Comprehensive Study of Observables in Compton Scattering on the Nucleon

Abstract

We present an analysis of $13$ observables in Compton scattering on the proton. Cross sections, asymmetries with polarised beam and/or targets, and polarisation-transfer observables are investigated for energies up to the $\Delta (1232)$ resonance to determine their sensitivity to the proton's dipole scalar and spin polarisabilities. The Chiral Effective Field Theory Compton amplitude we use is complete at N${}^4$LO, $\mathcal{O}(e^2{\delta }^4)$, for photon energies $\omega \sim m_{\pi }$, and so has an accuracy of a few per cent there. At photon energies in the resonance region it is complete at NLO, $\mathcal{O}(e^2{\delta }^0)$, and so its accuracy there is about $20$\%. We find that for energies from pion-production threshold to about $250\mathrm{MeV}$, multiple asymmetries have significant sensitivity to presently ill-determined combinations of proton spin polarisabilities. We also argue that the broad outcomes of this analysis will be replicated in complementary theoretical approaches, e.g., dispersion relations. Finally, we show that below the pion-production threshold, $6$ observables suffice to reconstruct the Compton amplitude, and above it $11$ are required. Although not necessary for polarisability extractions, this opens the possibility to perform "complete" Compton-scattering experiments. An interactive Mathematica notebook, including results for the neutron, is available from [email protected] .

75 pages LaTeX2e (pdflatex) including 37 figures as .pdf files using includegraphics; minor corrections. Text-identical to published version but including the Online Supplement. Higher-resolution figures are available at http://home.gwu.edu/~hgrie/Compton/one-N-comprehensive-observables-delta4.v2.0.high-resolution-figures.tgz

References in corpus (7)

• Electromagnetic excitation of the Delta(1232)-resonance
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Compton scattering from the proton in an effective field theory with explicit Delta degrees of freedom
• New Measurement of Compton Scattering from the Deuteron and an Improved Extraction of the Neutron Electromagnetic Polarizabilities
• Proton spin polarizabilities from polarized Compton scattering
• Measurements of Double-Polarized Compton Scattering Asymmetries and Extraction of the Proton Spin Polarizabilities
• Higher order forward spin polarizability

Cited by in corpus (8)

• Dispersion Theory in Electromagnetic Interactions
• Designing Optimal Experiments: An Application to Proton Compton Scattering
• Spin polarizabilities of the proton by measurement of Compton double-polarization observables
• Elastic Compton Scattering from 3He and the Role of the Delta
• Nucleon polarizabilities in covariant baryon chiral perturbation theory with explicit $\Delta$ degrees of freedom
• First concurrent extraction of the leading-order scalar and spin proton polarizabilities
• Electromagnetic currents for dressed hadrons
• Energy of a point-like neutron in an external electromagnetic field