Energy Weighting for the Upgrade of the CMS HCAL

In these simulation studies an energy weighting method is applied to the signals of the CMS hadronic calorimeter readout with a longitudinal segmentation for a possible upgrade. Tabulated weighting factors are used to compensate for the different response of hadronic and electromagnetic energy depositions of simulated pion showers in the hadronic calorimeter. The weighting improves the relative energy resolution: \begin{align} \left(\sigma_{E} / E\right)^2 &= \left[\left((92.2\pm 0.6)\%/\sqrt{E}\right)^2 + ((6.5\pm 0.1)\%)^2\right]\;\rm{\hspace{0mm}(before\ weighting)}, \nonumber \\ \left(\sigma_{E,\rm{weight}} / E\right)^2 &= \left[\left((85.4\pm0.5)\%/\sqrt{E}\right)^2 + ((4.4\pm0.1)\%)^2\right]\;\rm{\hspace{0mm}(after\ weighting)}, \nonumber \end{align} where $E$ in the square root has units of $\rm{GeV}$.