Diffusion Changes 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 comprable 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 acts to increase the effective "thickness" seen by each channel, and therefore the most-probable-value (MPV) of particle energy loss. We find, for example, that this effect shifts the MPV $dE/dx$ of a 1 GeV muon 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 Landau as a "standard candle". The impact of diffusion on these calibrations is assessed