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.
Built on
J. Pumplin et al., Uncertainties of predictions from parton distribution functions. 2. The Hessian method
S. Carrazza, S. Forte, Z. Kassabov, and J. Rojo, “On the accuracy and Gaussianity of the PDF4LHC15 combined sets of parton distributions.” to be published in the 2015 Les Houches proceedings, 2016