Automated Parton-Shower Variations in Pythia 8

Abstract: In the era of precision physics measurements at the LHC, efficient and exhaustive estimations of theoretical uncertainties play an increasingly crucial role. In the context of Monte Carlo (MC) event generators, the estimation of such uncertainties traditionally requires independent MC runs for each variation, for a linear increase in total run time. In this work, we report on an automated evaluation of the dominant (renormalization-scale and non-singular) perturbative uncertainties in the PYTHIA 8 event generator, with only a modest computational overhead. Each generated event is accompanied by a vector of alternative weights (one for each uncertainty variation), with each set separately preserving the total cross section. Explicit scale-compensating terms can be included, reflecting known coefficients of higher-order splitting terms and reducing the effect of the variations. The formalism also allows for the enhancement of rare partonic splittings, such as $g \to b \bar{b}$ and $q\to q \gamma$, to obtain weighted samples enriched in these splittings while preserving the correct physical Sudakov factors.