Directional modulation of electron-ion pairs recombination in liquid argon

Motivated by the ongoing study of a possible directional signal in liquid argon dark matter detectors, we introduce a new model describing the recombination of electron-ion pairs in ionizing tracks in liquid argon in the presence of a drift field. The emphasis is on the three-dimensional distribution of electrons and ions and on their orientation relative to that of the electric field. We successfully apply our model to describe the angular dependence of the ionization signal of protons recently reported in measurements performed by the ArgoNeuT Collaboration with a liquid argon time projection chamber.