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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[*]  
 x & \...
 ... & \zeta & + & a ( y - y_0 ) , 
 \end{array} \right.\end{array}\end{displaymath} (41)
where we have introduced the following short-hand for the helix parameters:
 \xi & \equiv & d_\rho \cr
 ...zeta & \equiv & d_z \cr
 a & \equiv & \tan \lambda .\end{array}\end{displaymath}   
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.

Keisuke Fujii