Reconstruction of Monte Carlo replicas from Hessian parton distributions

TL;DR

This paper presents a numerical method to convert Hessian-based parton distribution functions into Monte-Carlo replicas, preserving key properties and enabling diverse collider applications.

Contribution

It introduces a novel numerical approach for converting Hessian PDFs into Monte-Carlo replicas, including formulas and a software tool, enhancing uncertainty quantification in particle physics.

Findings

Successfully reproduces CT14 Hessian uncertainties and positivity

Provides a correction for bias in asymmetric uncertainties

Offers a software for conversion using multiple sampling methods

Abstract

We explore connections between two common methods for quantifying the uncertainty in parton distribution functions (PDFs), based on the Hessian error matrix and Monte-Carlo sampling. CT14 parton distributions in the Hessian representation are converted into Monte-Carlo replicas by a numerical method that reproduces important properties of CT14 Hessian PDFs: the asymmetry of CT14 uncertainties and positivity of individual parton distributions. The ensembles of CT14 Monte-Carlo replicas constructed this way at NNLO and NLO are suitable for various collider applications, such as cross section reweighting. Master formulas for computation of asymmetric standard deviations in the Monte-Carlo representation are derived. A correction is proposed to address a bias in asymmetric uncertainties introduced by the Taylor series approximation. A numerical program is made available for conversion of Hessian PDFs into Monte-Carlo replicas according to normal, log-normal, and Watt-Thorne sampling procedures.