A relation between track length and deposited energy in a homogeneous calorimeter by Geant4 simulation at high energy

We performed a Geant4 simulation study on showers generated by electrons and hadrons in a large homogeneous calorimeter. We found that the energy deposit can be expressed as a linear function of the track length. The line does not pass through the origin, and the energy deposit at the intercept is proportional to the incident energy. Moreover, for both electrons and hadrons, the slope of the line is independent of the incident energy. The energy resolution of the calorimeter can be expressed in terms of the distribution around the correlation line, which we found to be very good at about $ 19\% / \sqrt{E(\rm{GeV})}$ for pions.