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Data-Driven Model Reduction, Scientific Frontiers, and Applications ()

Anirban Bhattacharya, Department of Statistics
Reexamining the Proton-Radius Problem Using Constrained Gaussian Processes

Abstract

The "proton radius puzzle" refers to an eight-year-old problem that highlights major inconsistencies in the extraction of the charge radius of the proton from muonic Lamb-shift experiments as compared against experiments using elastic electron scattering. For the latter, the determination of the charge radius involves an extrapolation of the experimental form factor to zero momentum transfer. Within a Bayesian paradigm, we develop a model flexible enough to fit the data without any parametric assumptions on the form factor. The Bayesian estimation is guided by imposing only two physical constraints on the form factor: (a) its value at zero momentum transfer (normalization) and (b) its overall shape, assumed to be a monotonically decreasing function of the momentum transfer. Variants of these assumptions are explored to assess the impact of these constraints.