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:  

$$\begin{array} {lll} \kappa' = \kappa + \Delta \kappa_{dE/dx},\end{array}$$ (11)

where the second term on the right-hand side is the correction calculated from the average energy loss in the material. This implies

$$\begin{array} {lll} \left(\frac{\partial {\bf a}'}{\partial {\bf a}} \right) = 1,\end{array}$$ (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.