Parton distributions with scale uncertainties: a Monte Carlo sampling approach

We present the MCscales approach for incorporating scale uncertainties in parton distribution functions (PDFs). The new methodology builds on the Monte Carlo sampling for propagating experimental uncertainties into the PDF space that underlies the NNPDF approach, but it extends it to the space of factorisation and renomalisation scales. A prior probability is assigned to each scale combinations set in the theoretical predictions used to obtain each PDF replica in the Monte Carlo ensemble and a posterior probability is obtained by selecting replicas that satisfy fit-quality criteria. Our approach allows one to exactly match the scale variations in the PDFs with those in the computation of the partonic cross sections, thus accounting for the full correlations between the two. We illustrate the opportunities for phenomenological exploration made possible by our methodology for a variety of LHC observables. Sets of PDFs enriched with scale information are provided, along with a set of tools to use them.

Automated summary

We introduce the MCscales approach that incorporates scale uncertainties in PDFs using Monte Carlo sampling. This new methodology extends the existing NNPDF approach to factorization and renormalization scales. Our approach assigns a prior probability to each scale combination set and obtains a posterior probability by selecting replicas that satisfy fit-quality criteria. It allows for an exact match between scale variations in PDFs and partonic cross section calculations, accounting for their full correlations. We demonstrate the potential of our methodology for exploring various LHC observables and provide enriched sets of PDFs with scale information, along with tools for their use.