Predictions of covariant chiral perturbation theory for nucleon polarisabilities and polarised Compton scattering

Abstract

We update the predictions of the SU(2) baryon chiral perturbation theory for the dipole polarisabilities of the proton, $\{{\alpha }_{E1},{\beta }_{M1}{\}}_p=\{11.2(0.7),3.9(0.7)\}\times 10^{-4}$fm${}^3$, and obtain the corresponding predictions for the quadrupole, dispersive, and spin polarisabilities: $\{{\alpha }_{E2},{\beta }_{M2}{\}}_p=\{17.3(3.9),-15.5(3.5)\}\times 10^{-4}$fm${}^5$, $\{{\alpha }_{E1\nu },{\beta }_{M1\nu }{\}}_p=\{-1.3(1.0),7.1(2.5)\}\times 10^{-4}$fm${}^5$, and $\{{\gamma }_{E1E1},{\gamma }_{M1M1},{\gamma }_{E1M2},{\gamma }_{M1E2}{\}}_p=\{-3.3(0.8),2.9(1.5),0.2(0.2),1.1(0.3)\}\times 10^{-4}$fm${}^4$. The results for the scalar polarisabilities are in significant disagreement with semi-empirical analyses based on dispersion relations, however the results for the spin polarisabilities agree remarkably well. Results for proton Compton-scattering multipoles and polarised observables up to the Delta(1232) resonance region are presented too. The asymmetries ${\Sigma }_3$ and ${\Sigma }_{2x}$ reproduce the experimental data from LEGS and MAMI. Results for ${\Sigma }_{2z}$ agree with a recent sum rule evaluation in the forward kinematics. The asymmetry ${\Sigma }_{1z}$ near the pion production threshold shows a large sensitivity to chiral dynamics, but no data is available for this observable. We also provide the predictions for the polarisabilities of the neutron: $\{{\alpha }_{E1},{\beta }_{M1}{\}}_n=\{13.7(3.1),4.6(2.7)\}\times 10^{-4}$fm${}^3$, $\{{\alpha }_{E2},{\beta }_{M2}{\}}_n=\{16.2(3.7),-15.8(3.6)\}\times 10^{-4}$fm${}^5$, $\{{\alpha }_{E1\nu },{\beta }_{M1\nu }{\}}_n=\{0.1(1.0),7.2(2.5)\}\times 10^{-4}$fm${}^5$, and $\{{\gamma }_{E1E1},{\gamma }_{M1M1},{\gamma }_{E1M2},{\gamma }_{M1E2}{\}}_n=\{-4.7(1.1),2.9(1.5),0.2(0.2),1.6(0.4)\}\times 10^{-4}$fm${}^4$. The neutron dynamical polarisabilities and multipoles are examined too. We also discuss subtleties related to matching dynamical and static polarisabilities.

34 pages, 18 figures, minor updates and corrections, published version

References in corpus (12)

• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Unitary Isobar Model - MAID2007
• Electromagnetic excitation of the Delta(1232)-resonance
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Chiral Effective-Field Theory in the Delta(1232) Region: Pion Electroproduction on the Nucleon
• 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
• What different variants of chiral EFT predict for the proton Compton differential cross section - and why
• Manifestly-covariant chiral PT calculation of nucleon Compton scattering

Cited by in corpus (28)

• Nucleon Polarizabilities: from Compton Scattering to Hydrogen Atom
• The proton structure in and out of muonic hydrogen
• Two-photon exchange correction to muon-proton elastic scattering at low momentum transfer
• Dispersion Theory in Electromagnetic Interactions
• Nucleon Polarisabilities at and Beyond Physical Pion Masses
• Nucleon resonances in Compton scattering
• Designing Optimal Experiments: An Application to Proton Compton Scattering
• Determination of the scalar polarizabilities of the proton using beam asymmetry ${\Sigma }_3$ in Compton scattering
• Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
• 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
• Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions
• Evaluation of the forward Compton scattering off protons: II. Spin-dependent amplitude and observables
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions
• Spin polarizabilities of the proton by measurement of Compton double-polarization observables
• Spin-dependent sum rules connecting real and virtual Compton scattering verified
• Virtual Compton Scattering and Nucleon Generalized Polarizabilities
• Partial-wave analysis of proton Compton scattering data below the pion-production threshold
• Comprehensive Study of Observables in Compton Scattering on the Nucleon
• Nucleon polarizabilities in covariant baryon chiral perturbation theory with explicit $\Delta$ degrees of freedom
• Single-pion contribution to the Gerasimov--Drell--Hearn sum rule and related integrals
• First concurrent extraction of the leading-order scalar and spin proton polarizabilities
• Dipole-dipole dispersion interactions between neutrons
• Electromagnetic polarizabilities of the spin-$\frac{1}{2}$ singly heavy baryons in heavy baryon chiral perturbation theory
• Dipole-dipole interactions between neutrons
• Electromagnetic polarizabilities of the spin-$\frac{3}{2}$ baryons in heavy baryon chiral perturbation theory
• Few-neutron systems with the long-range Casimir-Polder force
• Energy of a point-like neutron in an external electromagnetic field