Track Parameter Resolutions

Analytical estimation of tracking performance in cylindrical-shaped silicon detectors using covariance propagation and multiple-scattering models.

This project provides a lightweight framework for studying how detector geometry, sensor resolution, material budget, magnetic field strength, and track properties affect:

• Track position resolution
• Momentum resolution
• Extrapolation uncertainty
• Multiple scattering contributions

The repository was originally developed to gain an intuitive understanding of track reconstruction performance and to reproduce the main effects that drive detector design decisions.

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Physical Model

The framework models a charged particle traversing a layered silicon detector inside a magnetic field.

For each detector layer, the following quantities are specified:

• Radial position
• Material thickness
• Transverse hit resolution
• Longitudinal hit resolution

From this the following features can be calculated:

Position Resolution Studies

Calculate transverse track position uncertainty

detector.transverse_track_position_uncertainty(
    momentum=1.0,
    mass=0.139,
    number_of_hits=7,
    extrapolation_radius=0.01,
    polar_angle=90
)

Includes:

• Detector resolution effects
• Multiple scattering in detector layers
• Multiple scattering in air between layers
• Extrapolation uncertainty

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Longitudinal Resolution Studies

Calculate uncertainty along the beam direction

detector.longitudinal_track_position_uncertainty(
    momentum=1.0,
    mass=0.139,
    number_of_hits=7,
    extrapolation_radius=0.01,
    polar_angle=90
)

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Momentum Resolution

Estimate relative transverse momentum resolution

detector.transverse_momentum_reso(
    momentum=1.0,
    mass=0.139,
    number_of_hits=7,
    polar_angle=90
)

The momentum resolution is extracted from the curvature parameter covariance obtained from the parabolic fit.

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Example Detector Setup

detector = DetectorSetup(
    average_layer_radii,
    layer_thickness,
    detector_resolutions_rphi,
    detector_resolutions_z,
    radiation_length_medium,
    magnetic_field_strength
)

where:

Parameter	Description
average_layer_radii	Detector layer radii [m]
layer_thickness	Material thickness in units of radiation length
detector_resolutions_rphi	Transverse hit resolution [m]
detector_resolutions_z	Longitudinal hit resolution [m]
radiation_length_medium	Radiation length of medium between layers [m]
magnetic_field_strength	Magnetic field strength [T]

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Notebook Walkthrough

The accompanying notebook demonstrates the use of the Python code. The notebook is intended to be educational and can be read sequentially together with a paper or other literature on analytical tracking-performance estimation.

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Limitations

This framework intentionally uses simplified models.

Not included:

• Full helix fitting
• Energy loss
• Non-uniform magnetic fields
• Detector inefficiencies
• Pattern recognition effects
• Non-Gaussian scattering tails

The objective is analytical understanding rather than full detector simulation.