Track Extrapolation

  In this section, we will show how to extrapolate a helical track through a material to the other detector region where the magnetic field is not necessarily present. For simplicity, we assume that the energy loss and the multiple scattering in the material take place at a single point in space: ${\bf x} = {\bf x}_{int}$.The track extrapolation is easiest when this interaction point is chosen as the pivot:

$$\begin{array} {lll} \nonumber {\bf x}_0 = {\bf x}_{int} = {\bf x}(\phi=0,{\bf a};{\bf x}_0).\end{array}$$

In what follows, it shoud be understood that the track parameters and error matrrix are pre-transformed to this pivot, according to the procedure explained in the last section, unless otherwise stated.