2008

• Track fitting using Kalman filter

• Extrapolation tracks from the TPC

2

Track fitting overview

Warning: not P0D actual scintillator plane layout!

Scintillator plane Recon. position + direction

Particle trajectory

• 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

3

The Kalman filter

kkkk

kkkk

vxHy

wxFx

111

• A linear discrete-time system: System matrix

Measurement matrix

Process noise

Measurement noise

State to be estimated

Measurements

k

k

x

x

ˆ

ˆ• State notation:

State estimate BEFORE using measurement k

State estimate AFTER using measurement k

• Iterative formula:

)ˆ(ˆˆ

ˆˆ 11

kkkkkk

kkk

xHyKxx

xFxPrediction step:

Update step:

Kalman filter gain

Contain new information

4

Kalman filter for track fitting

),0(0010

0001RNxy kk

),0(

1000

0100

010

001

1 QNxz

z

x kk

05.0000

005.000

0000

0000

Q

0.20

00.2R

)/,/,,( dzdydzdxyxx

State:

Dynamic system:

Measurement:

zero-mean Gaussian

Random, small direction change

5

Forward-backward smoothing

Forward filtering

Backward filtering

fkx̂

bkx̂

kx̂

bkffkfk xKxKx ˆ)1(ˆˆ

Smoothing

Measurement:

charge-weighted position

Calculated from forward, backward cov. matrices

6

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.

mmmm

7

TPC track extrapolation

Motivation: improve 0 purity

0 sample after all 0 selection cuts

A CC event passing all 0

selection cuts

Muon track obscured by showers

Muon track obscured by showers

P0D TPC

P0D TPC

8

Extrapolation procedure and result

TPC

1ˆkx

kx̂

k-1k

4cm

ga

te

Extrapolate using Kalman filter:

• Hits within the gate are used as new position measurement. Measurement update the filter.

• If the gate is empty, stop extrapolating.

scintillator planes

Note: 3D extrapolation, alternate x,y scintillator planes A TPC track successfully

extrapolated into the P0D

9

Summary and to-do list

• Summary:Track fitting using Kalman filterExtrapolation TPC tracks

• To do:Full-spill reconstruction

Through-and-through muon tracking

Muon decay tagging

Improve 0 reconstruction

10

Forward-backward smoothing

Forward filtering

Backward filtering

fkx̂

bkx̂

kx̂

bkffkfk xKxKx ˆ)1(ˆˆ

Smoothing

11

Fitting results

Angle (degrees) Delta z(mm)

12

Charge-weighted position

Original hits Charge weighted position

MC hits and weighted positions