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Energy Loss Correction

When the pivot is chosen at the energy loss point, the only track parameter that is subject to the energy loss correction is the curvature:  
 \begin{displaymath}
\begin{array}
{lll}
 \kappa' = \kappa + \Delta \kappa_{dE/dx},\end{array}\end{displaymath} (11)
where the second term on the right-hand side is the correction calculated from the average energy loss in the material[*]. This implies
\begin{displaymath}
\begin{array}
{lll}
 \left(\frac{\partial {\bf a}'}{\partial {\bf a}} \right) = 1,\end{array}\end{displaymath} (12)
therefore, the error matrix remains the same.

Notice that, unless the pivot is chosen at the energy loss point, all the helix parameters but $\tan\lambda$ are affected by the energy loss, which demonstrates the advantage of having the freedom to arbitrarily choose the pivotal position in our helix parametrization.



Keisuke Fujii
12/4/1998