On the determination of uncertainties in parton densities

Abstract

We review various methods used to estimate uncertainties in quantum correlation functions, such as parton distribution functions (PDFs). Using a toy model of a PDF, we compare the uncertainty estimates yielded by the traditional Hessian and data resampling methods, as well as from explicitly Bayesian analyses using nested sampling or hybrid Markov chain Monte Carlo techniques. We investigate how uncertainty bands derived from neural network approaches depend on details of the network training, and how they compare to the uncertainties obtained from more traditional methods with a specific underlying parametrization. Our results show that utilizing a neural network on a simplified example of PDF data has the potential to inflate uncertainties, in part due to the cross validation procedure that is generally used to avoid overfitting data.

32 pages, 9 figures

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• Updated QCD global analysis of single transverse-spin asymmetries I: Extracting $\tilde{H}$, and the role of the Soffer bound and lattice QCD
• Light quark and antiquark constraints from new electroweak data
• A Stress Test of Global PDF Fits: Closure Testing the MSHT PDFs and a First Direct Comparison to the Neural Net Approach
• Extraction of the neutron F2 structure function from inclusive proton and deuteron deep-inelastic scattering data
• PartonDensity.jl: a novel parton density determination code
• Determination of proton PDF uncertainties with Markov chain Monte Carlo
• Constraints on the $U(1{)}_{B-L}$ model from global QCD analysis