Assessing uncertainties in parton showers at double logarithmic accuracy for jet quenching studies

A bstract We present a systematic study of how different choices of ordering and phase-space constraints in parton showers affect the space-time structure of vacuum parton cascades and their interface with jet quenching models. Using a simplified Monte Carlo shower implemented at double logarithmic accuracy, we analyse variations in emission patterns and resulting phase-space arising from three ordering variables: inverse formation time, invariant mass, and opening angle. These are coupled with two kinematic reconstruction schemes defined by different phase-space constraints. We show that, while global features are relatively stable, differences emerge in the temporal evolution of the cascade. To probe the impact of these differences, we introduce a simplified model for in-medium energy loss based on formation time and colour decoherence, enabling us to evaluate the sensitivity of quenching observables to the underlying space-time structure of the vacuum shower. We further quantify the role of time-ordering violations and propose strategies to preserve a consistent space-time interpretation. Lastly, we explore a range of alternative quenching models confirming the robustness of our conclusions. Our findings highlight the importance of maintaining a coherent space-time structure in parton shower algorithms when modelling jet propagation in an extended QCD medium, as this structure becomes a physically meaningful and testable component of the jet itself.