Designing Optimal Experiments: An Application to Proton Compton Scattering

Abstract

Interpreting measurements requires a physical theory, but the theory's accuracy may vary across the experimental domain. To optimize experimental design, and so to ensure that the substantial resources necessary for modern experiments are focused on acquiring the most valuable data, both the theory uncertainty and the expected pattern of experimental errors must be considered. We develop a Bayesian approach to this problem, and apply it to the example of proton Compton scattering. Chiral Effective Field Theory ($\chi$EFT) predicts the functional form of the scattering amplitude for this reaction, so that the electromagnetic polarizabilities of the nucleon can be inferred from data. With increasing photon energy, both experimental rates and sensitivities to polarizabilities increase, but the accuracy of $\chi$EFT decreases. Our physics-based model of $\chi$EFT truncation errors is combined with present knowledge of the polarizabilities and reasonable assumptions about experimental capabilities at HI$\gamma$S and MAMI to assess the information gain from measuring specific observables at specific kinematics, \emph{i.e.}, to determine the relative amount by which new data are apt to shrink uncertainties. The strongest gains would likely come from new data on the spin observables ${\Sigma }_{2x}$ and ${\Sigma }_{2x^{\prime }}$ at $\omega \simeq 140$ to $200$ MeV and $40^{\circ }$ to $120^{\circ }$. These would tightly constrain ${\gamma }_{E1E1}-{\gamma }_{E1M2}$. New data on the differential cross section between $100$ and $200$\,MeV and over a wide angle range will substantially improve constraints on ${\alpha }_{E1}-{\beta }_{M1}$, ${\gamma }_{\pi }$ and ${\gamma }_{M1M1}-{\gamma }_{M1E2}$. Good signals also exist around $160$ MeV for ${\Sigma }_3$ and ${\Sigma }_{2z^{\prime }}$. Such data will be pivotal in the continuing quest to pin down the scalar polarizabilities and refine understanding of the spin polarizabilities.

arXiv comment47 pages LaTeX2e (pdflatex) including 33 figures as .jpg files using includegraphics. Improved presentation with corrections do not affect the conclusions by details of the figures. Higher-resolution figures are available at https://home.gwu.edu/~hgrie/Compton/one-N-comprehensive-observables-delta4.v2.0.high-resolution-figures.tgz. Final version with minor corrections published in EPJA57(2021)81

References in corpus (33)

• Quantifying truncation errors in effective field theory
• Effective theory of the Delta(1232) in Compton scattering off the nucleon
• Quantifying Correlated Truncation Errors in Effective Field Theory
• Bayesian truncation errors in chiral effective field theory: nucleon-nucleon observables
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Low-Energy Compton Scattering of Polarized Photons on Polarized Nucleons
• Exploring Bayesian parameter estimation for chiral effective field theory using nucleon-nucleon phase shifts
• Nucleon Polarizabilities: from Compton Scattering to Hydrogen Atom
• Polarizability of the Nucleon and Compton Scattering
• The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability
• Compton scattering from the proton in an effective field theory with explicit Delta degrees of freedom
• Higher Order Polarizabilities of the Proton
• Signatures of Chiral Dynamics in Low Energy Compton Scattering off the Nucleon
• Deuteron Compton scattering below pion photoproduction threshold
• New Measurement of Compton Scattering from the Deuteron and an Improved Extraction of the Neutron Electromagnetic Polarizabilities
• Hadron Polarizabilities
• Measurements of Double-Polarized Compton Scattering Asymmetries and Extraction of the Proton Spin Polarizabilities
• Predictions of covariant chiral perturbation theory for nucleon polarisabilities and polarised Compton scattering
• Nucleon Polarisabilities at and Beyond Physical Pion Masses
• On the mass difference between proton and neutron
• Evaluation of the forward Compton scattering off protons: I. Spin-independent amplitude
• Exploring experimental conditions to reduce uncertainties in the optical potential
• Higher order forward spin polarizability
• Determination of the scalar polarizabilities of the proton using beam asymmetry ${\Sigma }_3$ in Compton scattering
• Proton scalar dipole polarizabilities from real Compton scattering data, using fixed-t subtracted dispersion relations and the bootstrap method
• First extraction of the scalar proton dynamical polarizabilities from real Compton scattering data
• Compton Scattering from the Deuteron below Pion-Production Threshold
• Evaluation of the forward Compton scattering off protons: II. Spin-dependent amplitude and observables
• Nucleon Polarizabilities from Deuteron Compton Scattering within a Green's-Function Hybrid Approach
• Spin polarizabilities of the proton by measurement of Compton double-polarization observables
• Partial-wave analysis of proton Compton scattering data below the pion-production threshold
• Comprehensive Study of Observables in Compton Scattering on the Nucleon
• Elastic Compton Scattering from 3He and the Role of the Delta

Cited by in corpus (12)

• Machine Learning in Nuclear Physics
• Get on the BAND Wagon: A Bayesian Framework for Quantifying Model Uncertainties in Nuclear Dynamics
• What is ab initio in nuclear theory?
• The Present and Future of QCD
• Toward emulating nuclear reactions using eigenvector continuation
• Model reduction methods for nuclear emulators
• Training and Projecting: A Reduced Basis Method Emulator for Many-Body Physics
• Nuclear Structure at the Crossroads
• What Can Possibly Go Wrong?
• Wave-function-based emulation for nucleon-nucleon scattering in momentum space
• A further study on the renormalization group aspect of perturbative corrections
• Energy of a point-like neutron in an external electromagnetic field