General information

Introduction

For a track with an initial trajectory from a prefit of the measurements (internal seed) or an external prediction (external seed) the description of multiple scattering is added by offsets in a local system. Along the initial trajectory points are defined with can describe a measurement or a (thin) scatterer or both. Measurements are arbitrary functions of the local track parameters at a point (e.g. 2D: position, 4D: slope+position). The refit provides corrections to the local track parameters (in the local system) and the corresponding covariance matrix at any of those points. Outliers can be down-weighted by use of M-estimators.

The broken lines trajectory is defined by (2D) offsets at the first and last point and all points with a scatterer. The prediction for a measurement is obtained by interpolation of the enclosing offsets and for triplets of adjacent offsets kink angles are determined. This requires for all points the jacobians for propagation to the previous and next offset. These are calculated from the point-to-point jacobians along the initial trajectory.

Additional local or global parameters can be added and the trajectories can be written to special binary files for calibration and alignment with Millepede-II. (V. Blobel, NIM A, 566 (2006), pp. 5-13).

Besides simple trajectories describing the path of a single particle composed trajectories are supported. These are constructed from the trajectories of multiple particles and some external parameters (like those describing a decay) and transformations at the first points from the external to the local track parameters.

The conventions for the coordinate systems follow: Derivation of Jacobians for the propagation of covariance matrices of track parameters in homogeneous magnetic fields A. Strandlie, W. Wittek, NIM A, 566 (2006) 687-698.

Calling sequence

1. Create list of points on initial trajectory:
   std::vector<GblPoint> list
2. For all points on initial trajectory:
   • Create points and add appropriate attributes:
     
     • point = GblPoint(..)
     • point.addMeasurement(..)
     • Add additional local or global parameters to measurement:
       
       • point.addLocals(..)
       • point.addGlobals(..)
     • point.addScatterer(..)
   • Add point (ordered by arc length) to list:
     list.push_back(point)
3. Create (simple) trajectory from list of points:
   traj = GblTrajectory (list)
4. Optionally with external seed:
   traj = GblTrajectory (list,seed)
5. Fit trajectory, return error code, get Chi2, Ndf (and weight lost by M-estimators):
   ierr = traj.fit(..)
6. For any point on initial trajectory:
   • Get corrections and covariance matrix for track parameters:
     [..] = traj.getResults(label)
7. Optionally write trajectory to MP binary file:
   traj.milleOut(..)

Implementation

Matrices are implemented with ROOT (root.cern.ch). User input or output is in the form of TMatrices. Internally SMatrices are used for fixes sized and simple matrices based on std::vector<> for variable sized matrices.

References

• V. Blobel, C. Kleinwort, F. Meier, Fast alignment of a complex tracking detector using advanced track models, Computer Phys. Communications (2011), doi:10.1016/j.cpc.2011.03.017
• C. Kleinwort, General Broken Lines as advanced track fitting method, NIM A, 673 (2012), 107-110, doi:10.1016/j.nima.2012.01.024