An Unbiased Hessian Representation for Monte Carlo PDFs

Abstract

We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for the determination of the optimal basis. We validate the methodology by first showing that it faithfully reproduces a native Monte Carlo PDF set (NNPDF3.0), and then, that if applied to Hessian PDF set (MMHT14) which was transformed into a Monte Carlo set, it gives back the starting PDFs with minimal information loss. We then show that, when applied to a large Monte Carlo PDF set obtained as combination of several underlying sets, the methodology leads to a Hessian representation in terms of a rather smaller set of parameters (CMC-H PDFs), thereby providing an alternative implementation of the recently suggested Meta-PDF idea and a Hessian version of the recently suggested PDF compression algorithm (CMC-PDFs). The mc2hessian conversion code is made publicly available together with (through LHAPDF6) a Hessian representations of the NNPDF3.0 set, and the CMC-H PDF set.

27 pages, 17 figures; v2: replaced plots in Fig.1 which had a conflict with google chrome inline viewer; v3: final version, to be published in EPJC; figs 5,10,11,13 updated with new (more accurate) choice of parameters

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• LHAPDF6: parton density access in the LHC precision era
• Parton distributions in the LHC era: MMHT 2014 PDFs
• Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs
• aMCfast: automation of fast NLO computations for PDF fits
• APFEL Web: a web-based application for the graphical visualization of parton distribution functions
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