A new fast track-fit algorithm based on broken lines

Volker BLOBEL

The determination of the particle momentum in HEP tracking chambers
requires a fit of a parametrization to the measured points.
Various effects can result in  deviations to the ideal helix curve in the
magnetic field of a solenoid, and the fit with a pure helix parametrization
is not optimal. One effect is multiple scattering, which causes
a "random walk" of the particle and affects especially low-momentum
tracks and very accurate measurements.
The  method based on broken lines is non-recursive and allows to
reconstruct the particle trajectory taking into account details of
the multiple scattering. It provides optimal parameters and their
covariance matrices at track start and end, and optimal values at
each measured point along the trajectory including the variances.
Allowing sparse-matrix techniques the method has a execution
time proportional to the number of track hits and is, under test conditions,
a factor six faster than the Kalman filter.
Combined with robust estimation techniques like Least-median-of-squares
Combined with robust estimation techniques like Least-median-of-squares
and M-estimates the algorithm can be used effectively during track
recognition, where its speed allows a fast rejection of outliers.