Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs

TL;DR

This paper evaluates the Monte Carlo method for propagating experimental uncertainties in proton PDFs, compares it with the Hessian approach, and explores parameterisation bias and the impact of recent LHC data.

Contribution

It demonstrates the effectiveness of Monte Carlo replicas in uncertainty estimation, assesses parameterisation bias, and introduces efficient methods for generating PDF predictions and incorporating new data.

Findings

Monte Carlo replicas agree with Hessian uncertainties within established criteria.

Parameterisation bias is small except for low-x valence quarks.

Inclusion of recent LHC data significantly impacts PDF predictions.

Abstract

We investigate the Monte Carlo approach to propagation of experimental uncertainties within the context of the established "MSTW 2008" global analysis of parton distribution functions (PDFs) of the proton at next-to-leading order in the strong coupling. We show that the Monte Carlo approach using replicas of the original data gives PDF uncertainties in good agreement with the usual Hessian approach using the standard Delta(chi^2) = 1 criterion, then we explore potential parameterisation bias by increasing the number of free parameters, concluding that any parameterisation bias is likely to be small, with the exception of the valence-quark distributions at low momentum fractions x. We motivate the need for a larger tolerance, Delta(chi^2) > 1, by making fits to restricted data sets and idealised consistent or inconsistent pseudodata. Instead of using data replicas, we alternatively produce PDF sets randomly distributed according to the covariance matrix of fit parameters including appropriate tolerance values, then we demonstrate a simpler method to produce an arbitrary number of random predictions on-the-fly from the existing eigenvector PDF sets. Finally, as a simple example application, we use Bayesian reweighting to study the effect of recent LHC data on the lepton charge asymmetry from W boson decays.