Track Model

We consider a high momentum track originating from the interaction point (IP) region. When we take our local coordinate system in such a way that the z axis is along the magnetic field, the y axis in the radial direction which is approximately along the transverse momentum of the track, and the x axis makes the overall system right-handed, the helical track can be approximated by  

$$\begin{array} {lll} \left\{ \begin{array} {lllllll} x & \... ... & \zeta & + & a ( y - y_0 ) , \end{array} \right.\end{array}$$ (41)

where we have introduced the following short-hand for the helix parameters:

$$\begin{array} {lll} \nonumber \xi & \equiv & d_\rho \cr \e... ...zeta & \equiv & d_z \cr a & \equiv & \tan \lambda .\end{array}$$

Notice that the last approximation ($\vert\xi \eta \vert \ll \vert y-y_0\vert$), which is justified by our choice of the coordinate system ($r \leftrightarrow y \Rightarrow \eta \equiv \phi_0 \simeq 0$), makes the r-$\phi$ and the r-z fittings decouple from each other. We will, thus, the r-$\phi$ and the r-z fittings separately in what follows. Notice also that the problem then becomes a linear one, which simplifies the necessary calculations considerably.