measurement of through-going particle momentum by means of multiple scattering with the t600 tpc...

Measurement of Measurement of through-going particle through-going particle

momentum by means of momentum by means of Multiple Scattering with Multiple Scattering with

the T600 TPC the T600 TPC

Talk given by Antonio Jesús Melgarejo (Universidad de Granada)On behalf of the ICARUS Collaboration

Cryogenic Liquid Detectors for Future Particle PhysicsL’Aquila, 13 March 2006

A.J.Melgarejo (U.Granada)A.J.Melgarejo (U.Granada)

Why Multiple Scattering Methods?Why Multiple Scattering Methods?

The momentum of partially contained events can not The momentum of partially contained events can not be measured by calorimetrybe measured by calorimetry

However multiple scattering based techniques can be However multiple scattering based techniques can be usedused

We explore two techniques to measure the momentum We explore two techniques to measure the momentum using multiple scattering:using multiple scattering: Classical MethodClassical Method Kalman FilterKalman Filter

As we will show, by taking into acount energy losses As we will show, by taking into acount energy losses and correlation between measurements in adition to and correlation between measurements in adition to multiple scattering we are able to improve our multiple scattering we are able to improve our resolution in momentum measurementresolution in momentum measurement


The Classical Multiple The Classical Multiple Scattering MethodScattering Method

A particle traversing a medium is deflected through A particle traversing a medium is deflected through many small angle scatterings. many small angle scatterings.

The resulting angle distribution follows the equationThe resulting angle distribution follows the equation

where p is the particle momentum and we are where p is the particle momentum and we are considering detector noiseconsidering detector noise

By splitting a track in segments of a given length and By splitting a track in segments of a given length and measuring the RMS of the angle distribution it is measuring the RMS of the angle distribution it is possible to make an estimation of the particle possible to make an estimation of the particle momentummomentum

2

232

10 0

13.61 0.038ln ·RMS

meas

MeV l lz C l

cp X X

T600 Event T600 Event ReconstructionReconstruction

Decay Electron hits

Muon Hitsdelta rays


TheThe Kalman Filter Kalman Filter TechniqueTechnique

Kalman Filter is a technique to deal with noises Kalman Filter is a technique to deal with noises that affect signalsthat affect signals

It can distinguish multiple scattering effects It can distinguish multiple scattering effects from those asocciated to detector errorsfrom those asocciated to detector errors

It provides the best estimator for a state of a It provides the best estimator for a state of a system after some steps in its propagation. system after some steps in its propagation.

Energy losses and correlation effects can be Energy losses and correlation effects can be included when computing the propagationincluded when computing the propagation

As far as we know Kalman Filter has never As far as we know Kalman Filter has never before been used in an homogeneous non before been used in an homogeneous non magnetized mediummagnetized medium


Predicted Position

Measured Position

Filtered Position

Smoothed Position

Practical Case: Particle Traversing a Medium

Final Prediction of Kalman Filter

Predicted Trajectory

Smoothed Trajectory

Filtered Trajectory

The Kalman Filter The Kalman Filter TechniqueTechnique

1 1 1k k kkFx x w

kk kkm xH

State vector evolution

Measurement vector

(0, )k kNw QNoise in the system

(0, )k kN R Noise in the measurementk

x

yx x

zy

z

Angle between segments in the present step.Related with momentum through Multiple Scatteringformula

Positions

Slopes

Measurement Matrix

Multiple Scattering

Noise in the detector

Transportation Matrix

Incorporates energy losses

The complete set of used formulas can be found on R.Fruhwirth, Nucl. Instrum. Meth A 262 444 (1987)


MonteCarlo SimulationMonteCarlo Simulation

We make a full simulation using the FLUKA We make a full simulation using the FLUKA packagepackage

Electronics and detector noise are simulated Electronics and detector noise are simulated with ICARUS collaboration softwarewith ICARUS collaboration software

We generate samples of 1000 muons with We generate samples of 1000 muons with initial momenta in the range 0.25-3 GeVinitial momenta in the range 0.25-3 GeV

Momentum is Momentum is measured independently for measured independently for every muonevery muon

MonteCarlo ResultsMonteCarlo Results

Classical Method needsoffline corrections to take into account energy losses

MonteCarlo ResultsMonteCarlo Results

Resolution

20 %

10 %


Real Data AnalysisReal Data Analysis

MonteCarlo analysis shows that Kalman filter is MonteCarlo analysis shows that Kalman filter is an optimal method for momentum an optimal method for momentum measurementmeasurement

To confirm this fact we will study a real data To confirm this fact we will study a real data samplesample

We use a set of 1009 We use a set of 1009 stopping muonsstopping muons whose whose momentum, known by calorimetry, is below 1 momentum, known by calorimetry, is below 1 GeVGeV

This range is not optimal for Kalman Filter but if This range is not optimal for Kalman Filter but if agreement between MonteCarlo and real data agreement between MonteCarlo and real data occurs it is straifghtforward to extrapolate this occurs it is straifghtforward to extrapolate this result to higher energiesresult to higher energies


Momentum measurement Momentum measurement using calorimetryusing calorimetry

Measured energy is related to deposited Measured energy is related to deposited energy by the formula:energy by the formula:

0t t

meas depQ R Q e

Measured and publishedby ICARUS Collaboration

Measured individually for every event

This will be our reference momentum

Results (I)Results (I)

Distribution of the computed momentaDistribution of the computed momenta

Momentum measured using calorimetry

Momentum measured using Kalman Filter

Results (II)Results (II)

Kalman Filterresults are in good agreementwith calorimetry

Momentum measured using calorimetry

Momentum measured using Kalman Filter

Profile of the measurementsProfile of the measurements

Results (III)Results (III)

At last, we split our sample using the At last, we split our sample using the calorimetry measured momentum on 100 MeV calorimetry measured momentum on 100 MeV intervals intervals

For each event on each interval we compute For each event on each interval we compute the relative error between Kalman Filter and the relative error between Kalman Filter and calorimetry momentacalorimetry momenta

We plot for each interval the mean and the We plot for each interval the mean and the RMS of this magnitude distributionRMS of this magnitude distribution

KF cal

cal

P P

P

On average Kalman Filter and Calorimetry differences are very low

Errors decrease with increasing momentum and values are

in agreement with MC simulations


ConclusionsConclusions The MonteCarlo analysis shows that Kalman The MonteCarlo analysis shows that Kalman

Filter is a good tool for momentum Filter is a good tool for momentum measurement of partially-contained particles in measurement of partially-contained particles in liquid argon TPCs liquid argon TPCs

The real data analysis shows that momentum The real data analysis shows that momentum can be measured with an error of the order of can be measured with an error of the order of 15% being optimal in the range of a few GeV15% being optimal in the range of a few GeV This tool is optimal to study non contained This tool is optimal to study non contained

atmospheric neutrino atmospheric neutrino eventsevents Kalman Filter based techniques will be a Kalman Filter based techniques will be a

powerful tool for momentum measurement in powerful tool for momentum measurement in future liquid argon neutrino detectorsfuture liquid argon neutrino detectors

The EndThe End

measurement of through-going particle momentum by means of multiple scattering with the t600 tpc...

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