Transcript Update on muon momentum measurement: Analysis of the T600

Measurement of
through-going particle
momentum by means of
Multiple Scattering with
the T600 TPC
Talk given by Antonio Jesús Melgarejo (Universidad de Granada)
On behalf of the ICARUS Collaboration
Cryogenic Liquid Detectors for Future Particle Physics
L’Aquila, 13 March 2006
Why Multiple Scattering Methods?
 The momentum of partially contained events can not
be measured by calorimetry
 However multiple scattering based techniques can be
used
 We explore two techniques to measure the momentum
using multiple scattering:
 Classical Method
 Kalman Filter
 As we will show, by taking into acount energy losses
and correlation between measurements in adition to
multiple scattering we are able to improve our
resolution in momentum measurement
A.J.Melgarejo (U.Granada)
The Classical Multiple
Scattering Method
 A particle traversing a medium is deflected through
many small angle scatterings.
 The resulting angle distribution follows the equation
2

RMS
meas

 13.6MeV
 l 
l 
3
2
 
z
1

0.038ln

C
·
l





1

  cp
X0 
 X0 


2
where p is the particle momentum and we are
considering detector noise
 By splitting a track in segments of a given length and
measuring the RMS of the angle distribution it is
possible to make an estimation of the particle
momentum
A.J.Melgarejo (U.Granada)
T600 Event
Reconstruction
Muon Hits
delta rays
Decay Electron hits
The Kalman Filter
Technique
 Kalman Filter is a technique to deal with noises
that affect signals
 It can distinguish multiple scattering effects
from those asocciated to detector errors
 It provides the best estimator for a state of a
system after some steps in its propagation.
 Energy losses and correlation effects can be
included when computing the propagation
 As far as we know Kalman Filter has never
before been used in an homogeneous non
magnetized medium
A.J.Melgarejo (U.Granada)
Practical Case: Particle Traversing a Medium
Final Prediction of Kalman Filter
Predicted Position
Measured Position
Filtered Position
Predicted Trajectory
Filtered Trajectory
Smoothed Trajectory
Smoothed Position
A.J.Melgarejo (U.Granada)
The Kalman Filter
Technique
 
 
 x 
 y 
xk   x 
 
 z 
 y 
 
 z 
State
vector
evolution
Noisestep.
in the system
Angle
between
segments in the present
wk Scattering
N (0, Qk )
xk Related
Fk 1with
xk 1momentum
 wk 1 through Multiple
formula
Transportation Matrix
Positionsenergy losses
Incorporates
Measurement vector
mk  Hk xk   k
Slopes
Measurement Matrix
Multiple Scattering
Noise in the measurement
k
N (0, Rk )
Noise in the detector
The complete set of used formulas can be found on R.Fruhwirth, Nucl. Instrum. Meth A 262 444 (1987)
MonteCarlo Simulation
 We make a full simulation using the FLUKA
package
 Electronics and detector noise are simulated
with ICARUS collaboration software
 We generate samples of 1000 muons with
initial momenta in the range 0.25-3 GeV
 Momentum is measured independently for
every muon
A.J.Melgarejo (U.Granada)
MonteCarlo Results
Classical Method needs
offline corrections to
take into account
energy losses
MonteCarlo Results
Resolution
20 %
10 %
Real Data Analysis
 MonteCarlo analysis shows that Kalman filter is
an optimal method for momentum
measurement
 To confirm this fact we will study a real data
sample
 We use a set of 1009 stopping muons whose
momentum, known by calorimetry, is below 1
GeV
 This range is not optimal for Kalman Filter but if
agreement between MonteCarlo and real data
occurs it is straifghtforward to extrapolate this
result to higher energies
A.J.Melgarejo (U.Granada)
Momentum measurement
using calorimetry
 Measured energy is related to deposited
energy by the formula:
Measured individually
for every event
Qmeas  R  Qdep  e

t t0

Measured and published
by ICARUS Collaboration
This will be our reference momentum
A.J.Melgarejo (U.Granada)
Results (I)
 Distribution of the computed momenta
Momentum
measured using
Kalman Filter
Momentum
measured using
calorimetry
Results (II)
 Profile of the measurements
Momentum
measured using
Kalman Filter
Kalman Filter
results are in
good agreement
with calorimetry
Momentum
measured using
calorimetry
Results (III)
 At last, we split our sample using the
calorimetry measured
momentum
on
100
MeV
On average Kalman Filter and
intervals Calorimetry differences are very low
 For each event on each interval we compute
the relative error between Kalman Filter and
calorimetry momenta
PKF  Pcal
Errors decrease
Pcal with increasing
momentum and values are
each
interval
thesimulations
mean
in agreement
with MC
 We plot for
and the
RMS of this magnitude distribution
Conclusions
 The MonteCarlo analysis shows that Kalman
Filter is a good tool for momentum
measurement of partially-contained particles in
liquid argon TPCs
 The real data analysis shows that momentum
can be measured with an error of the order of
15% being optimal in the range of a few GeV
 This tool is optimal to study non contained
atmospheric neutrino events
 Kalman Filter based techniques will be a
powerful tool for momentum measurement in
future liquid argon neutrino detectors
A.J.Melgarejo (U.Granada)
The End