Parton distributions with scale uncertainties: a Monte Carlo sampling approach

Abstract

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.

Determination of the theory uncertainties from missing higher orders on NNLO parton distributions with percent accuracy

“…However, it is also possible to include MHOUs on the hard cross-section by constructing a theory covariance matrix for the hard cross-section itself. An advantage of doing so is that it is then also possible to keep into account the correlation between the theory uncertainty in the process used for PDF determination, and that on the hard cross-section, which might become relevant if the experimental uncertainties are small and the predicted process was also used for PDF determination [22,48]. This can be done by determining the cross-correlation of MHO and PDF uncertainties between the predicted process and those used for PDF determination [49].…”

“…In this respect, it is interesting to observe that an altogether different option for the inclusion of MHOUs on predictions that accounts for MHOUs on PDFs, and their full correlation to MHOUs on the hard cross-sections, is to include the scale variation in the Monte Carlo sampling [22]. A comparative study of this methodology to that adopted in the present paper, as well as to different prescriptions for scale variation (such as, for instance different prescriptions for the connstruction of the theory covariance matrix of Sect.…”

“…Such a construction is now greatly facilitated by the availability of the EKO [14] evolution code, and its inclusion in a new pipeline for producing theory predictions for PDF determination [15], recently used for the construction of the NNPDF4.0QED PDF set [16] and currently adopted by NNPDF as a standard. Other approaches to the determination of MHOUs have been proposed [17][18][19][20][21][22]; also, MHOUs on NNLO PDFs have been recently estimated based on an approximate N 3 LO PDF determination [23].…”