Simulation of Deflection Uncertainties on Directional Reconstructions of Muons Using PROPOSAL

Large scale neutrino detectors and muon tomography rely on the muon direction in the detector to infer the muon's or parent neutrino's origin. However, muons accumulate deflections along their propagation path prior to entering the detector, which may need to be accounted for as an additional source of uncertainty. In this paper, the deflection of muons is studied with the simulation tool PROPOSAL, which accounts for multiple scattering and deflection on stochastic interactions. Deflections along individual interactions depend on the muon energy and the interaction type, and can reach up to the order of degrees -- even at TeV to PeV energies. The accumulated deflection angle can be parametrized in dependence of the final muon energy, independent of the initial muon energy. The median accumulated deflection of a propagated muon with a final energy of 500 GeV is $\theta_{\text{acc}} = 0.10{\deg}$ with a 99 % central interval of $[0.01{\deg}, 0.39{\deg}]$. This is on the order of magnitude of the directional resolution of present neutrino detectors. Furthermore, comparisons with the simulation tools MUSIC and Geant4 as well as two different muon deflection measurements are performed.