Transcript Track parameters

The LiC Detector Toy
M. Valentan, M. Regler, R. Frühwirth
Austrian Academy of Sciences
Institute of High Energy Physics, Vienna
The MATLAB program allows a fast evaluation of the optimal resolution for charged particles with uncorrupted data.
Detector inefficiency and multiple scattering are included. Detector surfaces can be cylinders or planes.
Input
Simulation
Detector Description
Event loop
• Coaxial cylinders
- Stereo angle
-  in T
By default the event loop first generates a vertex (uniformly distributed in a
certain range). However, the user can enter the vertex positions (x0,y0,z0),
provided by an arbitrary vertex generator.
•PC z dependent
Frame Detector 1 Detector 2
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
• Plane wheels
Track loop
- Coordinates defined
by two angles
Inner Tracker (IT)
Number of layers
Radii [mm]
Upper limit in z [mm]
Lower limit in z [mm]
Efficiency Rphi
Efficiency 2nd layer (eg. z)
Stereo angle alpha [Rad]
Thickness [rad. lengths]
error distribution
0 normal-sigma(RPhi) [1e-6m]
sigma(z)
[1e-6m]
1 uniform-d(RPhi) [1e-6m]
d(z)
[1e-6m]
: 5
:
:
:
:
:
:
:
:
:
:
:
:
90, 90,
160,
300, 340
110, -90,
360,
640, 2730
90,-110, -360, -640,-2730
0,
0, 0.95, 0.95,
0
-1, -1, 0.95, 0.95,
-1
10*pi/180
0.07,0.07,0.0175,0.0175, 0.14
1
50
50
Momentum variables
• Arbitrary size and
position
Track parameters ,,
(according to the chosen multiplicity).
The state vector is propagated to the
beam tube, where it is transformed to
variables similar to the DELPHIconvention ,z,, including
spatial variables.
• 2D measurement
- single and passive
layers steered by
inefficiency
Multiple scattering takes place on
every massive barrier, using
independent normal distributed
random quantities (according to
the Highland formula).
A local cartesian coordinate
system is used with one axis
tangent to the track.
• Strips or pads
Track simulation
Simulation Parameters
Number of events
rsp. tracks
Momentum and direction
The track model is a helix.
Tracking includes multiple
scattering.
• Start parameters uniformly
distributed in the defined
ranges
• Simulation features:
Simulation features
Test features
Output features
Strip detectors (single layer and
double sided; inner layer with any
stereo angle)
Pixel detectors (by crossing 2
strip detectors with strictly
correlated inefficiency)
Coordinates
- Multiple scattering
- Measurement errors
Vertex
Arbitrary inefficiency without
spatial or angular dependence
Measurement of R and z'
(according to stereo angle
chosen)
Strips, Pads or normal
distributed
uncorrupted data only
• Test features:
- Pulls and MC-pulls
- ²
Simulation of digital and normal
distributed errors.
The z dependence in the TPC can
be used as an example for a
template.
• Output features:
- Histograms of pulls
- Histograms of residuals
- 6D cartesian, Harvester
Reconstruction
Reconstruction
Track fitting uses the Kalman filter, a recursive least-squares estimator. It
proceeds from the outermost layer towards the beam tube.
Track loop
Initialization of the track parameters with large errors
Detector loop
Propagate track parameters,
using a reference track and a
linearized model
Output
Pull quantities
Test statistics (sample log file, 10000 tracks)
Monte-Carlo pulls
Phi
mean: -0.0014137
std: 0.99745
z
-0.020775
1.0021
Pulls at innermost detector
RPhi
z
mean: 0.0085271
0.0029371
std: 0.99706
0.998
Chi^2
ndf:
mean:
theta
0.006437
0.99926
u
beta
-0.0035657
0.99836
kappa
-0.0024358
0.997
At the beam tube
v
R, z – barrel region
u,v - forward region
-0.0095907
0.0042998
1.0031
1.0088
Average number of
degrees of freedom
21.8725
21.9226
Extrapolation
Linear error propagation
Add multiple scattering
MC residuals
(fitted - true)
Barrel region
Forward region
Scale factor relative to the barrel region: 50
Compute weighted mean of
extrapolated track parameters
and measurement
Update
Compute local χ2 statistic and
accumulate total χ2
10000 track with 0.7454<2.3562
10000 track with 0.49087<0.098175
Up:
Monte-Carlo residuals at the
beam tube, computed from
generated and fitted state vectors
Up:
Monte-Carlo residuals at the
beam tube, computed from
generated and fitted state vectors
Left:
Relative deviation pT/pT
Left:
Relative deviation pT/pT
Right:
Relative deviation pT/pT2
Right:
Relative deviation pT/pT2
Store final track parameters, error matrix and total χ2
Scale factor relative to the barrel region: 100