Measurement of the Z boson cross-section in - Harvard University ...

Chapter 4: Data Collection and Event Reconstruction 110
Two bremsstrahlung recovery mechanisms exist in the inner detector reconstruc-
tion framework, namely, the dynamic noise adjustment (DNA) method and the
Gaussian-sum filter (GSF) method. The basic concept of both methods is to take into
account the change in track curvature due to bremsstrahlung, and thereby follow the
track accurately. Both methods use inner detector information only and significantly
improve electron reconstruction for energies below ≈ 25 GeV. So as not to degrade
the reconstruction of non-electrons, these algorithms are run only on tracks that are
likely to correspond to electrons, based on TRT and EM calorimeter information.
The DNA algorithm runs during the Kalman filtering/smoothing process de-
scribed earlier. At each silicon layer, the algorithm performs a simple one-parameter
fit to estimate an increase in track curvature due to bremsstrahlung in that layer.
If no bremsstrahlung is found, the track fitting reverts to the default Kalman filter.
Otherwise, the algorithm returns a single parameter, namely, the fraction of energy
retained by the electron. This parameter is passed to the Kalman filter as a noise
term [105], which is adjusted dynamically according to the estimated z 9 and the
thickness of the layer, hence the name dynamic noise adjustment.
The GSF method is a non-linear generalization of the Kalman filter [89]. Energy-
loss due to bremsstrahlung follows a Bethe-Heitler distribution [53], which is very
non-Gaussian, so that approximating it with a Gaussian would be quite inaccurate.
A weighted sum of Gaussians is found to give a much better estimate. The Gaussian-
sum filter uses this estimate at each material surface traversed by the electron track
and determines the probability of bremsstrahlung. This technique has a slightly better
9 z is a parameter in the Bethe-Heitler equation, which describes electron energy loss due to
bremsstrahlung [53].