Specialized minimal PDFs for optimized LHC calculations

TL;DR

This paper introduces specialized minimal PDF sets (SM-PDFs) that efficiently represent uncertainties for specific processes in LHC physics, enabling accurate, process-tailored calculations with minimal error sets.

Contribution

The authors develop a method to construct SM-PDFs that preserve correlations and can be expanded to recover the full prior PDF set, tailored for different LHC processes.

Findings

SM-PDFs tailored for Higgs, top, and electroweak processes

Around 4 to 11 eigenvectors suffice for accurate process description

Method maintains information and correlations across process sets

Abstract

We present a methodology for the construction of parton distribution functions (PDFs) designed to provide an accurate representation of PDF uncertainties for specific processes or classes of processes with a minimal number of PDF error sets: specialized minimal PDF sets, or SM-PDFs. We construct these SM-PDFs in such a way that sets corresponding to different input processes can be combined without losing information, specifically on their correlations, and that they are robust upon smooth variations of the kinematic cuts. The proposed strategy never discards information, so that the SM-PDF sets can be enlarged by the addition of new processes, until the prior PDF set is eventually recovered for a large enough set of processes. We illustrate the method by producing SM-PDFs tailored to Higgs, top quark pair, and electroweak gauge boson physics, and determine that, when the PDF4LHC15 combined set is used as the prior, around 11, 4 and 11 Hessian eigenvectors respectively are enough to fully describe the corresponding processes.