An Unbiased Hessian Representation for Monte Carlo PDFs

TL;DR

This paper introduces a new method to convert Monte Carlo parton distribution functions into a Hessian representation using a subset of replicas and a genetic algorithm, enabling efficient PDF compression and improved analysis.

Contribution

It presents an unbiased linear basis approach with a genetic algorithm for converting Monte Carlo PDFs into Hessian form, validated on multiple sets and made publicly available.

Findings

Faithfully reproduces original Monte Carlo PDFs

Minimizes information loss in conversion

Provides a smaller, efficient Hessian representation

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.