Revisiting the proton-radius problem using constrained Gaussian processes

Abstract

Background: 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. Purpose: To estimate the proton radius by introducing a novel non-parametric approach to model the electric form factor of the proton. Methods: 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. Results: So far our results are inconclusive in regard to the proton puzzle, as they depend on both, the assumed constrains and the range of experimental data used. For example, if only low momentum-transfer data is used, adopting only the normalization constraint provides a value compatible with the smaller muonic result, while imposing only the shape constraint favors the larger electronic value. Conclusions: We have presented a novel technique to estimate the proton radius from electron scattering data based on a non-parametric Gaussian process. We have shown the impact of the physical constraints imposed on the form factor and of the range of experimental data used. In this regard, we are hopeful that as this technique is refined and with the anticipated new results from the PRad experiment, we will get closer to resolve of the puzzle.

References in corpus (16)

• Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
• Test of lepton universality using $B^{+}\to K^{+}{\ell }^{+}{\ell }^{-}$ decays
• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• High-precision determination of the electric and magnetic form factors of the proton
• Muonic hydrogen and the proton radius puzzle
• The electric and magnetic form factors of the proton
• The Proton Radius Puzzle
• Model independent extraction of the proton charge radius from electron scattering
• The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting
• Extraction of the proton radius from electron-proton scattering data
• Defining the Proton Radius: a Unified Treatment
• The Proton Radius from Electron Scattering Data
• Robust extraction of proton charge radius from electron-proton scattering data
• Nucleon form factors in dispersively improved Chiral Effective Field Theory II: Electromagnetic form factors
• Accurate nucleon electromagnetic form factors from dispersively improved chiral effective field theory
• Reply to Comment on "High-Precision Determination of the Electric and Magnetic Form Factors of the Proton"

Cited by in corpus (14)

• The proton charge radius
• Precise determination of proton magnetic radius from electron scattering data
• Fresh extraction of the proton charge radius from electron scattering
• Pion charge radius from pion+electron elastic scattering data
• Hadron and light nucleus radii from electron scattering
• How Analytic Choices Can Affect the Extraction of Electromagnetic Form Factors from Elastic Electron Scattering Cross Section Data
• Non-parametric Bayesian approach to extrapolation problems in configuration interaction methods
• Understanding the systematic differences in extractions of the proton electric form factors at low-$Q^2$
• Pauli radius of the proton
• Reinterpretation of classic proton charge form factor measurements
• Elastic Positron-Proton Scattering at Low Q${}^2$
• Merits and constraints of low-${\mathbf{K}}^2$ experimental data for the proton radius determination
• Gaussian process error modeling for chiral effective-field-theory calculations of $np\leftrightarrow d\gamma$ at low energies
• The Soft Multivariate Truncated Normal Distribution with Applications to Bayesian Constrained Estimation