Effect of Diffusion on the Peak Value of Energy Loss Observed in a LArTPC

Liquid Argon Time Projection Chamber (LArTPC) detectors observe ionization electrons to measure charged particle trajectories and energy. In a LArTPC, the long time ($\sim$ms) between when the ionization is produced and when it is collected means that diffusion can smear the charge by an amount comparable to the spatial resolution of the detector, given by the spacing between charge sensing channels ($\sim$mm). This smearing has an impact on the distribution of energy losses measured by each channel. In particular, the smearing increases the length of the charged particle trajectory observed by each channel, and therefore the most-probable-value (MPV) of particle energy loss recorded by that channel. We find, for example, that this effect shifts the MPV $dE/dx$ of a muon with an energy of 1 GeV by ${\sim}4$% for a 2 ms drift time and 4.7 mm wire spacing, as in the DUNE-FD LArTPC. This has implications for the energy-scale calibration and electron lifetime measurements in a LArTPC, which both use the MPV of the muon energy loss distribution as a "standard candle". The impact of diffusion on these calibrations is assessed.